sunyiyou/math_arithmetic_matrix_inverse_level_4

1{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, -4, -11, 2, 0, 4, -8],\n [0, 5, 17, 5, -16, 3, -17],\n [0, 0, -17, 2, 14, -7, 3],\n [0, 0, 0, -3, -4, -16, 18],\n [0, 0, 0, 0, -15, 6, -5],\n [0, 0, 0, 0, 0, -12, -11],\n [0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}2{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 10, -1, 7, 15, -9, 17],\n [0, 12, -4, -11, -5, 4, 2],\n [0, 0, 5, 7, 6, 10, -4],\n [0, 0, 0, -10, 5, -18, -11],\n [0, 0, 0, 0, 16, 16, 14],\n [0, 0, 0, 0, 0, -7, 15],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}3{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -18, 16, 18, -5, -16, -18],\n [-14, 7, -5, 8, -10, -4, -4],\n [7, -6, 13, 13, -15, 11, 18],\n [4, -4, 10, 17, -6, 13, -12],\n [3, 9, -17, -13, 9, 9, 1],\n [11, -8, 9, 6, 14, -18, 8],\n [-6, -16, -13, -11, 8, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "262", "dataset": "MATH"}4{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[14, 5, -4, 13, 13, 5, -7],\n [0, -16, 18, -2, -17, -17, 9],\n [0, 0, 13, 14, -18, 0, -17],\n [0, 0, 0, 13, -15, -8, -2],\n [0, 0, 0, 0, 3, -8, -3],\n [0, 0, 0, 0, 0, -16, 1],\n [0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-133", "dataset": "MATH"}5{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, 14, -1, -18, -8, 9, 6],\n [4, 12, 11, 16, -12, -3, 7],\n [-17, -18, -7, -14, 18, 13, -10],\n [16, 0, -3, -16, 1, 5, 14],\n [5, -8, -11, 17, 1, 16, 6],\n [16, 6, 10, -1, -1, -17, 16],\n [-3, 17, 14, -15, 14, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}6{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[1, -11, -12, -16, -2, 14, -7],\n [3, 3, 11, -11, 8, 8, 15],\n [2, 11, 14, 9, 14, -14, 0],\n [-15, 16, -2, 9, 11, 10, -13],\n [16, 18, 5, 10, 12, 16, 14],\n [2, 13, 4, 14, -16, -1, 6],\n [12, -16, 5, 13, 3, 4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}7{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, -17, 7, -2, 14, -10, 10],\n [0, 16, 6, 5, -6, -12, 17],\n [0, 0, -11, -3, -5, -7, 4],\n [0, 0, 0, -17, 13, 4, 3],\n [0, 0, 0, 0, -4, 18, 14],\n [0, 0, 0, 0, 0, 11, 16],\n [0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1474", "dataset": "MATH"}8{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[7, 18, 7, 4, -10, -7, -18],\n [-18, 15, 13, 6, -18, -3, -14],\n [3, 10, -16, -7, 7, -3, 18],\n [3, 10, -5, 9, -14, 11, -14],\n [-7, -3, 7, 7, 2, 17, 14],\n [11, 18, 4, -9, -14, 17, 15],\n [12, -9, 0, 13, -18, -14, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}9{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 5, -3, -17, 9, 13, 8],\n [1, 5, -7, 16, 14, 14, 18],\n [-7, -16, -18, 14, -9, 10, -6],\n [-7, 12, -17, 16, 4, -2, 7],\n [-11, 10, 7, -9, 7, 15, -12],\n [-15, -8, 10, 17, 6, 2, 17],\n [-9, 18, -10, 5, 16, 16, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "764", "dataset": "MATH"}10{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 4, 6, -2, 5, 11, 2],\n [4, 4, 4, 3, -2, -2, -4],\n [6, 4, -6, -6, 16, -6, 0],\n [-2, 3, -6, 9, -6, 12, -4],\n [5, -2, 16, -6, 6, -6, 4],\n [11, -2, -6, 12, -6, 16, -2],\n [2, -4, 0, -4, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}11{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, -6, -10, 8, -17, -14, 10],\n [18, 0, -11, -18, 3, -2, -12],\n [6, -15, 17, -13, 12, 0, 8],\n [-9, 7, 0, -16, -6, 9, 1],\n [9, -11, -18, -16, -6, 9, 6],\n [14, -13, 13, 2, -3, 2, -8],\n [18, 17, 16, 0, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}12{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-4, 12, -18, -16, -3, 4, -8],\n [-7, -9, 13, -3, -11, -7, 5],\n [9, -11, 9, 17, 7, -11, 9],\n [9, 18, 17, 8, -2, -10, 14],\n [1, -6, 9, 10, -6, 16, -13],\n [-1, -14, 6, -17, -9, 11, -14],\n [14, -18, -1, 13, -8, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}13{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[6, -8, -3, -3, 0, 11, 14],\n [-8, 2, -14, 4, -10, 0, 5],\n [-3, -14, 4, 10, 16, -12, -2],\n [-3, 4, 10, -5, 2, -12, -5],\n [0, -10, 16, 2, 9, -3, 4],\n [11, 0, -12, -12, -3, -14, 6],\n [14, 5, -2, -5, 4, 6, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}14{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-17, -8, 15, 15, -1, 11, -4],\n [8, 15, 14, 5, -4, 11, -2],\n [-14, 10, -15, -9, -2, -9, -2],\n [1, 5, -14, 15, -13, -17, -6],\n [-8, 4, -3, 12, -8, -3, -11],\n [-15, -15, 6, -16, 13, -16, 8],\n [10, 13, 0, 2, -14, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}15{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[3, 8, -1, -11, -4, -4, 2],\n [8, -5, 2, 6, -14, 12, 3],\n [-1, 2, 7, 6, -6, -8, 12],\n [-11, 6, 6, 7, 2, 5, 0],\n [-4, -14, -6, 2, -12, 1, 1],\n [-4, 12, -8, 5, 1, 9, -8],\n [2, 3, 12, 0, 1, -8, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-71", "dataset": "MATH"}16{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -15, -9, -16, -1, 17, 3],\n [0, -11, 0, 18, -13, 7, 15],\n [0, 0, 14, 3, 2, -13, -13],\n [0, 0, 0, 11, 12, 5, -10],\n [0, 0, 0, 0, 5, 12, -13],\n [0, 0, 0, 0, 0, -4, -13],\n [0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}17{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-13, 7, -15, 0, 1, 14, 1],\n [0, -18, 7, -5, 18, -8, 17],\n [0, 0, 14, -13, -9, -14, 4],\n [0, 0, 0, -17, 1, -18, 18],\n [0, 0, 0, 0, -4, 5, 16],\n [0, 0, 0, 0, 0, -10, 15],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-852", "dataset": "MATH"}18{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[14, -6, 12, 17, 5, -4, 10],\n [0, -14, 10, -15, -7, -17, 8],\n [0, 0, 17, 7, 8, -14, 1],\n [0, 0, 0, -11, 4, 7, -7],\n [0, 0, 0, 0, 14, -7, 17],\n [0, 0, 0, 0, 0, 12, -10],\n [0, 0, 0, 0, 0, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "469", "dataset": "MATH"}19{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, 7, 17, 4, -18, -4, 2],\n [-10, -10, -9, 7, 16, 6, 7],\n [-8, -17, -12, -1, 8, 15, 8],\n [-2, 5, 6, -12, -13, 5, 14],\n [10, 3, 7, 9, 2, -12, -2],\n [1, 1, 3, 9, -12, -18, 13],\n [-6, 11, 4, 0, 13, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804", "dataset": "MATH"}20{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, -3, -10, 2, -8, -4, 4],\n [-3, 9, 12, -3, -6, -11, 4],\n [-10, 12, -9, 2, 2, 15, 0],\n [2, -3, 2, -12, 0, 2, 0],\n [-8, -6, 2, 0, 18, -2, 8],\n [-4, -11, 15, 2, -2, 5, -5],\n [4, 4, 0, 0, 8, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}21{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -13, -1, 2, 17, 15, -2],\n [0, 6, -7, 4, 3, 2, 8],\n [0, 0, 8, 15, -7, -12, -9],\n [0, 0, 0, 9, -17, -18, 17],\n [0, 0, 0, 0, -8, 17, 16],\n [0, 0, 0, 0, 0, 17, 1],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}22{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -13, -2, -3, -2, 6, 12],\n [-13, 18, 1, 8, 0, 6, 10],\n [-2, 1, -7, -2, 2, -4, -4],\n [-3, 8, -2, 4, 12, -3, -12],\n [-2, 0, 2, 12, -7, -8, 1],\n [6, 6, -4, -3, -8, -2, 0],\n [12, 10, -4, -12, 1, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}23{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, -11, 4, 10, -1, 12, 11],\n [0, -1, -2, -5, 12, 5, 16],\n [0, 0, 18, 7, 4, -4, -15],\n [0, 0, 0, -6, -1, 14, -3],\n [0, 0, 0, 0, -6, -6, -1],\n [0, 0, 0, 0, 0, -3, -9],\n [0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-447", "dataset": "MATH"}24{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 11, -15, -1, 18, 6, -18],\n [0, -10, -4, 5, -15, -7, 18],\n [0, 0, 5, -8, -6, 15, 6],\n [0, 0, 0, 1, 10, -9, 15],\n [0, 0, 0, 0, -14, 4, -10],\n [0, 0, 0, 0, 0, 5, -16],\n [0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8150", "dataset": "MATH"}25{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[18, 15, -8, -16, 9, 10, -10],\n [-16, 6, 15, -7, -10, -4, 6],\n [-14, -8, 15, 5, -4, -11, -14],\n [7, -1, -13, 18, -6, 9, -14],\n [-6, -2, 13, 10, -16, 15, 8],\n [-6, 14, -13, 5, 0, -3, 9],\n [14, -6, 6, 17, 8, -12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}26{"messages": [{"content": "Find the value at position (2, 6) of the inverse of matrix 1/252 * A where A =\n[[12, 10, 2, 14, 13, -2, -4],\n [10, -17, -6, -10, 10, -3, -7],\n [2, -6, 8, -1, 4, 14, 2],\n [14, -10, -1, 11, 0, 4, 2],\n [13, 10, 4, 0, 18, -2, -8],\n [-2, -3, 14, 4, -2, 8, 0],\n [-4, -7, 2, 2, -8, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}27{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -5, 10, -7, 17, 16, -7],\n [-12, 10, -8, 14, -13, -4, 13],\n [-8, 4, 7, 15, 15, 10, -15],\n [-2, 16, -6, -4, 10, 10, -8],\n [13, -17, -5, 1, 3, -8, 8],\n [-16, -2, 9, 10, 2, -3, 18],\n [1, -13, 0, -14, -16, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "403", "dataset": "MATH"}28{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[15, 6, 1, 3, -3, -4, -2],\n [6, 8, -2, 1, 8, 2, 0],\n [1, -2, -12, -5, 0, 2, -2],\n [3, 1, -5, 11, -1, -12, -5],\n [-3, 8, 0, -1, -17, 4, -2],\n [-4, 2, 2, -12, 4, -1, 12],\n [-2, 0, -2, -5, -2, 12, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}29{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, 3, 5, -2, -7, 13, -4],\n [-3, 3, 9, 1, 14, -9, 13],\n [14, -17, 14, 14, -6, 11, 14],\n [-6, 7, 3, -17, 7, -4, 15],\n [-8, -16, -13, -10, -13, -10, 12],\n [13, -7, -11, -11, 9, 1, -12],\n [-8, 1, -3, -15, -13, 3, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1225", "dataset": "MATH"}30{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, -5, -8, -1, -7, 4, -7],\n [-6, 6, 0, 17, -11, 10, 13],\n [-1, -13, -1, 0, 3, 18, 13],\n [-16, 9, -9, 16, 10, -4, 14],\n [-12, -7, 11, 2, 12, 5, 1],\n [18, -15, 9, 1, 5, 13, 17],\n [15, 17, -17, -4, 15, 17, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42", "dataset": "MATH"}31{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -16, -1, 2, -4, 14, 16],\n [0, -11, 17, 11, 4, -5, -5],\n [0, 0, -14, -5, 6, 1, -17],\n [0, 0, 0, 9, -17, 16, 18],\n [0, 0, 0, 0, 4, 12, -8],\n [0, 0, 0, 0, 0, 10, -9],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-567", "dataset": "MATH"}32{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 5, 14, 18, 16, -5, 2],\n [5, -4, -6, -6, 0, -14, -4],\n [14, -6, 7, 12, -4, 9, 1],\n [18, -6, 12, -5, 2, -8, -6],\n [16, 0, -4, 2, 4, -5, 6],\n [-5, -14, 9, -8, -5, 10, 2],\n [2, -4, 1, -6, 6, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8693", "dataset": "MATH"}33{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-1, -2, 7, -11, -7, 8, -11],\n [0, -15, 14, -18, 0, 12, -3],\n [0, 0, 7, 9, -17, -13, -10],\n [0, 0, 0, -10, -6, 12, -8],\n [0, 0, 0, 0, -13, 15, -1],\n [0, 0, 0, 0, 0, 5, -12],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}34{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[2, 0, 10, 6, 14, 13, 16],\n [0, -8, 16, -11, -5, -9, -17],\n [0, 0, 2, 7, -11, -17, -13],\n [0, 0, 0, 6, -7, -14, 15],\n [0, 0, 0, 0, 4, -13, 2],\n [0, 0, 0, 0, 0, -8, -4],\n [0, 0, 0, 0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2278", "dataset": "MATH"}35{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-15, 8, 10, 9, 16, -11, -3],\n [17, 11, -1, -17, -6, -15, 7],\n [6, 11, -8, -12, 12, -9, -6],\n [12, -12, 17, 1, -15, -12, -18],\n [-6, 3, 2, 3, 9, -10, 7],\n [-10, -4, -9, 5, -11, 5, -3],\n [7, 8, 18, -15, 5, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "437", "dataset": "MATH"}36{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 6, -1, 0, 17, -9, 14],\n [-14, 16, 15, 14, 2, -2, 3],\n [18, -4, 16, 9, -12, 13, -8],\n [-9, -10, -5, -6, 6, -17, 16],\n [-12, 2, -1, -16, -8, 5, 0],\n [-15, 7, 13, 17, 18, 14, 17],\n [-16, -10, -11, 14, -13, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2388", "dataset": "MATH"}37{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -14, 8, 13, 2, -11, -11],\n [-16, -16, 3, -13, -17, 4, -17],\n [-2, 16, 15, 4, 11, -11, 3],\n [17, -14, -6, 10, 12, -3, 11],\n [-3, -7, -2, -3, -7, -11, 1],\n [-16, -3, 11, 4, 9, -14, 1],\n [-18, 11, 2, 1, -13, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "467", "dataset": "MATH"}38{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 13, 14, -3, -7, 15, -5],\n [0, 14, 4, -17, 2, -17, 8],\n [0, 0, -8, -16, 4, 7, -15],\n [0, 0, 0, 3, -4, 3, 18],\n [0, 0, 0, 0, 5, 11, -5],\n [0, 0, 0, 0, 0, -10, -4],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1166", "dataset": "MATH"}39{"messages": [{"content": "Find the value at position (4, 5) of the inverse of matrix 1/252 * A where A =\n[[-5, 8, 8, 3, 10, -4, 9],\n [8, 17, 0, -10, -4, -8, -15],\n [8, 0, 6, 0, 4, 1, 1],\n [3, -10, 0, -4, -2, 2, 14],\n [10, -4, 4, -2, -5, -8, -5],\n [-4, -8, 1, 2, -8, 4, 3],\n [9, -15, 1, 14, -5, 3, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"}40{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 12, -4, -10, 4, 0, -10],\n [0, 2, -10, 9, -12, -3, -3],\n [0, 0, -15, -2, 18, 10, 17],\n [0, 0, 0, 8, 9, 3, -5],\n [0, 0, 0, 0, -17, 8, 2],\n [0, 0, 0, 0, 0, -18, -6],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1586", "dataset": "MATH"}41{"messages": [{"content": "Find the value at position (7, 3) of the inverse of matrix 1/252 * A where A =\n[[-2, 16, -8, 2, 7, -15, 15],\n [0, 16, 10, 10, 2, -6, -2],\n [0, 0, -17, 10, 14, -9, 2],\n [0, 0, 0, -11, 3, -11, -4],\n [0, 0, 0, 0, -14, 13, -18],\n [0, 0, 0, 0, 0, 4, -18],\n [0, 0, 0, 0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}42{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, 17, -8, -4, 0, -12, 9],\n [-14, -14, 11, 13, -11, -9, 13],\n [9, -2, 12, -11, 6, -10, -17],\n [-4, -16, 17, -15, -5, 6, -9],\n [2, 17, -7, 8, -17, -6, 13],\n [12, -3, 13, 13, 15, -8, -9],\n [-4, -2, -1, -10, 6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}43{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, 11, 1, 2, 13, 2, 16],\n [13, 11, -7, -1, 2, -6, 2],\n [-11, -12, 4, 13, -8, 3, 3],\n [6, 3, 9, 10, -6, -1, -17],\n [10, 2, -4, 8, 12, -4, 4],\n [5, -6, 3, 18, 14, -16, 0],\n [4, 10, 11, 6, 18, -11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79", "dataset": "MATH"}44{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -18, -14, -16, -18, -15, 16],\n [0, 15, 6, -9, 2, 8, 8],\n [0, 0, -10, 17, 3, 7, -7],\n [0, 0, 0, 15, 1, -8, -3],\n [0, 0, 0, 0, -15, -15, 1],\n [0, 0, 0, 0, 0, 2, 2],\n [0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}45{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-5, -16, 5, 18, -3, -15, 5],\n [0, 11, -1, 0, 12, 0, 0],\n [0, 0, -7, 11, 12, 17, 0],\n [0, 0, 0, -1, 9, -8, 14],\n [0, 0, 0, 0, 8, -4, -13],\n [0, 0, 0, 0, 0, -14, -9],\n [0, 0, 0, 0, 0, 0, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4367", "dataset": "MATH"}46{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -14, 10, 18, 1, 2, -9],\n [0, 17, -13, 7, -15, 16, -18],\n [0, 0, -13, 12, 1, 5, 6],\n [0, 0, 0, 5, 11, 3, 9],\n [0, 0, 0, 0, -9, -3, -3],\n [0, 0, 0, 0, 0, 17, 1],\n [0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}47{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -6, 0, -1, 8, 10, -9],\n [-6, 2, -4, -2, 8, -6, -9],\n [0, -4, 4, 0, 12, -4, 2],\n [-1, -2, 0, 14, 0, 2, -7],\n [8, 8, 12, 0, 9, -8, -6],\n [10, -6, -4, 2, -8, -9, 8],\n [-9, -9, 2, -7, -6, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}48{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -7, 5, -9, 16, 13, -12],\n [0, 1, 7, -15, 3, -4, 2],\n [0, 0, 9, -5, 8, 9, 7],\n [0, 0, 0, -11, 14, 16, -13],\n [0, 0, 0, 0, -8, -7, -9],\n [0, 0, 0, 0, 0, 2, -11],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "421", "dataset": "MATH"}49{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, -3, -16, -16, 8, 14, 9],\n [-18, -11, 18, 13, 18, -15, 11],\n [-13, 0, 13, -10, -7, -8, -3],\n [-18, 2, 11, -6, 15, -15, 9],\n [12, 8, -14, 6, -16, 14, -15],\n [6, 1, 15, 7, -14, 16, 9],\n [10, -10, -13, 0, -8, -17, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-75", "dataset": "MATH"}50{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, 8, 16, -6, -8, -8, 8],\n [8, 7, 8, 0, 2, 8, -1],\n [16, 8, -1, 2, 10, -8, 0],\n [-6, 0, 2, -4, -4, 2, 15],\n [-8, 2, 10, -4, 16, 6, -9],\n [-8, 8, -8, 2, 6, -16, 1],\n [8, -1, 0, 15, -9, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385", "dataset": "MATH"}51{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[-2, -10, 16, -6, -4, -1, 14],\n [-13, 8, 4, 8, 15, -5, 17],\n [-11, 16, 0, 11, -5, 1, 6],\n [5, -5, 7, 4, 3, 0, -16],\n [0, -10, 9, 1, -12, -5, -10],\n [0, -5, 17, -2, 11, -10, 14],\n [6, -5, -8, 16, -5, 11, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}52{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 9, -11, -17, 3, -3, 10],\n [11, -7, 16, -8, 2, 2, -14],\n [1, 18, -16, 14, -10, -10, -15],\n [16, -2, 15, 5, 13, -18, -11],\n [4, -7, -7, -4, 0, 7, 10],\n [3, 2, 1, 10, -15, -12, 9],\n [9, -15, 3, -7, -16, 3, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}53{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -11, 6, 8, 4, 11, 4],\n [0, -1, -1, -17, -15, 11, 14],\n [0, 0, 18, 0, 9, 1, 14],\n [0, 0, 0, 10, -9, -17, -8],\n [0, 0, 0, 0, -10, 9, -16],\n [0, 0, 0, 0, 0, -16, -3],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3606", "dataset": "MATH"}54{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 5) rounded to the nearest integer?\n[[7, 14, 8, 2, 12, 2, 6],\n [14, 2, 6, 15, 2, 0, 2],\n [8, 6, -16, 0, -3, -6, -5],\n [2, 15, 0, 14, 12, 7, -1],\n [12, 2, -3, 12, -18, -4, 8],\n [2, 0, -6, 7, -4, 16, 2],\n [6, 2, -5, -1, 8, 2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}55{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -15, -14, 11, 5, -16, -8],\n [-15, 7, 8, 8, -13, -4, 11],\n [18, 18, 18, 16, 4, -13, -15],\n [-1, -10, 10, -6, -2, 13, 3],\n [-15, -14, 18, -6, 15, 3, 4],\n [-16, 15, 13, 2, 2, -8, -15],\n [-18, 9, 5, 16, -6, 15, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}56{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[17, -2, 16, -1, 3, 5, 0],\n [0, 2, -11, 9, -14, -2, 18],\n [0, 0, 8, 15, -8, -7, 2],\n [0, 0, 0, -2, 1, -7, -13],\n [0, 0, 0, 0, -13, 17, -8],\n [0, 0, 0, 0, 0, -8, -2],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}57{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, -11, -2, -2, 14, 13, -11],\n [0, -16, -14, -6, 12, -3, 13],\n [0, 0, 3, -16, -9, 2, -3],\n [0, 0, 0, 16, 11, 11, 16],\n [0, 0, 0, 0, 11, -12, -16],\n [0, 0, 0, 0, 0, -4, 18],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}58{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-8, 3, 14, 17, 4, 15, -10],\n [0, -11, -12, 17, -1, -16, 9],\n [0, 0, 9, -18, 17, 2, 16],\n [0, 0, 0, -6, 18, 5, -17],\n [0, 0, 0, 0, -9, 16, 6],\n [0, 0, 0, 0, 0, 6, 17],\n [0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2683", "dataset": "MATH"}59{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, 8, 11, 15, 18, -13, -12],\n [13, 13, 6, 14, -12, -7, -3],\n [-3, 17, -6, -12, 17, -10, 13],\n [-8, -11, 14, 4, 6, -11, 3],\n [-15, -16, 10, 10, 15, 15, 9],\n [-6, -4, 4, 7, -15, 7, -10],\n [-14, 13, 1, -8, -4, 13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}60{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -1, 0, -10, -4, 9, 2],\n [-1, -8, -12, 2, -14, 12, 4],\n [0, -12, 5, 10, 5, -15, -4],\n [-10, 2, 10, 15, -2, 12, -2],\n [-4, -14, 5, -2, -5, -11, -7],\n [9, 12, -15, 12, -11, 10, 0],\n [2, 4, -4, -2, -7, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}61{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-13, -3, -15, 16, 7, -7, -8],\n [0, 6, -1, 0, 4, -1, 7],\n [0, 0, 10, 15, -2, -3, -17],\n [0, 0, 0, -11, 11, 13, 17],\n [0, 0, 0, 0, 5, 3, 10],\n [0, 0, 0, 0, 0, 18, 9],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1667", "dataset": "MATH"}62{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, 8, 10, -16, -6, -9, 17],\n [-10, 8, 15, -18, 13, 6, 10],\n [-12, -16, 1, 1, 11, 16, 16],\n [8, 7, -5, -2, -1, 10, 1],\n [8, -1, -15, -18, -18, 7, 1],\n [4, -9, -8, -14, -18, -2, 3],\n [15, 10, -15, -14, -8, 2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}63{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-7, 7, 0, -12, -12, 7, -14],\n [2, -5, -15, 4, 1, -4, 10],\n [-11, 0, 9, 8, -15, -4, 16],\n [18, -18, -16, 5, 8, 17, 15],\n [10, 5, 5, -15, -16, 15, 4],\n [4, -14, 12, -13, 18, -9, -12],\n [2, 1, -16, 3, -15, 9, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-101", "dataset": "MATH"}64{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[17, -14, -6, 4, 11, 18, 6],\n [8, -5, 17, -3, 3, 2, 2],\n [-11, -3, 12, -9, 13, 15, -10],\n [-2, -8, 13, -9, 3, -2, -15],\n [6, 2, 18, -18, 6, 17, -2],\n [5, -17, -4, 13, -13, -18, 4],\n [-2, 15, 10, -10, -6, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}65{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[1, -16, -2, -7, -18, -2, -16],\n [7, -4, 17, 13, 13, -15, -1],\n [0, 16, -5, 14, -5, 15, -15],\n [5, 10, 0, -13, 14, 0, -18],\n [-14, 8, -3, -13, -6, 16, 0],\n [-7, -3, -9, 6, 1, 12, -15],\n [4, -17, 3, 18, -11, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}66{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, -3, 0, -1, -3, -11, 14],\n [-7, -8, -14, 8, -7, -2, -13],\n [14, -14, 9, -5, -14, 14, 0],\n [3, -14, -17, 11, -15, 14, -6],\n [1, -12, -4, 4, -5, 4, 0],\n [10, 1, 10, 5, -1, -9, -11],\n [7, 10, -9, -2, -17, -13, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}67{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -14, -1, 7, 1, 8, -7],\n [-12, -16, -9, 15, 6, 16, -3],\n [-17, 5, -9, 3, 7, 8, 10],\n [1, 8, 1, 0, 1, 16, -17],\n [11, 15, 3, -16, -13, -4, 8],\n [-9, -10, 14, 13, -13, 17, -17],\n [10, -15, -18, 0, 7, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}68{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-4, 3, 2, 3, 17, 15, 11],\n [0, 9, -18, -15, -12, -10, 17],\n [0, 0, -9, 17, -10, 13, 13],\n [0, 0, 0, 8, 16, 2, 6],\n [0, 0, 0, 0, -10, 8, 7],\n [0, 0, 0, 0, 0, 13, 14],\n [0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439", "dataset": "MATH"}69{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, -2, -11, 0, 8, 11, -12],\n [-2, -9, -6, -4, -4, -8, -4],\n [-11, -6, 9, 16, 5, 0, 4],\n [0, -4, 16, 18, -5, 2, -8],\n [8, -4, 5, -5, -15, -8, -10],\n [11, -8, 0, 2, -8, -16, 2],\n [-12, -4, 4, -8, -10, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}70{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -16, 1, 0, 16, -15, -14],\n [0, -15, -7, 8, 4, 6, 2],\n [0, 0, 13, 13, -14, 17, -3],\n [0, 0, 0, -13, 16, 3, -14],\n [0, 0, 0, 0, -3, -16, 11],\n [0, 0, 0, 0, 0, -6, 13],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7643", "dataset": "MATH"}71{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[11, 3, 14, 11, -2, 13, -5],\n [-9, 17, 15, -10, 9, -8, -5],\n [0, -4, 9, 5, -11, -10, 14],\n [14, 0, -16, -9, -18, 10, 15],\n [-6, -18, 15, 10, -6, 10, 5],\n [7, -2, -12, -6, -14, 7, -16],\n [-12, -18, -2, 6, -16, -4, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}72{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 7, -3, 6, 9, -10, -18],\n [10, 3, -3, -12, -5, 10, 0],\n [0, -17, -4, -16, -8, 11, -1],\n [-17, 13, -11, 3, -13, -7, 17],\n [-4, 9, -1, -17, -6, -4, 1],\n [10, 10, -16, 0, -16, -5, -15],\n [-8, 12, 13, 8, 11, -17, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1159", "dataset": "MATH"}73{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[9, 12, 15, -4, 6, 17, -11],\n [-10, 18, 13, -2, 16, 18, 0],\n [10, -12, 9, -10, 9, -13, 10],\n [-2, -3, 4, 12, -16, 2, 7],\n [17, 18, 3, -7, -6, -8, -3],\n [-11, -17, 11, 11, -7, -9, -8],\n [-4, -3, -2, 7, -17, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}74{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -1, 13, -16, -16, 11, -18],\n [11, 13, 9, 2, -6, 8, 17],\n [-12, 3, -9, -4, -4, -15, 13],\n [4, -13, 5, 1, 18, 1, -7],\n [14, 9, -11, -18, 18, 3, -13],\n [2, 13, 16, -4, -14, -13, 6],\n [10, -12, -6, -1, -17, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}75{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, 8, 1, -7, 12, 8, 13],\n [-9, -16, 8, 16, 12, -4, -3],\n [-6, 16, -8, 2, -8, 11, 16],\n [3, 12, -5, 5, 13, 17, 13],\n [-4, 16, -16, -3, -14, 2, -9],\n [0, 6, -15, 10, 0, -17, -9],\n [6, 1, 0, 4, 5, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5948", "dataset": "MATH"}76{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -14, -14, 2, -7, -15, 1],\n [0, -5, -8, 13, -8, -1, 8],\n [0, 0, -8, 2, -14, 4, 6],\n [0, 0, 0, -18, -12, -15, -18],\n [0, 0, 0, 0, -2, 10, -5],\n [0, 0, 0, 0, 0, 11, -16],\n [0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-629", "dataset": "MATH"}77{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 1) of the inverse. Round your answer to the nearest integer:\n[[-17, 17, 7, -8, -11, 3, 1],\n [0, 10, 7, 11, -2, 1, -3],\n [0, 0, 8, 4, 5, -10, 16],\n [0, 0, 0, 12, -11, -4, 12],\n [0, 0, 0, 0, 11, 10, 0],\n [0, 0, 0, 0, 0, 5, -9],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}78{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[4, -8, -11, 10, 11, -9, 9],\n [17, -6, 13, 17, 18, 7, 3],\n [-15, 12, -1, 5, 4, 3, -17],\n [12, -8, 9, 13, -14, -9, 5],\n [16, 4, -2, -18, 12, 12, 15],\n [-10, 3, -6, 6, -1, -7, -2],\n [-4, -4, -4, -6, -2, 13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742", "dataset": "MATH"}79{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -2, -4, 1, 2, -11, -8],\n [-2, -7, 3, -9, 5, 7, -4],\n [-4, 3, 13, 0, 6, 8, 0],\n [1, -9, 0, -5, 10, -6, 2],\n [2, 5, 6, 10, 11, -2, 0],\n [-11, 7, 8, -6, -2, -11, -14],\n [-8, -4, 0, 2, 0, -14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}80{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 6, 0, 7, 10, -2, 6],\n [6, -15, -12, 2, 0, 6, 10],\n [0, -12, -4, -8, -2, 8, -6],\n [7, 2, -8, -11, -5, 2, 9],\n [10, 0, -2, -5, -1, -2, 4],\n [-2, 6, 8, 2, -2, -6, -4],\n [6, 10, -6, 9, 4, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451", "dataset": "MATH"}81{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -2, 12, 3, -4, -13, 2],\n [-2, 15, -4, 1, 8, 0, -4],\n [12, -4, -11, -6, -2, -2, -4],\n [3, 1, -6, 14, 8, -4, -8],\n [-4, 8, -2, 8, 18, -6, 17],\n [-13, 0, -2, -4, -6, 9, -8],\n [2, -4, -4, -8, 17, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-331", "dataset": "MATH"}82{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[7, 16, 0, 12, -6, 2, 4],\n [16, 9, -10, 2, 10, -12, 2],\n [0, -10, -15, 2, -4, 2, -2],\n [12, 2, 2, 6, 3, -10, 8],\n [-6, 10, -4, 3, 0, -10, 3],\n [2, -12, 2, -10, -10, 16, -7],\n [4, 2, -2, 8, 3, -7, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-173", "dataset": "MATH"}83{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 6) rounded to the nearest integer?\n[[-15, 3, -11, -4, -6, 14, -12],\n [3, 6, 4, 6, -7, 12, 2],\n [-11, 4, 2, 2, -12, -14, -2],\n [-4, 6, 2, 2, 8, 3, 5],\n [-6, -7, -12, 8, -11, -12, -10],\n [14, 12, -14, 3, -12, -18, 0],\n [-12, 2, -2, 5, -10, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}84{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[11, -10, 12, 2, 15, 12, 6],\n [-7, -18, 3, 18, -18, -18, 2],\n [-4, -2, 3, 16, -3, -11, -2],\n [-2, 7, -6, -2, -2, -5, -13],\n [16, -5, -11, -4, 8, -6, 12],\n [16, -13, -14, 3, 4, 6, 15],\n [7, -14, 7, 1, -13, -13, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"}85{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, -2, -5, -5, -6, -12, -4],\n [0, 16, -2, 16, 0, 1, 17],\n [16, 13, 5, -2, -12, -18, 16],\n [13, 17, -6, -13, -5, 18, -4],\n [-15, -3, 9, -3, -15, 7, 9],\n [13, -17, 12, -16, -11, 5, -4],\n [12, -10, -17, -11, -12, -3, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-110", "dataset": "MATH"}86{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, -9, -1, -14, 10, 15, 4],\n [0, 11, -13, -15, 10, 4, -13],\n [0, 0, -4, 13, -10, 18, -9],\n [0, 0, 0, -8, -2, 13, -15],\n [0, 0, 0, 0, 13, 3, -13],\n [0, 0, 0, 0, 0, -8, -6],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-313", "dataset": "MATH"}87{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 4, -9, 0, -14, 4, 11],\n [6, 9, 15, 6, -9, -5, 11],\n [6, -5, 16, 15, -9, 16, -8],\n [-8, 2, 2, 3, -12, -2, -17],\n [-7, -1, -8, -3, -1, 16, 7],\n [-3, -13, -7, -6, -15, -17, 7],\n [8, 8, -4, -11, -12, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}88{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -2, 17, 2, -11, -14, 7],\n [-3, 17, 9, 10, -7, 18, 11],\n [4, -3, -5, -9, -12, 18, 10],\n [-16, -4, 17, 0, -6, 2, 18],\n [8, 10, 1, 6, -13, 17, -17],\n [3, 13, -3, -1, -14, 17, 11],\n [0, 4, 15, -6, 10, 17, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}89{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -10, 0, -13, -4, 1, -10],\n [13, -15, -1, -14, 1, 4, -8],\n [18, 3, -15, 10, 15, -6, -10],\n [12, -12, -15, 0, 11, 12, 16],\n [2, 12, 0, 12, 13, -17, -9],\n [-17, -17, 5, -2, 13, -3, -3],\n [12, 5, -18, -8, 2, -15, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}90{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 3, 6, 3, 10, -2, 8],\n [3, -18, 8, -14, -2, 3, -16],\n [6, 8, -8, -6, -12, 0, -12],\n [3, -14, -6, -17, 12, -1, 0],\n [10, -2, -12, 12, -6, 16, -5],\n [-2, 3, 0, -1, 16, 13, 7],\n [8, -16, -12, 0, -5, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}91{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 5) of the inverse. Round your answer to the nearest integer:\n[[-9, 13, 15, 1, -17, -18, 17],\n [0, 8, -17, 12, -5, -17, 10],\n [0, 0, 18, 9, 1, 5, 2],\n [0, 0, 0, -1, 5, -5, 15],\n [0, 0, 0, 0, 17, 3, -5],\n [0, 0, 0, 0, 0, 17, 1],\n [0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-346", "dataset": "MATH"}92{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/252 * A where A =\n[[2, -4, 14, 4, -10, 0, -7],\n [-4, 4, -10, 2, 7, 4, -10],\n [14, -10, 8, 1, 6, 0, 8],\n [4, 2, 1, 9, -7, -6, 8],\n [-10, 7, 6, -7, -10, -2, 0],\n [0, 4, 0, -6, -2, 8, -1],\n [-7, -10, 8, 8, 0, -1, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}93{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, -4, -2, -5, 5, -5, -8],\n [-4, -18, 4, -8, 2, 4, -6],\n [-2, 4, 14, -8, 10, -4, 0],\n [-5, -8, -8, -10, -3, 2, 2],\n [5, 2, 10, -3, 3, -3, 0],\n [-5, 4, -4, 2, -3, 9, -8],\n [-8, -6, 0, 2, 0, -8, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}94{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, 8, -8, 15, 0, -13, 9],\n [-18, 16, -11, -12, -8, -15, 6],\n [-7, 7, -7, 18, 5, -3, -6],\n [6, -15, -8, 13, -12, -8, 9],\n [4, 4, 9, 7, 6, 10, 0],\n [14, 17, -5, -5, 16, 11, 9],\n [-2, -16, -3, 11, 10, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}95{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, 6, -12, 3, -2, -1, -9],\n [-9, -12, 8, 14, -18, 15, -15],\n [-2, -15, 7, -15, -18, -12, 11],\n [-10, 16, -11, 5, 0, 17, 8],\n [13, -5, -1, 9, 10, -3, 16],\n [12, -15, 18, -2, 7, -15, 11],\n [11, 3, -8, -17, -7, 11, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}96{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -3, -6, -12, 10, 11, 11],\n [-3, -13, 0, 8, 0, 7, 14],\n [-6, 0, 18, 10, -2, 2, 12],\n [-12, 8, 10, -10, 0, -8, 6],\n [10, 0, -2, 0, -16, -14, -9],\n [11, 7, 2, -8, -14, -1, -14],\n [11, 14, 12, 6, -9, -14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}97{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[2, -6, 2, 2, 10, 8, 0],\n [-6, 3, 4, -2, 2, -15, 4],\n [2, 4, -12, 3, -16, -6, -8],\n [2, -2, 3, 16, -12, -2, -9],\n [10, 2, -16, -12, -11, -1, -10],\n [8, -15, -6, -2, -1, -6, -14],\n [0, 4, -8, -9, -10, -14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}98{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[3, 5, 18, -18, -9, -3, -11],\n [0, -7, 6, -2, 7, -5, 17],\n [0, 0, -14, 6, -1, -6, -5],\n [0, 0, 0, 8, 13, -10, 13],\n [0, 0, 0, 0, 15, -16, 7],\n [0, 0, 0, 0, 0, -6, -14],\n [0, 0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1888", "dataset": "MATH"}99{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, -8, 0, 16, 7, -5, 5],\n [-18, 3, 4, 0, -1, -7, 9],\n [9, 14, 0, 9, 18, 7, 16],\n [15, 16, -3, -6, 4, 3, -3],\n [9, 16, -11, 3, 2, 7, 2],\n [6, -18, -13, 4, 4, 4, 13],\n [11, -6, -1, 4, -4, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}100{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[4, 8, -1, 5, -12, 1, 8],\n [-13, 8, -10, 12, 2, 7, -6],\n [4, 1, 18, 9, -2, 9, -17],\n [6, -13, -8, -13, -8, -5, -17],\n [-16, 16, 14, 5, 0, -1, 5],\n [16, -18, 17, 6, 15, 6, -3],\n [15, 10, 0, 4, 0, 6, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}101{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-10, -18, 0, 14, 15, -3, -1],\n [15, 6, -13, 2, -13, 13, 12],\n [-9, 11, -1, 5, -10, 12, -4],\n [-15, -10, -10, 7, -15, -2, -3],\n [-4, 16, -14, -14, 1, -4, -1],\n [-17, 10, -6, -15, -9, 12, -11],\n [-16, -10, 11, -8, 16, 18, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58", "dataset": "MATH"}102{"messages": [{"content": "Find the value at position (1, 6) of the inverse of matrix 1/252 * A where A =\n[[17, -6, -7, 18, -9, -10, -12],\n [0, 4, 2, 4, 10, -5, 7],\n [0, 0, 6, 12, 1, -2, -17],\n [0, 0, 0, -13, -16, 16, -1],\n [0, 0, 0, 0, 3, 0, -3],\n [0, 0, 0, 0, 0, -5, 0],\n [0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}103{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 9, -3, 0, -2, -6, -12],\n [0, -9, 15, 17, 6, -13, 5],\n [0, 0, -13, 10, 6, -2, 5],\n [0, 0, 0, 9, -16, -8, -5],\n [0, 0, 0, 0, 1, 13, 3],\n [0, 0, 0, 0, 0, -15, 16],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55403", "dataset": "MATH"}104{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -11, 6, 2, 6, -10, 2],\n [-11, 13, -6, 12, 5, 14, 11],\n [6, -6, 4, -2, 0, -4, 4],\n [2, 12, -2, 17, 1, -4, -5],\n [6, 5, 0, 1, 13, 10, -6],\n [-10, 14, -4, -4, 10, 15, -6],\n [2, 11, 4, -5, -6, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}105{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/252 * A where A =\n[[-17, -2, 18, -5, 6, 11, 10],\n [0, 2, 3, 16, 18, -3, -2],\n [0, 0, -15, 2, 15, 11, -13],\n [0, 0, 0, -14, 1, -3, 18],\n [0, 0, 0, 0, 17, 3, 3],\n [0, 0, 0, 0, 0, -12, -18],\n [0, 0, 0, 0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}106{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[13, 14, 9, 17, -13, -3, 15],\n [0, 5, -6, -1, -6, 18, -2],\n [0, 0, 4, 11, 15, -15, -16],\n [0, 0, 0, -13, 3, -18, -15],\n [0, 0, 0, 0, -10, -7, -13],\n [0, 0, 0, 0, 0, 5, -12],\n [0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7354", "dataset": "MATH"}107{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 10, 15, -18, 12, 11, -1],\n [-2, -5, 4, 6, -4, 3, -16],\n [0, 15, 16, -18, 2, 10, -13],\n [18, -18, -18, 8, 2, -3, 7],\n [-3, 9, -18, 17, -9, -2, 4],\n [-12, -12, -4, 15, -15, -5, -5],\n [-3, -12, 13, 0, -17, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}108{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[18, -10, -3, 0, 8, -8, -17],\n [-10, 0, -4, 2, 6, 4, 8],\n [-3, -4, -12, 2, 2, 8, 13],\n [0, 2, 2, -14, -4, 14, -2],\n [8, 6, 2, -4, 7, 15, -8],\n [-8, 4, 8, 14, 15, 4, -15],\n [-17, 8, 13, -2, -8, -15, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-207", "dataset": "MATH"}109{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[13, -13, -9, -12, 7, 15, 11],\n [0, 2, -2, 14, -9, -7, -3],\n [0, 0, 8, 9, -2, -17, 17],\n [0, 0, 0, 6, 4, 3, 7],\n [0, 0, 0, 0, 18, 5, 14],\n [0, 0, 0, 0, 0, 5, -10],\n [0, 0, 0, 0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1849", "dataset": "MATH"}110{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, 10, 5, -9, -2, -1, 1],\n [18, -1, -2, -10, -5, 10, 12],\n [-15, -1, 1, -10, -6, -4, 8],\n [-4, 9, 18, 0, 7, 7, 6],\n [7, 7, 9, -1, 13, -16, -17],\n [14, 0, -2, 14, -7, -16, 7],\n [16, -11, 17, -12, 17, -3, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}111{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 6, -9, -3, -3, -11, 10],\n [9, -13, -3, 1, -3, -12, -5],\n [7, 7, -5, -12, 14, 7, 1],\n [-16, -15, 7, -8, -17, -5, 11],\n [-7, 7, 14, -6, -5, 5, 15],\n [7, 2, 9, 17, -17, -10, 4],\n [-4, -6, 4, -2, -17, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}112{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, -7, -17, 17, -5, -3, 0],\n [0, -13, -6, 17, 3, -1, -7],\n [0, 0, 13, 0, -13, 1, 8],\n [0, 0, 0, -8, -4, -16, -14],\n [0, 0, 0, 0, -16, 10, -13],\n [0, 0, 0, 0, 0, -8, -11],\n [0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}113{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -2, -2, -16, 12, -18, -7],\n [0, -6, 15, 2, 3, -15, -1],\n [0, 0, -17, -7, -2, -9, 15],\n [0, 0, 0, -7, -10, -17, -11],\n [0, 0, 0, 0, 1, -11, 17],\n [0, 0, 0, 0, 0, 2, 11],\n [0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5295", "dataset": "MATH"}114{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -9, -13, -2, 5, -9, -11],\n [2, -13, 2, 5, 14, -1, 9],\n [13, -7, 8, -9, 13, 7, 6],\n [-8, 4, 15, 4, 10, 12, -12],\n [14, 2, -17, -1, 14, 18, 15],\n [1, 16, -1, 5, -11, 11, -9],\n [4, -8, -17, 7, 17, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567", "dataset": "MATH"}115{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 2) rounded to the nearest integer?\n[[6, -6, 0, -8, 6, 9, 6],\n [-6, -3, -16, 0, 12, 11, -8],\n [0, -16, 7, 2, -2, 2, 14],\n [-8, 0, 2, -17, -8, 1, -4],\n [6, 12, -2, -8, -17, 8, -13],\n [9, 11, 2, 1, 8, 4, -9],\n [6, -8, 14, -4, -13, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}116{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-6, -4, -12, 9, 13, 16, -4],\n [17, 2, -13, -18, -15, -8, 7],\n [18, 4, 10, 2, 8, -6, 4],\n [-3, 11, -15, -3, 12, 6, -7],\n [7, 18, 14, 9, -10, -7, -14],\n [9, 16, -14, 15, 15, -6, -5],\n [-8, -15, 14, -12, -11, 18, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}117{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-4, -10, -10, 13, -2, -6, -11],\n [-10, 12, 7, 6, 5, 7, -3],\n [-10, 7, 17, 6, -15, -2, -8],\n [13, 6, 6, -15, 12, 6, -2],\n [-2, 5, -15, 12, -18, 10, 6],\n [-6, 7, -2, 6, 10, 4, -7],\n [-11, -3, -8, -2, 6, -7, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-302", "dataset": "MATH"}118{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[12, 12, 15, 5, 7, -3, -6],\n [-4, 8, -15, -3, 11, 11, 17],\n [-16, 3, 3, -7, 2, -15, 12],\n [12, 4, 1, -4, 4, 9, -3],\n [18, 2, -4, -2, 18, -6, 0],\n [11, -1, -5, 17, 17, 1, 0],\n [-12, -15, 15, -17, -14, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1059", "dataset": "MATH"}119{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -16, -6, -7, -5, 2, 0],\n [-16, 9, -10, 8, 0, 4, -5],\n [-6, -10, 12, 5, 12, 12, 4],\n [-7, 8, 5, 17, -4, -1, -16],\n [-5, 0, 12, -4, 9, 0, -6],\n [2, 4, 12, -1, 0, -1, -6],\n [0, -5, 4, -16, -6, -6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}120{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, 6, 1, 15, 2, 4, -13],\n [-6, 4, -10, -2, -17, 0, 0],\n [-12, 1, -10, -2, 8, -17, 17],\n [0, -2, -14, -1, -12, -2, 17],\n [-15, 6, -14, 11, -7, -15, 5],\n [10, -10, -15, 5, -5, -14, -1],\n [0, -7, -1, -2, 11, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2485", "dataset": "MATH"}121{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, 0, -4, -8, -2, 2, 0],\n [0, 9, 3, 8, -4, -1, 6],\n [-4, 3, -18, 8, -3, -10, -1],\n [-8, 8, 8, 8, 12, 8, 6],\n [-2, -4, -3, 12, -12, 8, 2],\n [2, -1, -10, 8, 8, -14, 2],\n [0, 6, -1, 6, 2, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}122{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-17, -5, 3, 12, 4, 1, -15],\n [0, 5, 6, -18, -12, 12, -7],\n [0, 0, -1, -17, -9, -4, 11],\n [0, 0, 0, 12, 15, -13, 15],\n [0, 0, 0, 0, 13, -16, -16],\n [0, 0, 0, 0, 0, 10, -2],\n [0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-277", "dataset": "MATH"}123{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-16, -14, 7, -8, -12, -9, 15],\n [0, -11, 12, -8, -12, -17, -13],\n [0, 0, 15, -3, 6, -7, -12],\n [0, 0, 0, 4, 8, -13, -17],\n [0, 0, 0, 0, 10, -11, 18],\n [0, 0, 0, 0, 0, 11, 12],\n [0, 0, 0, 0, 0, 0, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768", "dataset": "MATH"}124{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[15, 9, -17, 11, -6, -3, -14],\n [9, 1, 5, 8, 11, 8, 7],\n [-12, -14, 4, 9, 15, -4, 13],\n [7, 12, 0, -10, 10, -15, -16],\n [10, -8, 14, -8, 8, 14, 2],\n [12, -17, 8, 17, -8, -1, -18],\n [16, 16, 12, 9, -18, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}125{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -17, -1, -9, -14, -10, -17],\n [15, 12, -9, -7, 17, 2, -13],\n [-16, -9, -14, 7, 2, 7, 7],\n [-11, -14, -4, -3, -18, -3, 18],\n [-16, 12, -6, -3, 2, -17, 8],\n [7, 6, -8, -11, -11, 14, -12],\n [2, -11, 2, 1, -11, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-78", "dataset": "MATH"}126{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-10, -4, 11, 7, -9, 10, -3],\n [17, 1, 18, 3, -12, 4, 10],\n [-3, 9, 12, -5, 14, -10, 8],\n [5, -6, 7, 10, 9, 9, -11],\n [4, 10, -14, -12, 17, 8, -17],\n [6, -10, 8, -18, 4, -9, 6],\n [-16, -13, -13, -17, -1, 4, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}127{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -8, 10, 3, 1, -7, -2],\n [-8, -2, -6, 10, -10, -11, 4],\n [10, -6, -6, 0, 10, 4, 2],\n [3, 10, 0, -3, -6, -4, -10],\n [1, -10, 10, -6, -18, -6, 0],\n [-7, -11, 4, -4, -6, -8, -6],\n [-2, 4, 2, -10, 0, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}128{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[14, 18, -4, -17, -12, 13, -15],\n [1, 17, 13, 9, -6, -18, 16],\n [11, 17, 6, -3, 0, -18, -14],\n [3, 5, 18, 17, 17, -15, 17],\n [-1, -3, -1, 3, -17, 2, 17],\n [10, 7, 2, -2, -3, 12, -10],\n [12, -5, 18, -17, -5, 14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "472", "dataset": "MATH"}129{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, -12, -1, 18, -2, -3, -10],\n [-12, 10, 0, 6, -10, 4, -14],\n [-1, 0, -9, -2, -2, -8, 4],\n [18, 6, -2, -10, 3, -10, 10],\n [-2, -10, -2, 3, 10, -8, 4],\n [-3, 4, -8, -10, -8, 1, 12],\n [-10, -14, 4, 10, 4, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42917", "dataset": "MATH"}130{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, -15, -12, 14, -6, 12, 10],\n [-15, 11, 0, 7, -11, -2, -1],\n [-12, 0, -17, -13, -14, -4, -6],\n [14, 7, -13, -17, 2, -16, 15],\n [-6, -11, -14, 2, 6, 4, 0],\n [12, -2, -4, -16, 4, -16, 0],\n [10, -1, -6, 15, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17849", "dataset": "MATH"}131{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[7, -1, 2, 17, 3, 11, 11],\n [0, 15, -10, 1, 6, 0, -14],\n [0, 0, -11, 0, 4, 8, 13],\n [0, 0, 0, 10, 14, 0, 18],\n [0, 0, 0, 0, -12, 7, 13],\n [0, 0, 0, 0, 0, 7, -14],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}132{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, -4, 8, -8, -9, -2, -3],\n [-4, -17, -11, 6, 2, 7, -6],\n [8, -11, -2, 2, -10, -6, -6],\n [-8, 6, 2, 16, -2, 9, 2],\n [-9, 2, -10, -2, -9, 2, -7],\n [-2, 7, -6, 9, 2, 16, -12],\n [-3, -6, -6, 2, -7, -12, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299", "dataset": "MATH"}133{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-16, -8, 11, -15, -14, -18, 8],\n [9, 10, -1, -7, -6, -17, 18],\n [-3, 5, 16, 3, 17, -8, 10],\n [16, -4, 12, -3, -9, 13, -17],\n [5, 4, -17, 12, 7, 10, -16],\n [-5, 6, -18, -16, 7, -1, -10],\n [4, 2, -18, 2, 8, -13, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}134{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 1, 0, 6, 4, -8, -6],\n [1, 11, -3, 0, -8, -4, 0],\n [0, -3, -17, 8, 15, 10, -4],\n [6, 0, 8, -8, 3, -17, -3],\n [4, -8, 15, 3, -14, 8, 2],\n [-8, -4, 10, -17, 8, 7, -6],\n [-6, 0, -4, -3, 2, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-115", "dataset": "MATH"}135{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 16, -7, 11, -14, 15, 3],\n [0, -16, 1, 12, -14, 5, 14],\n [0, 0, 1, -3, -7, -6, 6],\n [0, 0, 0, 4, -6, 13, -4],\n [0, 0, 0, 0, -9, 5, -1],\n [0, 0, 0, 0, 0, -3, 16],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52", "dataset": "MATH"}136{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, 2, -2, -4, -6, 1, 2],\n [2, 11, -5, 5, -5, 8, 15],\n [-2, -5, 14, 16, 2, -2, 5],\n [-4, 5, 16, 15, 2, -3, 1],\n [-6, -5, 2, 2, -8, 2, -2],\n [1, 8, -2, -3, 2, 16, 5],\n [2, 15, 5, 1, -2, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}137{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 8, 1, 6, -17, -10, 9],\n [-16, 1, -13, 14, -18, 18, -13],\n [15, -4, 7, -5, -12, 12, 5],\n [12, 10, 13, -2, -5, 17, 5],\n [8, 6, 13, -1, -1, 18, 7],\n [-10, 16, -11, 1, 3, 0, 11],\n [9, 16, -8, 12, 17, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}138{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[0, 2, 0, 2, 17, 12, 4],\n [2, 7, -5, 10, -6, -6, 4],\n [0, -5, -8, 4, -12, -10, 2],\n [2, 10, 4, -5, -12, 6, -12],\n [17, -6, -12, -12, -5, 4, -12],\n [12, -6, -10, 6, 4, 3, 6],\n [4, 4, 2, -12, -12, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}139{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-11, -10, 16, 18, 2, -1, 14],\n [0, -2, 12, 15, -13, 3, -5],\n [0, 0, 17, -7, -17, -17, -4],\n [0, 0, 0, 13, -12, 11, 9],\n [0, 0, 0, 0, -13, 5, -13],\n [0, 0, 0, 0, 0, 15, -4],\n [0, 0, 0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-89", "dataset": "MATH"}140{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[15, -10, 4, 16, -12, -4, 1],\n [0, -16, 5, 15, 3, -8, -11],\n [0, 0, 18, 8, 9, 15, 13],\n [0, 0, 0, -3, 10, -10, 14],\n [0, 0, 0, 0, -14, -9, -13],\n [0, 0, 0, 0, 0, -10, -16],\n [0, 0, 0, 0, 0, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}141{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, -5, -18, -15, 11, -7, 16],\n [0, 12, 4, -15, -3, -12, 3],\n [0, 0, 14, 10, -7, -12, 7],\n [0, 0, 0, 17, 6, 5, -2],\n [0, 0, 0, 0, 9, 8, -4],\n [0, 0, 0, 0, 0, 18, -10],\n [0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}142{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[2, 14, 8, -5, -8, 2, 10],\n [14, -12, 10, -3, 14, -4, -12],\n [8, 10, 14, 0, 5, 0, 2],\n [-5, -3, 0, -3, 2, 5, 8],\n [-8, 14, 5, 2, 12, 0, -8],\n [2, -4, 0, 5, 0, -1, -2],\n [10, -12, 2, 8, -8, -2, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-552", "dataset": "MATH"}143{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 6, 13, 7, 3, 12, -9],\n [0, 9, -13, 1, -14, 4, -10],\n [0, 0, 3, -11, 1, -5, 18],\n [0, 0, 0, 12, 15, -12, 4],\n [0, 0, 0, 0, 15, 11, -2],\n [0, 0, 0, 0, 0, 17, 4],\n [0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2439", "dataset": "MATH"}144{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -10, -8, -1, -12, -4, -4],\n [-10, -3, 3, 4, -8, -2, 2],\n [-8, 3, 2, 14, -1, 3, -12],\n [-1, 4, 14, -12, 15, 3, -2],\n [-12, -8, -1, 15, -15, 11, 10],\n [-4, -2, 3, 3, 11, -3, 12],\n [-4, 2, -12, -2, 10, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}145{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[12, -17, -4, -8, 15, -15, -8],\n [0, -17, -3, -6, 18, -2, 2],\n [0, 0, -11, -6, 18, -17, -8],\n [0, 0, 0, -12, 0, -13, 10],\n [0, 0, 0, 0, 18, 9, 11],\n [0, 0, 0, 0, 0, -13, -1],\n [0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}146{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -10, -5, 0, -5, 11, 11],\n [-10, 10, 0, 6, 12, 4, -7],\n [-5, 0, 3, 2, -8, 3, -8],\n [0, 6, 2, 6, 4, 3, 8],\n [-5, 12, -8, 4, -3, -10, -4],\n [11, 4, 3, 3, -10, 6, 0],\n [11, -7, -8, 8, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}147{"messages": [{"content": "Find the value at position (5, 6) of the inverse of matrix 1/252 * A where A =\n[[8, -6, 12, 0, 6, 0, 12],\n [-6, 5, -3, 1, 12, 0, -12],\n [12, -3, -2, -4, 11, -2, 4],\n [0, 1, -4, -13, 2, 6, -7],\n [6, 12, 11, 2, -18, -12, -2],\n [0, 0, -2, 6, -12, 5, -10],\n [12, -12, 4, -7, -2, -10, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}148{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, 4, 0, 5, 0, -10, 5],\n [4, 12, -12, -9, -8, -8, -2],\n [0, -12, -8, -2, 10, -13, -10],\n [5, -9, -2, 5, -16, 2, 9],\n [0, -8, 10, -16, -8, -8, 8],\n [-10, -8, -13, 2, -8, 4, 0],\n [5, -2, -10, 9, 8, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}149{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, 14, 5, -5, 17, -14, -8],\n [0, 12, -6, -3, 5, -6, 5],\n [0, 0, -3, -18, -8, 16, 10],\n [0, 0, 0, 10, -16, -9, -5],\n [0, 0, 0, 0, 13, 7, -18],\n [0, 0, 0, 0, 0, -10, 3],\n [0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2548", "dataset": "MATH"}150{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 3, -1, -7, -10, -13, 0],\n [0, -3, -14, -3, -18, 18, 0],\n [0, 0, 7, 3, -11, 14, -17],\n [0, 0, 0, -9, 5, -15, 18],\n [0, 0, 0, 0, -1, 5, -17],\n [0, 0, 0, 0, 0, -9, -18],\n [0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40409", "dataset": "MATH"}151{"messages": [{"content": "Find the value at position (6, 6) of the inverse of matrix 1/252 * A where A =\n[[-12, 9, 12, 8, -2, 6, 2],\n [9, -13, 18, -2, 7, -2, -7],\n [12, 18, -4, -7, -1, 9, 2],\n [8, -2, -7, 3, -4, -6, 0],\n [-2, 7, -1, -4, -18, 3, -12],\n [6, -2, 9, -6, 3, 15, -2],\n [2, -7, 2, 0, -12, -2, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}152{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-3, -4, 9, 12, 4, -2, 15],\n [-6, -5, -8, 9, 13, 16, 12],\n [-2, -10, -9, -11, 2, -6, -14],\n [-13, 11, 12, -2, -8, 1, -10],\n [-17, 18, -18, -15, 17, 6, -16],\n [-10, 3, 4, -7, -9, 15, -9],\n [11, 3, -13, -17, 11, -17, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2984", "dataset": "MATH"}153{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -7, -18, -11, -6, -4, -11],\n [-9, -14, 0, -8, 1, 1, 2],\n [-1, -9, 15, 7, 11, -10, 12],\n [-15, -13, -5, -15, 7, -2, 0],\n [-13, 10, -8, -3, 11, 6, -8],\n [-12, 7, 3, 6, 0, 12, 7],\n [17, 4, -6, 6, -17, -17, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1044", "dataset": "MATH"}154{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 9, -6, 16, -6, 12, 2],\n [13, 15, -11, -17, 13, 9, 18],\n [-18, -9, -15, 16, -9, -8, -5],\n [-7, -2, -3, 16, -17, -8, -16],\n [10, -1, 1, -5, 15, 12, -1],\n [11, 6, 0, -11, 9, -11, 12],\n [-16, -16, 3, -2, 17, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}155{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 7) of the inverse. Round your answer to the nearest integer:\n[[-10, 6, 5, -11, 9, 2, -6],\n [6, 16, -3, -9, -5, 6, 12],\n [5, -3, 1, -12, -4, -6, 2],\n [-11, -9, -12, -6, 0, -8, 4],\n [9, -5, -4, 0, -6, 12, -6],\n [2, 6, -6, -8, 12, -5, 6],\n [-6, 12, 2, 4, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}156{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -8, -3, 4, -3, -5, -5],\n [-8, -3, -3, -8, 7, 0, -6],\n [-3, -3, 9, 0, -11, 13, -2],\n [4, -8, 0, -8, 6, 8, 4],\n [-3, 7, -11, 6, 1, 0, -14],\n [-5, 0, 13, 8, 0, 6, -8],\n [-5, -6, -2, 4, -14, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}157{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, -1, -16, -9, -18, 8, 8],\n [0, -14, -12, 0, 10, -4, 16],\n [0, 0, 11, 1, 18, -16, -10],\n [0, 0, 0, 4, 2, -3, -10],\n [0, 0, 0, 0, 17, -18, -1],\n [0, 0, 0, 0, 0, 5, 17],\n [0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-480", "dataset": "MATH"}158{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, -4, 6, -8, 4, 8, 0],\n [-4, 6, 2, 12, 0, -6, -6],\n [6, 2, -14, -8, 6, -2, 10],\n [-8, 12, -8, 14, -10, -2, -7],\n [4, 0, 6, -10, 7, -7, -8],\n [8, -6, -2, -2, -7, 15, -4],\n [0, -6, 10, -7, -8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "647", "dataset": "MATH"}159{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, -5, 10, -18, -15, 13, 14],\n [0, -2, 4, 13, -4, -6, -17],\n [0, 0, 5, -8, 3, -4, -9],\n [0, 0, 0, -18, -2, 12, -9],\n [0, 0, 0, 0, -7, -5, -9],\n [0, 0, 0, 0, 0, -9, 9],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-731", "dataset": "MATH"}160{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 0, -1, 8, 2, -4, 10],\n [0, 14, -8, -4, 6, -5, 4],\n [-1, -8, 11, -3, 14, 8, 2],\n [8, -4, -3, -6, -2, 14, 5],\n [2, 6, 14, -2, 16, -2, 4],\n [-4, -5, 8, 14, -2, 14, 4],\n [10, 4, 2, 5, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "634", "dataset": "MATH"}161{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 8, 18, 11, 8, -4, 7],\n [0, -15, 10, -18, 3, -8, -9],\n [0, 0, 7, 2, -6, -10, -8],\n [0, 0, 0, -13, -6, 3, 12],\n [0, 0, 0, 0, -14, 17, 13],\n [0, 0, 0, 0, 0, 2, -6],\n [0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}162{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, 18, 11, -11, -18, -7, -14],\n [5, -13, 6, -18, 6, -18, 13],\n [-16, 0, 10, -17, -10, -2, 17],\n [-2, -7, 1, -16, -15, -2, 18],\n [-4, 14, -3, -8, 1, 5, -3],\n [11, 15, -18, 5, 5, -10, 3],\n [-7, -2, 6, 9, -4, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}163{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/252 * A where A =\n[[3, 2, 10, 0, -11, 5, -2],\n [2, 16, 4, 1, -3, -2, -8],\n [10, 4, 12, 4, -1, 10, 0],\n [0, 1, 4, 3, 5, 14, 3],\n [-11, -3, -1, 5, 7, 0, -3],\n [5, -2, 10, 14, 0, 17, 5],\n [-2, -8, 0, 3, -3, 5, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}164{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 6) rounded to the nearest integer?\n[[-3, -3, -6, -4, -2, 8, -6],\n [-3, -6, 2, -10, -5, -4, 0],\n [-6, 2, -17, 3, 5, 9, 1],\n [-4, -10, 3, -12, 10, -10, -3],\n [-2, -5, 5, 10, -13, 4, -4],\n [8, -4, 9, -10, 4, 17, -17],\n [-6, 0, 1, -3, -4, -17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}165{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -16, -18, 0, 3, -5, -5],\n [0, 14, -6, -7, 14, 14, 10],\n [0, 0, 12, -3, 12, 6, 14],\n [0, 0, 0, -9, 12, -6, -16],\n [0, 0, 0, 0, 13, -6, 14],\n [0, 0, 0, 0, 0, 5, 3],\n [0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-224", "dataset": "MATH"}166{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, -11, -4, -15, 15, -14, 14],\n [0, 15, 7, -18, -15, 7, 14],\n [0, 0, 1, -3, 2, 7, 4],\n [0, 0, 0, -18, -10, -16, 7],\n [0, 0, 0, 0, -16, 15, 14],\n [0, 0, 0, 0, 0, 2, 0],\n [0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1651", "dataset": "MATH"}167{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-11, 9, 0, -2, 4, 1, -2],\n [9, 1, 6, -8, 2, 10, -6],\n [0, 6, -16, 8, 6, 10, 16],\n [-2, -8, 8, 18, 10, 0, -8],\n [4, 2, 6, 10, 16, 5, 7],\n [1, 10, 10, 0, 5, 5, -8],\n [-2, -6, 16, -8, 7, -8, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "773", "dataset": "MATH"}168{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, 8, 6, -6, -11, -14, -7],\n [0, 16, 14, 3, -10, -1, 10],\n [0, 0, -2, 15, -16, -14, -5],\n [0, 0, 0, 4, 8, -9, 6],\n [0, 0, 0, 0, 3, -2, 4],\n [0, 0, 0, 0, 0, -6, -11],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1932", "dataset": "MATH"}169{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[4, -4, -8, -8, -8, 14, -9],\n [-4, 6, 9, 7, -2, 0, -14],\n [-8, 9, -4, 0, -12, 4, 0],\n [-8, 7, 0, -9, 8, -1, 0],\n [-8, -2, -12, 8, -16, -3, -2],\n [14, 0, 4, -1, -3, 11, 6],\n [-9, -14, 0, 0, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}170{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, 17, -4, 14, 7, -3, 17],\n [0, 1, -6, 14, -14, 18, -5],\n [0, 0, -5, -15, 0, -15, 11],\n [0, 0, 0, -10, -6, -5, -9],\n [0, 0, 0, 0, -13, 7, -17],\n [0, 0, 0, 0, 0, 10, -17],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}171{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-10, 7, -5, 7, 9, -10, 6],\n [7, 0, 10, -9, -3, -4, 10],\n [-5, 10, 13, -14, -4, -10, -18],\n [7, -9, -14, 17, 4, 14, 6],\n [9, -3, -4, 4, -3, 0, -12],\n [-10, -4, -10, 14, 0, -6, 10],\n [6, 10, -18, 6, -12, 10, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}172{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, 14, 13, -1, -2, 15, -12],\n [0, 11, -7, 16, -8, -15, 6],\n [0, 0, 12, -15, -18, -16, 18],\n [0, 0, 0, 16, -6, 16, -17],\n [0, 0, 0, 0, 17, 11, -12],\n [0, 0, 0, 0, 0, 12, -3],\n [0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197", "dataset": "MATH"}173{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-12, -11, -12, -16, -2, -17, -4],\n [10, 3, -15, -13, 7, -8, 7],\n [-2, 5, 9, 16, 12, -6, 16],\n [-3, -4, -1, 18, 8, 16, 16],\n [9, -10, -7, -4, 2, 16, 14],\n [0, 4, -6, -18, 10, 5, -3],\n [6, 4, 9, -3, -8, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2051", "dataset": "MATH"}174{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, -12, -18, 13, -10, 10, 7],\n [0, 10, 14, -12, -7, 12, 13],\n [0, 0, 17, -16, -18, 8, 14],\n [0, 0, 0, -14, 4, -4, -13],\n [0, 0, 0, 0, -13, -4, -3],\n [0, 0, 0, 0, 0, -9, 0],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "740", "dataset": "MATH"}175{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, -3, -17, 12, 9, -12, 11],\n [-12, 17, 10, 5, -15, 10, -14],\n [10, 11, 10, 7, 0, 7, 18],\n [8, 11, 11, -16, -12, -10, -6],\n [-4, -14, 10, 16, 8, 8, -11],\n [13, 1, -9, -6, 10, 16, -11],\n [10, 12, 11, 3, 2, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}176{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[-17, -8, 11, -16, -10, -16, 2],\n [-8, 6, 8, -3, -10, 12, -6],\n [11, 8, 1, -16, 8, 6, -2],\n [-16, -3, -16, -6, 4, 4, -12],\n [-10, -10, 8, 4, 2, 0, -2],\n [-16, 12, 6, 4, 0, 15, 8],\n [2, -6, -2, -12, -2, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}177{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, 2, -16, -1, 5, -9, 8],\n [-7, -12, -2, -18, 7, -4, 14],\n [18, 12, 16, -18, -11, -7, 0],\n [6, 13, -7, -6, 9, -18, -13],\n [-11, -15, -14, 6, 3, 9, 4],\n [-15, -15, 2, 18, -17, -12, -3],\n [-2, 1, 4, 15, -8, 15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}178{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[7, -17, 4, 3, 15, -4, -9],\n [0, 10, 4, -2, -10, 17, -10],\n [0, 0, 14, 12, -13, -9, -3],\n [0, 0, 0, -3, 10, -13, 7],\n [0, 0, 0, 0, -9, -18, 7],\n [0, 0, 0, 0, 0, 9, -12],\n [0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1841", "dataset": "MATH"}179{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[3, -4, 6, -17, 0, -7, 6],\n [-4, -1, 8, -6, -2, -14, 12],\n [6, 8, 7, 2, 12, -2, -10],\n [-17, -6, 2, 3, -12, -15, -6],\n [0, -2, 12, -12, -3, 2, -6],\n [-7, -14, -2, -15, 2, 16, 3],\n [6, 12, -10, -6, -6, 3, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}180{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -10, -4, 11, 6, 2, 1],\n [-10, -15, -1, -5, -3, 2, 0],\n [-4, -1, 14, -2, 2, 0, -6],\n [11, -5, -2, 14, 3, 4, 4],\n [6, -3, 2, 3, -1, 10, 6],\n [2, 2, 0, 4, 10, 5, -2],\n [1, 0, -6, 4, 6, -2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}181{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -9, 18, 7, -2, -18, 6],\n [0, -9, 1, -12, -3, 18, 10],\n [0, 0, 1, 7, 0, -7, 2],\n [0, 0, 0, -4, -18, 7, 16],\n [0, 0, 0, 0, -4, 5, 2],\n [0, 0, 0, 0, 0, -15, 3],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}182{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-14, -6, 8, 4, 3, -8, 3],\n [-6, 9, 0, -4, 14, 13, -2],\n [8, 0, -11, 6, -8, 5, -2],\n [4, -4, 6, 18, -1, -8, -4],\n [3, 14, -8, -1, -10, 16, -11],\n [-8, 13, 5, -8, 16, 15, -2],\n [3, -2, -2, -4, -11, -2, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1614", "dataset": "MATH"}183{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, -1, 2, 2, -8, 11, 7],\n [-1, -14, 2, -12, 10, -14, -4],\n [2, 2, -7, -7, -6, -5, 7],\n [2, -12, -7, -1, 6, 6, -7],\n [-8, 10, -6, 6, 8, 10, -4],\n [11, -14, -5, 6, 10, 0, -4],\n [7, -4, 7, -7, -4, -4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}184{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 1, 4, -8, 0, 8, 9],\n [1, 7, 4, 6, -8, -1, 0],\n [4, 4, -3, 0, -11, -2, 2],\n [-8, 6, 0, -13, 12, 0, 1],\n [0, -8, -11, 12, 2, -14, 7],\n [8, -1, -2, 0, -14, 3, -1],\n [9, 0, 2, 1, 7, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-76279", "dataset": "MATH"}185{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -8, 8, 5, 16, -11, -1],\n [0, 5, 4, -7, 11, 12, 9],\n [0, 0, -6, 6, -12, -13, 5],\n [0, 0, 0, -10, 17, 10, 5],\n [0, 0, 0, 0, -13, -12, 18],\n [0, 0, 0, 0, 0, 4, 8],\n [0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6193", "dataset": "MATH"}186{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 1) rounded to the nearest integer?\n[[-5, 13, 7, -13, 17, -14, -6],\n [13, -3, -18, -6, -8, -11, 6],\n [13, 5, 9, -5, -16, 17, 8],\n [1, -4, 8, 9, 6, 14, -5],\n [-11, -5, -18, -3, -1, -12, -4],\n [5, -6, -10, -4, 16, 5, 14],\n [-3, -11, 10, 4, 12, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}187{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (6, 1) of the inverse. Round your answer to the nearest integer:\n[[8, -3, -13, 14, -1, -3, -7],\n [0, 10, 11, 7, 3, 14, 10],\n [0, 0, -10, 5, -4, 17, -6],\n [0, 0, 0, -11, 18, -5, -7],\n [0, 0, 0, 0, -18, 15, -15],\n [0, 0, 0, 0, 0, -16, -4],\n [0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}188{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 5, -2, 2, -8, -12, -14],\n [0, -1, 16, 1, -4, -14, -6],\n [0, 0, 18, -13, -12, 7, -11],\n [0, 0, 0, 2, 12, 2, 6],\n [0, 0, 0, 0, -5, -15, 1],\n [0, 0, 0, 0, 0, -14, 11],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5981", "dataset": "MATH"}189{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, -4, -2, -6, -7, -8, -4],\n [-4, -15, -3, -6, 6, 4, -14],\n [-2, -3, -14, -12, 9, 4, 6],\n [-6, -6, -12, 2, -3, -2, -2],\n [-7, 6, 9, -3, -1, 2, -16],\n [-8, 4, 4, -2, 2, 15, -14],\n [-4, -14, 6, -2, -16, -14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "323", "dataset": "MATH"}190{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[12, -12, 4, -18, -1, 6, -8],\n [-12, 7, 9, -5, 7, 12, 0],\n [4, 9, 3, -2, -6, 6, 9],\n [-18, -5, -2, -5, -14, 0, 12],\n [-1, 7, -6, -14, 9, -4, -8],\n [6, 12, 6, 0, -4, -11, 0],\n [-8, 0, 9, 12, -8, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}191{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[8, -4, -8, 7, 5, -6, 13],\n [18, -15, -6, -10, 15, 18, -12],\n [-18, -7, 2, -8, -5, 15, 15],\n [6, -15, 7, -3, -9, -17, 16],\n [0, -13, 0, -11, -5, -9, -16],\n [10, -4, 4, 4, -1, 0, 9],\n [7, -9, -15, -17, -16, -12, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}192{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[12, 4, -1, 12, 0, 1, 2],\n [4, 4, 5, 4, -4, 4, 7],\n [-1, 5, 0, 0, 5, 0, 6],\n [12, 4, 0, -7, -16, 9, 0],\n [0, -4, 5, -16, -12, -10, -2],\n [1, 4, 0, 9, -10, 3, 8],\n [2, 7, 6, 0, -2, 8, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632", "dataset": "MATH"}193{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, 12, -1, 10, 0, -11, -2],\n [12, 18, 9, 4, -6, 0, -2],\n [-1, 9, 14, 2, -8, -2, 11],\n [10, 4, 2, 8, -12, 0, -14],\n [0, -6, -8, -12, -5, 12, -16],\n [-11, 0, -2, 0, 12, 4, -10],\n [-2, -2, 11, -14, -16, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-442", "dataset": "MATH"}194{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, 1, 4, -6, 1, 10, 2],\n [1, 17, 9, 2, -1, 4, 14],\n [4, 9, 7, -4, 0, -4, 16],\n [-6, 2, -4, -2, 4, 6, -6],\n [1, -1, 0, 4, -14, -10, -4],\n [10, 4, -4, 6, -10, 4, 7],\n [2, 14, 16, -6, -4, 7, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-93", "dataset": "MATH"}195{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 6, -16, -2, 6, -7, 12],\n [6, 0, 1, -8, -6, -4, -6],\n [-16, 1, -3, 1, 4, -8, 8],\n [-2, -8, 1, 14, 3, 4, -6],\n [6, -6, 4, 3, 3, 0, 0],\n [-7, -4, -8, 4, 0, -13, 8],\n [12, -6, 8, -6, 0, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "740", "dataset": "MATH"}196{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -3, -13, 6, -4, -15, -15],\n [0, 15, 8, 12, 13, -10, -11],\n [0, 0, 4, 2, -7, -17, -6],\n [0, 0, 0, 11, 10, -11, -7],\n [0, 0, 0, 0, 12, -2, 6],\n [0, 0, 0, 0, 0, 12, 18],\n [0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474", "dataset": "MATH"}197{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -6, 17, 15, -13, -11, -11],\n [14, 15, -4, 17, 16, 3, 4],\n [3, -14, 12, -6, 9, 1, 14],\n [-3, 10, 4, 5, 15, -12, 18],\n [-15, 15, 3, -14, 4, -4, 12],\n [-10, 6, 6, 2, -10, 3, 4],\n [-15, 10, -4, -18, 11, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}198{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, 17, 3, -6, -12, -11, 9],\n [0, 6, -3, -9, -8, 12, -7],\n [0, 0, 13, -2, 16, -18, 10],\n [0, 0, 0, -3, -7, 2, -2],\n [0, 0, 0, 0, -7, -4, 15],\n [0, 0, 0, 0, 0, 4, 14],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3271", "dataset": "MATH"}199{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-13, -13, 14, 11, 16, 4, -9],\n [0, 9, 4, -15, 1, 0, 8],\n [15, -15, -12, -12, 7, 7, 0],\n [-10, 1, -3, -2, 3, -6, -7],\n [-9, -18, 13, 11, -11, 2, 3],\n [-1, -17, -10, -16, 7, 2, 11],\n [9, 17, 7, 15, -11, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}200{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -2, -1, 13, 4, 4, 16],\n [0, 5, 9, -3, -3, -13, -17],\n [0, 0, 15, -2, 8, 10, 18],\n [0, 0, 0, 15, -7, 4, -4],\n [0, 0, 0, 0, 16, -18, -14],\n [0, 0, 0, 0, 0, -1, 2],\n [0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3387", "dataset": "MATH"}201{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[15, -13, 9, 12, 16, 4, -13],\n [0, -17, 5, -2, -18, -13, -14],\n [0, 0, -16, -18, 8, 5, 0],\n [0, 0, 0, 11, 13, -18, -6],\n [0, 0, 0, 0, -2, -2, -15],\n [0, 0, 0, 0, 0, 7, 10],\n [0, 0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}202{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[-16, 12, 18, -17, -17, 15, 1],\n [14, -15, -8, -14, 6, 18, 15],\n [-10, -13, -1, -5, 0, -5, -2],\n [16, 10, -2, -11, -18, 17, -12],\n [-14, 5, 9, -2, 18, 1, -16],\n [18, 7, -4, -11, -6, -16, -18],\n [-10, 12, 7, -2, 15, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}203{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-14, -6, -18, 6, -15, 17, -9],\n [9, -13, 8, -7, -16, 14, -9],\n [12, -4, -12, 17, -5, -5, -16],\n [-16, 3, 0, 16, -7, -14, -9],\n [14, -6, 16, 13, -8, 5, 16],\n [0, -13, 16, -15, 14, -6, 17],\n [0, -7, -8, -13, -7, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}204{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-11, -14, -12, -3, -5, 18, -15],\n [0, -2, 17, -13, -3, 10, 17],\n [0, 0, 17, 10, -5, -15, 17],\n [0, 0, 0, 2, -3, -4, -14],\n [0, 0, 0, 0, 14, 17, 14],\n [0, 0, 0, 0, 0, 18, 13],\n [0, 0, 0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "214", "dataset": "MATH"}205{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[18, 13, -8, -18, 6, 5, -2],\n [0, 8, -1, 8, 3, -3, -17],\n [0, 0, -16, 8, -2, -3, -13],\n [0, 0, 0, 14, 8, 10, 18],\n [0, 0, 0, 0, -17, -13, -15],\n [0, 0, 0, 0, 0, 8, 17],\n [0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-76", "dataset": "MATH"}206{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -10, 3, -11, 8, 0, 6],\n [0, 5, 5, 0, -17, -5, 13],\n [0, 0, -6, -7, -11, -4, 7],\n [0, 0, 0, 17, 8, -10, -18],\n [0, 0, 0, 0, -11, -3, -16],\n [0, 0, 0, 0, 0, 4, 8],\n [0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1581", "dataset": "MATH"}207{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -16, 9, -2, 12, -9, 3],\n [0, 2, 17, 4, -7, 6, 1],\n [0, 0, 10, -6, -16, -17, -3],\n [0, 0, 0, -14, -12, 15, 13],\n [0, 0, 0, 0, 2, 9, 1],\n [0, 0, 0, 0, 0, 3, 18],\n [0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10435", "dataset": "MATH"}208{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, 7, -5, 17, -11, 3, 3],\n [0, 8, -9, 6, 12, 2, 8],\n [0, 0, 12, 7, 2, 17, -18],\n [0, 0, 0, -15, -10, 11, -15],\n [0, 0, 0, 0, 18, -11, 14],\n [0, 0, 0, 0, 0, -10, -1],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}209{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[4, -2, -12, -3, 17, 1, 5],\n [0, -13, 9, -14, -17, 2, 18],\n [0, 0, -2, 18, -4, -12, -5],\n [0, 0, 0, 12, -6, -1, -2],\n [0, 0, 0, 0, 10, 15, -2],\n [0, 0, 0, 0, 0, -7, 9],\n [0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3398", "dataset": "MATH"}210{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[14, -8, -10, -5, -10, -16, 10],\n [0, 17, 13, -12, 9, -1, -14],\n [0, 0, 7, -7, 0, -18, -16],\n [0, 0, 0, -17, -14, 10, 14],\n [0, 0, 0, 0, -4, 1, -11],\n [0, 0, 0, 0, 0, 7, 14],\n [0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-141", "dataset": "MATH"}211{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (6, 3) of the inverse. Round your answer to the nearest integer:\n[[-17, -18, 12, -3, 3, -1, -2],\n [11, -9, 16, 2, -3, -13, -16],\n [2, -6, -1, 5, 8, -15, 3],\n [5, -9, -17, -13, -1, -2, 4],\n [11, 2, -9, -6, -7, -10, -15],\n [5, 15, -14, -4, -15, -11, 5],\n [9, 8, -18, 15, -2, 18, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}212{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[5, 9, 14, -11, 12, -7, 14],\n [9, 0, -11, -6, -2, 0, -6],\n [14, -11, -4, -16, -8, 7, -8],\n [-11, -6, -16, -6, -8, 2, -2],\n [12, -2, -8, -8, 4, -2, -10],\n [-7, 0, 7, 2, -2, 18, 4],\n [14, -6, -8, -2, -10, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}213{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-16, -16, -2, 2, -4, -4, 6],\n [-16, 5, 2, -2, 10, 4, -6],\n [-2, 2, 0, 2, 2, -11, -6],\n [2, -2, 2, -17, 2, 8, -2],\n [-4, 10, 2, 2, -2, -4, 0],\n [-4, 4, -11, 8, -4, -1, 14],\n [6, -6, -6, -2, 0, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-110", "dataset": "MATH"}214{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, -3, 4, 18, -10, -16, -11],\n [0, -7, 12, 6, -3, -5, -6],\n [0, 0, 18, -15, -17, 16, -16],\n [0, 0, 0, -9, -18, -2, -3],\n [0, 0, 0, 0, -4, -17, -8],\n [0, 0, 0, 0, 0, 16, -11],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9584", "dataset": "MATH"}215{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[-2, 18, -10, 1, 9, 1, 17],\n [8, -11, 13, -18, -2, -10, 1],\n [13, -17, 13, -10, 11, 1, -18],\n [-14, 16, 17, -18, -5, -10, 11],\n [5, -15, -5, 6, -15, 6, -9],\n [16, -12, -6, -15, 17, -5, -1],\n [-11, 13, 8, 18, 4, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}216{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[6, -3, 2, -6, 7, -7, 4],\n [-3, -9, -8, 7, -2, 6, -9],\n [2, -8, -17, -5, 1, -6, -12],\n [-6, 7, -5, -18, -10, -2, 0],\n [7, -2, 1, -10, -2, -2, 3],\n [-7, 6, -6, -2, -2, -4, 10],\n [4, -9, -12, 0, 3, 10, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}217{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-13, 0, 6, -11, 6, -2, -8],\n [0, 9, 2, 6, 10, 6, -5],\n [6, 2, 6, 4, 2, 6, 7],\n [-11, 6, 4, 15, 4, -8, -4],\n [6, 10, 2, 4, -7, -4, 8],\n [-2, 6, 6, -8, -4, -6, 0],\n [-8, -5, 7, -4, 8, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1685", "dataset": "MATH"}218{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 6, -6, 2, 9, 10, 7],\n [6, -3, -6, 8, 12, 13, 4],\n [-6, -6, -4, 5, 4, 4, 10],\n [2, 8, 5, 9, 7, -10, 3],\n [9, 12, 4, 7, 4, 0, -2],\n [10, 13, 4, -10, 0, -2, -6],\n [7, 4, 10, 3, -2, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}219{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 6) rounded to the nearest integer?\n[[15, 9, -9, 10, 12, 10, 0],\n [9, 1, 0, -13, -4, 11, 0],\n [-9, 0, -13, -12, -8, 2, 12],\n [10, -13, -12, -8, 3, -16, 4],\n [12, -4, -8, 3, 16, 10, 10],\n [10, 11, 2, -16, 10, 1, 10],\n [0, 0, 12, 4, 10, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}220{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[10, 0, -6, -2, 3, 10, 16],\n [0, 17, 8, -8, 0, -2, 10],\n [-6, 8, 0, 0, 0, -2, -16],\n [-2, -8, 0, -8, 10, -2, 8],\n [3, 0, 0, 10, -11, -9, -2],\n [10, -2, -2, -2, -9, 8, 6],\n [16, 10, -16, 8, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-896", "dataset": "MATH"}221{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, -1, -7, 8, -2, 0, 0],\n [-1, 7, 4, 3, -6, 8, -2],\n [-7, 4, -6, 8, -12, 6, -2],\n [8, 3, 8, 15, 4, 0, -14],\n [-2, -6, -12, 4, -4, -12, 0],\n [0, 8, 6, 0, -12, 16, 8],\n [0, -2, -2, -14, 0, 8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1894", "dataset": "MATH"}222{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[8, -12, -16, 14, -17, -3, 6],\n [-4, 5, -4, 12, -5, -5, -13],\n [-5, -2, -1, 1, -2, -3, 13],\n [-10, 8, 14, -9, -2, 17, -2],\n [-1, 4, 15, -11, -6, 4, 1],\n [3, 4, 16, -16, 15, 14, -2],\n [0, 11, 4, -4, -5, -17, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}223{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-13, 5, 0, 10, 1, -16, 8],\n [5, 3, 6, -6, 2, 6, -8],\n [0, 6, 17, -14, 6, 2, -1],\n [10, -6, -14, 7, -6, -8, 1],\n [1, 2, 6, -6, 13, 6, 2],\n [-16, 6, 2, -8, 6, -11, 0],\n [8, -8, -1, 1, 2, 0, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3876", "dataset": "MATH"}224{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -1, -7, 0, 3, -4, -18],\n [0, -11, 3, 6, -17, -10, -10],\n [0, 0, 11, -4, -4, -12, -8],\n [0, 0, 0, -12, -15, 16, 17],\n [0, 0, 0, 0, 2, -18, 17],\n [0, 0, 0, 0, 0, 4, 16],\n [0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6050", "dataset": "MATH"}225{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, -12, -17, 11, -6, 4, 10],\n [18, 1, 14, 10, -4, 4, -16],\n [18, 10, -11, 3, 10, -17, -18],\n [1, 2, 18, -11, 8, 16, -13],\n [0, -1, -18, 6, 8, -12, 10],\n [12, 17, 0, -13, 6, 12, -10],\n [1, -9, 18, 8, -6, -17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1733", "dataset": "MATH"}226{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 2) rounded to the nearest integer?\n[[14, -2, -2, -8, -4, 4, 4],\n [-2, -2, 4, 2, -2, -2, 2],\n [-2, 4, -13, 5, 12, 12, -4],\n [-8, 2, 5, 8, 4, -6, -14],\n [-4, -2, 12, 4, 2, -6, 6],\n [4, -2, 12, -6, -6, -6, 12],\n [4, 2, -4, -14, 6, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}227{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, -8, 12, -13, -8, -6, -7],\n [0, 16, 17, -2, 9, 9, 3],\n [0, 0, 13, -8, 5, -16, 11],\n [0, 0, 0, -1, 12, -6, 7],\n [0, 0, 0, 0, 5, 15, -11],\n [0, 0, 0, 0, 0, -3, 7],\n [0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3528", "dataset": "MATH"}228{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-6, 5, 11, -17, 0, 6, -5],\n [-13, -7, 1, 4, 11, 11, 11],\n [11, 17, 15, -3, 5, -5, 7],\n [-11, -5, 12, -17, -15, -18, 1],\n [-5, 6, 6, -16, -14, 7, -15],\n [-12, 11, 11, 0, 16, 14, 14],\n [-5, -9, 9, -5, 17, -3, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}229{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 14, -13, -4, -16, 16, -5],\n [-17, 10, -15, 7, -7, -17, -2],\n [16, -9, 3, 2, -4, 16, 2],\n [2, 2, 13, -14, -10, -1, 2],\n [-11, 15, -9, 5, 5, 13, 14],\n [15, -8, 12, -1, 4, 3, -1],\n [1, -6, -18, -15, 5, 17, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}230{"messages": [{"content": "Find the value at position (3, 4) of the inverse of matrix 1/252 * A where A =\n[[-17, -2, -4, -2, 6, 12, 4],\n [-2, 16, 1, 14, -6, 0, 2],\n [-4, 1, -15, 16, 5, 7, 0],\n [-2, 14, 16, 3, -9, 6, 6],\n [6, -6, 5, -9, 15, -8, 1],\n [12, 0, 7, 6, -8, 6, 7],\n [4, 2, 0, 6, 1, 7, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325", "dataset": "MATH"}231{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[15, 6, 5, -5, 2, 8, 0],\n [6, -10, 2, -4, 2, 16, -14],\n [5, 2, -5, 0, 0, -9, 6],\n [-5, -4, 0, 14, -9, 9, -12],\n [2, 2, 0, -9, 7, -2, 3],\n [8, 16, -9, 9, -2, 15, 2],\n [0, -14, 6, -12, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51", "dataset": "MATH"}232{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[6, -2, -1, -10, 6, -13, -12],\n [-2, -13, -3, 0, 10, -2, -6],\n [-1, -3, -8, 5, 6, -6, 8],\n [-10, 0, 5, 11, 0, -8, 0],\n [6, 10, 6, 0, -1, 1, 0],\n [-13, -2, -6, -8, 1, 2, 6],\n [-12, -6, 8, 0, 0, 6, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}233{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 8, 15, 14, 9, 12, 13],\n [1, 16, 12, 12, 3, -10, -10],\n [-4, -6, 3, -3, 13, -17, 7],\n [-5, 15, -11, 17, 2, 9, -13],\n [1, 12, 14, -12, -11, -10, -17],\n [-2, 18, -2, 16, 11, -13, -15],\n [18, 16, -10, -13, -6, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-117", "dataset": "MATH"}234{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 6, -4, 11, -8, -11, 0],\n [6, -4, 6, 12, 10, -4, -4],\n [-4, 6, 8, 4, 4, 10, -2],\n [11, 12, 4, -1, 6, 10, -16],\n [-8, 10, 4, 6, -3, -3, 2],\n [-11, -4, 10, 10, -3, -1, 2],\n [0, -4, -2, -16, 2, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}235{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[17, -18, 10, -18, -11, -3, 9],\n [3, -1, 3, -7, 0, 6, -14],\n [15, -9, -12, 18, -4, 5, 7],\n [7, 7, -9, -2, -5, -17, -6],\n [8, -10, -12, -9, -10, 3, 4],\n [-12, -10, 8, 5, 10, -2, 1],\n [-12, -12, 9, 0, 1, -12, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "326", "dataset": "MATH"}236{"messages": [{"content": "Find the value at position (7, 5) of the inverse of matrix 1/252 * A where A =\n[[6, -4, 8, -9, 10, 5, -8],\n [-4, 5, -4, -18, 2, 0, -12],\n [8, -4, 9, 2, -4, 12, 9],\n [-9, -18, 2, -12, -4, -8, 3],\n [10, 2, -4, -4, 7, -4, -7],\n [5, 0, 12, -8, -4, 13, 2],\n [-8, -12, 9, 3, -7, 2, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}237{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[9, 8, -18, 14, -15, -12, -10],\n [-3, -14, 15, 4, 6, -6, 5],\n [-8, -2, 18, -6, 8, 1, 14],\n [13, -11, 10, 0, -13, 2, 3],\n [-9, -9, 10, -3, -18, -2, 11],\n [7, 0, 2, -2, 2, 0, -12],\n [-2, -18, 18, -13, 7, -17, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301", "dataset": "MATH"}238{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 18, 12, -7, 16, 11, -13],\n [-4, -4, -3, 1, -6, 12, 15],\n [10, -16, -10, -8, -8, 6, 3],\n [-10, 1, 2, -9, 3, 10, -10],\n [-14, -8, -18, -18, -14, 3, 7],\n [-13, 13, -8, -9, 15, 12, -7],\n [-3, -16, -17, -14, -8, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}239{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, 8, 10, -1, -9, 14, 6],\n [8, -11, -4, 8, -14, -10, -14],\n [10, -4, -3, 2, 0, -1, -6],\n [-1, 8, 2, -16, 2, -8, -11],\n [-9, -14, 0, 2, 2, 4, -8],\n [14, -10, -1, -8, 4, 3, 6],\n [6, -14, -6, -11, -8, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}240{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 4, -4, 2, 4, -14, 7],\n [4, -4, -1, 0, 3, -4, -1],\n [-4, -1, -9, 4, -8, -8, 14],\n [2, 0, 4, -3, 0, -6, -4],\n [4, 3, -8, 0, -16, 5, 0],\n [-14, -4, -8, -6, 5, 16, 6],\n [7, -1, 14, -4, 0, 6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-309", "dataset": "MATH"}241{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 5, 17, 13, 17, 9, -5],\n [0, -13, -10, 2, -7, 11, 12],\n [0, 0, 8, 6, -14, -13, -14],\n [0, 0, 0, -4, 17, -12, 13],\n [0, 0, 0, 0, -13, 0, 9],\n [0, 0, 0, 0, 0, -9, 4],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-140", "dataset": "MATH"}242{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-4, -9, 2, 10, 13, -9, -6],\n [0, 4, 12, -15, -16, 2, -17],\n [0, 0, -4, 14, -13, -12, 0],\n [0, 0, 0, -7, 3, -6, 9],\n [0, 0, 0, 0, 8, 15, 18],\n [0, 0, 0, 0, 0, -1, 10],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1612", "dataset": "MATH"}243{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[4, -14, 15, 5, -2, 12, -12],\n [-2, 9, 3, -4, 18, -4, 6],\n [2, -17, 8, 13, 2, -15, 0],\n [-17, 7, 15, -5, -4, 1, 15],\n [17, 0, -10, -12, 11, -6, 8],\n [16, -6, -4, -10, 4, 17, -16],\n [15, 0, 9, 4, -12, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}244{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -10, 6, -2, -12, 2, -12],\n [-10, -3, -2, 10, -10, 14, -16],\n [6, -2, 10, -10, -7, -7, 1],\n [-2, 10, -10, -9, 10, 5, -10],\n [-12, -10, -7, 10, 13, 0, 0],\n [2, 14, -7, 5, 0, 2, -16],\n [-12, -16, 1, -10, 0, -16, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}245{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, -8, -16, -13, -13, 1, 2],\n [-17, 7, 12, 7, 13, -9, 4],\n [-13, 4, 9, 11, -5, 18, 13],\n [15, 3, 12, -12, 2, -3, 1],\n [0, 13, -4, -14, -8, -4, 10],\n [-15, 17, 4, -4, -16, 13, -9],\n [3, -5, -2, 2, -4, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}246{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[5, -7, -9, 12, -8, -3, -10],\n [-5, 0, 12, -10, 17, 7, -11],\n [5, -11, 0, 11, 3, -10, -15],\n [18, -11, -18, 9, -13, 17, -8],\n [-14, 5, -1, 1, 9, -6, -14],\n [11, -18, 3, -1, -14, 12, -13],\n [8, 6, 10, 9, -3, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}247{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 0, -4, -5, -2, 1, 2],\n [0, -2, 4, 7, 2, 9, -6],\n [-4, 4, 10, -6, 0, 0, -2],\n [-5, 7, -6, 18, -2, -7, 7],\n [-2, 2, 0, -2, -14, -4, 6],\n [1, 9, 0, -7, -4, 8, -16],\n [2, -6, -2, 7, 6, -16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-670", "dataset": "MATH"}248{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[13, -11, -14, 11, -11, 0, 11],\n [-4, 17, 8, -6, -5, 18, 11],\n [-6, -3, -12, 8, 16, -4, 9],\n [16, -12, 1, 13, 13, 7, 1],\n [-1, -4, 3, 3, 2, -17, -1],\n [4, -6, -10, -12, -18, -17, -15],\n [-5, 13, 17, -17, -5, 1, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "573", "dataset": "MATH"}249{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, 9, 2, 4, 13, -11, 12],\n [18, -3, 8, -1, 16, -4, 8],\n [-2, -17, 12, 18, 15, 15, -16],\n [-2, -5, -5, 16, -18, 10, -15],\n [14, -2, 9, 7, -11, 15, -1],\n [12, 8, -3, -9, -7, 3, -3],\n [-7, -8, 1, -18, 8, -16, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}250{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -10, 18, -18, -15, -4, 8],\n [0, 4, -4, 8, 12, -11, 11],\n [0, 0, 3, -16, -4, 16, 14],\n [0, 0, 0, -11, -3, -9, 18],\n [0, 0, 0, 0, -5, 16, 10],\n [0, 0, 0, 0, 0, -9, -1],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "379", "dataset": "MATH"}251{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, 12, -17, 0, -7, -9, 12],\n [0, 4, 4, -4, 7, -16, 4],\n [0, 0, -1, -13, 8, 17, -4],\n [0, 0, 0, -12, 1, -9, 7],\n [0, 0, 0, 0, -2, 5, 8],\n [0, 0, 0, 0, 0, -16, -4],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2390", "dataset": "MATH"}252{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, -4, 6, 1, -4, 2, 4],\n [-4, -18, -9, 2, 7, 14, 7],\n [6, -9, 15, -5, 1, 0, 9],\n [1, 2, -5, -16, -7, 12, 0],\n [-4, 7, 1, -7, 18, -6, -3],\n [2, 14, 0, 12, -6, 12, 13],\n [4, 7, 9, 0, -3, 13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}253{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[4, 2, -6, -9, -2, 3, 0],\n [2, -4, -5, 7, -1, 4, -2],\n [-6, -5, 17, 12, 0, -6, 12],\n [-9, 7, 12, 8, -4, 7, 8],\n [-2, -1, 0, -4, -9, -2, 8],\n [3, 4, -6, 7, -2, -18, -10],\n [0, -2, 12, 8, 8, -10, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}254{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[10, -16, -12, 17, 10, 18, 17],\n [4, -3, 12, 15, -18, -1, -4],\n [-2, -9, 1, -13, -11, 15, 13],\n [-15, 1, 5, 5, 7, 6, 17],\n [-12, -9, -7, -18, 6, -3, -14],\n [0, -15, -13, 7, -10, -5, -10],\n [-4, 18, 1, -11, 13, 2, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}255{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 12, -13, -15, 10, -16, -18],\n [0, 2, 12, -12, -2, 0, -16],\n [0, 0, 10, -5, 16, 9, 11],\n [0, 0, 0, -14, 16, -5, 17],\n [0, 0, 0, 0, -11, -4, -14],\n [0, 0, 0, 0, 0, -13, -3],\n [0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}256{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 3, 12, -16, 11, 2, 16],\n [-13, 9, 13, 18, 6, 13, 16],\n [3, 5, 11, 13, 12, 4, 14],\n [6, 17, 5, 12, -6, -9, 4],\n [-1, 13, 14, 17, 9, -3, -3],\n [-1, -11, -3, -8, -13, -18, -7],\n [9, -2, -18, 13, -11, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "603", "dataset": "MATH"}257{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, 17, 6, -9, 0, -4, -3],\n [-17, 10, -15, 10, 12, -2, -9],\n [8, -4, 12, 2, 7, 17, -2],\n [-16, -5, -6, 8, -18, -2, 15],\n [-5, -2, -16, 15, 6, -17, 15],\n [7, 12, -10, 11, 1, 2, 10],\n [6, 6, -10, 7, 18, -3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}258{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-7, 8, 12, 8, 2, -2, -2],\n [8, 0, -6, -1, 12, 2, -2],\n [12, -6, 3, -12, 10, 5, 9],\n [8, -1, -12, -1, 1, -2, 12],\n [2, 12, 10, 1, 9, 5, 0],\n [-2, 2, 5, -2, 5, 10, 10],\n [-2, -2, 9, 12, 0, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}259{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-1, 8, 12, 8, -18, -13, -8],\n [15, 1, 2, 2, -1, 2, 0],\n [-15, -6, -1, 10, 6, -6, 8],\n [0, -18, 0, -18, -2, 2, 3],\n [-4, 13, -15, 13, -15, -18, 14],\n [-12, -10, -18, -3, -1, -13, -17],\n [-10, -15, 4, -11, 6, -3, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}260{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, -1, 8, -4, -2, -14, -3],\n [0, 15, 0, -11, -9, -14, 7],\n [0, 0, -6, -10, 1, 9, 18],\n [0, 0, 0, 11, -10, -2, 17],\n [0, 0, 0, 0, 14, 13, -8],\n [0, 0, 0, 0, 0, 9, 11],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "422", "dataset": "MATH"}261{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[10, 17, 16, -13, 4, -11, -17],\n [0, 2, 12, 17, 8, 17, 4],\n [0, 0, 18, 7, -12, 3, 4],\n [0, 0, 0, -9, 11, 7, -12],\n [0, 0, 0, 0, -6, 6, -11],\n [0, 0, 0, 0, 0, 1, -4],\n [0, 0, 0, 0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38423", "dataset": "MATH"}262{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -6, 5, -5, 9, -8, -13],\n [0, -18, 6, -17, 13, -6, 14],\n [0, 0, 8, -15, 5, 4, 10],\n [0, 0, 0, 7, 1, -3, -16],\n [0, 0, 0, 0, 14, -4, -2],\n [0, 0, 0, 0, 0, -12, -10],\n [0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}263{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 0, -4, -2, 13, 0, 0],\n [0, 2, 0, -8, -6, -6, 2],\n [-4, 0, -8, -1, -8, 16, -6],\n [-2, -8, -1, 3, 18, 8, -9],\n [13, -6, -8, 18, -1, 7, 12],\n [0, -6, 16, 8, 7, -15, 5],\n [0, 2, -6, -9, 12, 5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}264{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[6, -2, 13, 5, -12, -6, 8],\n [0, 17, 7, 12, -9, 7, 3],\n [0, 0, 8, 14, 1, -6, -5],\n [0, 0, 0, -3, 16, 15, -16],\n [0, 0, 0, 0, 13, 12, -17],\n [0, 0, 0, 0, 0, 4, 14],\n [0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2295", "dataset": "MATH"}265{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[12, 6, -15, -8, -2, -17, -13],\n [-10, -14, 1, 10, 2, -10, 9],\n [-11, 12, 1, 8, -11, 2, 9],\n [4, -13, -16, -14, -10, -12, -15],\n [-14, -8, -4, 15, -6, -12, -13],\n [11, 3, 6, 9, 1, -16, -14],\n [-18, -4, 7, -16, 15, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}266{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-6, -18, 3, -4, 7, -1, -10],\n [-18, -10, 4, -17, -5, -1, -3],\n [10, -8, -13, -16, -5, -17, 13],\n [12, -8, 3, -16, 12, 14, 5],\n [-18, -4, 18, 8, 8, -7, -16],\n [11, 13, 4, -17, -12, 15, 13],\n [13, -5, -16, 13, 17, -2, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}267{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, 8, 0, -5, 3, -10, 14],\n [8, 7, -4, -4, 6, 0, -6],\n [0, -4, 16, 2, -4, -1, -12],\n [-5, -4, 2, -13, 2, -7, -10],\n [3, 6, -4, 2, -10, 5, -8],\n [-10, 0, -1, -7, 5, 9, 8],\n [14, -6, -12, -10, -8, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}268{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-17, -11, 14, 9, -9, -18, 15],\n [0, -10, -14, -9, -7, -1, 2],\n [0, 0, -16, -14, 6, -11, -2],\n [0, 0, 0, 2, -12, -12, 8],\n [0, 0, 0, 0, -17, -12, -1],\n [0, 0, 0, 0, 0, -5, 17],\n [0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}269{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 4) rounded to the nearest integer?\n[[7, -17, -12, -13, 6, 8, 12],\n [-17, 0, -15, 14, -5, 13, -7],\n [-12, -15, -13, 8, 2, -10, -2],\n [-13, 14, 8, 18, 2, 0, 5],\n [6, -5, 2, 2, 4, -13, -6],\n [8, 13, -10, 0, -13, -10, -11],\n [12, -7, -2, 5, -6, -11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}270{"messages": [{"content": "Find the value at position (1, 4) of the inverse of matrix 1/252 * A where A =\n[[-18, -16, -2, -11, -2, 6, -7],\n [10, 6, 17, 6, 10, -8, -15],\n [-5, -2, -17, -11, 17, -9, -12],\n [17, -3, -5, -3, 6, -15, 10],\n [-13, -18, -18, -16, -18, -18, 2],\n [11, 13, 14, 3, 11, -15, 4],\n [6, -7, -2, -4, -9, 16, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}271{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 1, 13, -15, -14, -11, 3],\n [0, 3, 11, 18, -3, -4, -14],\n [0, 0, -9, -14, 4, -4, -1],\n [0, 0, 0, 2, -17, 3, -11],\n [0, 0, 0, 0, 11, 0, 4],\n [0, 0, 0, 0, 0, 14, -12],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "305", "dataset": "MATH"}272{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 4, 0, -18, 14, 14, 13],\n [9, 18, -7, -10, -8, 14, 0],\n [15, -12, 12, -17, 0, 13, -9],\n [-11, 7, 11, -8, 1, 1, -10],\n [-11, -4, 15, 5, 14, 8, 2],\n [-14, 16, 2, -15, -3, 12, 7],\n [16, -13, 14, 2, -3, 15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2225", "dataset": "MATH"}273{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, -17, 5, 9, -18, -18, 9],\n [0, 1, -11, -18, 7, 6, -9],\n [0, 0, -7, -2, -14, -5, 15],\n [0, 0, 0, 17, -4, 0, -14],\n [0, 0, 0, 0, -7, 17, -7],\n [0, 0, 0, 0, 0, -14, 6],\n [0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220", "dataset": "MATH"}274{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, 5, 5, -12, 2, 1, -9],\n [6, 17, -4, -13, 18, -17, -7],\n [-15, 4, -6, -2, 12, -3, 7],\n [9, -18, -7, 18, 1, -17, 17],\n [-4, 3, 13, 1, 17, 14, -4],\n [-16, 10, 8, -14, 12, 3, 16],\n [-12, -13, 7, -18, 0, -12, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}275{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-7, 0, 0, 2, -3, 8, 8],\n [0, 0, -6, -17, -2, -8, 4],\n [0, -6, -1, 4, -1, 5, 10],\n [2, -17, 4, -17, 16, -4, -11],\n [-3, -2, -1, 16, 1, -6, -2],\n [8, -8, 5, -4, -6, -3, 8],\n [8, 4, 10, -11, -2, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1878", "dataset": "MATH"}276{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, -15, 14, -5, 0, -14, 17],\n [0, -1, 12, 11, 2, 11, -15],\n [0, 0, 8, -3, 11, -6, 17],\n [0, 0, 0, 1, -14, 13, -13],\n [0, 0, 0, 0, 10, -14, 6],\n [0, 0, 0, 0, 0, -10, 2],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38471", "dataset": "MATH"}277{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, 4, 2, -1, -2, -6, -8],\n [4, -5, 0, -3, -10, -6, -8],\n [2, 0, 0, 6, 12, 10, -6],\n [-1, -3, 6, 7, 2, -10, 12],\n [-2, -10, 12, 2, -11, 4, -16],\n [-6, -6, 10, -10, 4, 7, -8],\n [-8, -8, -6, 12, -16, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}278{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, -4, 2, 2, 8, 7, 4],\n [-4, 8, -12, -2, -4, -8, 4],\n [2, -12, 10, -8, -6, 3, 0],\n [2, -2, -8, 16, 4, 17, -2],\n [8, -4, -6, 4, 18, 9, -4],\n [7, -8, 3, 17, 9, 11, -10],\n [4, 4, 0, -2, -4, -10, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-99", "dataset": "MATH"}279{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, -11, 13, -5, -6, 2, 5],\n [-1, 7, 13, 14, 12, -1, 16],\n [-7, 6, 12, -9, 15, -16, -11],\n [13, 10, 3, 1, -13, 10, -2],\n [12, 15, 18, -15, -17, -7, 16],\n [-13, -11, 2, 16, -4, -12, -4],\n [-13, -2, -15, 3, 13, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}280{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-4, 3, 9, -10, 15, 17, -10],\n [0, 1, -11, 9, 0, -3, -8],\n [0, 0, -9, -1, 16, -16, 8],\n [0, 0, 0, -12, -9, -4, 12],\n [0, 0, 0, 0, 7, -7, 6],\n [0, 0, 0, 0, 0, 7, -2],\n [0, 0, 0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1092", "dataset": "MATH"}281{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[13, 4, 15, 0, -17, -17, -4],\n [0, 16, -14, 8, 5, -12, -13],\n [0, 0, 11, -11, -12, -13, -15],\n [0, 0, 0, 6, 14, 16, -14],\n [0, 0, 0, 0, 10, -11, 15],\n [0, 0, 0, 0, 0, -14, 13],\n [0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-106", "dataset": "MATH"}282{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, 4, -16, 5, -2, 12, -3],\n [4, 4, 2, 11, -8, 0, 4],\n [-16, 2, 2, -16, -5, -4, 4],\n [5, 11, -16, -13, -3, 3, 16],\n [-2, -8, -5, -3, -12, -6, 2],\n [12, 0, -4, 3, -6, 5, 14],\n [-3, 4, 4, 16, 2, 14, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}283{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, -8, -2, -2, -10, 14, -4],\n [-8, 1, 4, -3, -16, -14, 8],\n [-2, 4, -16, 2, -14, 2, 4],\n [-2, -3, 2, 0, 1, -16, -3],\n [-10, -16, -14, 1, -1, -10, 5],\n [14, -14, 2, -16, -10, 12, 0],\n [-4, 8, 4, -3, 5, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}284{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 1) rounded to the nearest integer?\n[[8, 8, -1, 8, 10, -8, -17],\n [8, 8, 10, -6, 2, 10, -4],\n [-1, 10, -18, -7, -12, -1, -4],\n [8, -6, -7, -11, 6, 2, -6],\n [10, 2, -12, 6, -9, -10, 7],\n [-8, 10, -1, 2, -10, 9, 14],\n [-17, -4, -4, -6, 7, 14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}285{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 1, -6, -11, -5, -1, 0],\n [1, -11, -4, 1, -1, 0, -2],\n [-6, -4, 7, 13, 4, 10, -2],\n [-11, 1, 13, -14, 2, -7, 10],\n [-5, -1, 4, 2, 5, -8, 0],\n [-1, 0, 10, -7, -8, -11, -1],\n [0, -2, -2, 10, 0, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-281", "dataset": "MATH"}286{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[17, -13, 13, 2, -12, 7, -4],\n [0, -4, -3, 13, 18, -1, 1],\n [0, 0, 11, -16, -18, 3, 10],\n [0, 0, 0, 13, -13, -18, 2],\n [0, 0, 0, 0, 15, 0, 1],\n [0, 0, 0, 0, 0, -4, 16],\n [0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}287{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[15, 0, 5, -15, 17, -6, 13],\n [0, -3, -16, 1, -9, 3, -16],\n [0, 0, -11, -10, -4, 13, -16],\n [0, 0, 0, 2, 0, 3, 1],\n [0, 0, 0, 0, 1, -1, -8],\n [0, 0, 0, 0, 0, -9, -18],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4945", "dataset": "MATH"}288{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, -15, 4, -8, -10, 11, -11],\n [-14, -7, -18, -4, 6, -1, 7],\n [-16, 3, 7, 0, 17, 2, 7],\n [-6, 17, 5, 7, 2, -1, -4],\n [-4, -13, 12, 9, -11, 10, 2],\n [-2, 5, 17, 12, 15, -17, -16],\n [11, -11, -12, -7, 0, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}289{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-4, 2, -11, -10, 2, 2, -4],\n [2, -5, 0, 7, 2, -1, 16],\n [-11, 0, 10, -17, -16, -11, -8],\n [-10, 7, -17, 16, -4, 6, -11],\n [2, 2, -16, -4, -18, -9, -8],\n [2, -1, -11, 6, -9, 4, 7],\n [-4, 16, -8, -11, -8, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}290{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -1, 5, 4, -7, 4, 2],\n [7, -11, 11, 15, -17, -14, 12],\n [14, -15, -13, 4, 0, -11, -6],\n [-18, -13, -12, 8, -4, 15, 4],\n [5, -4, 16, -15, 18, -2, 12],\n [-9, 8, -13, -13, -4, -15, -12],\n [7, 12, -17, 9, -6, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-132", "dataset": "MATH"}291{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, -6, 5, 10, -14, 16, 0],\n [0, -14, -5, 3, -10, 7, -14],\n [0, 0, -16, 9, -5, -5, -8],\n [0, 0, 0, 6, -3, -4, 15],\n [0, 0, 0, 0, -2, -18, -12],\n [0, 0, 0, 0, 0, 1, 7],\n [0, 0, 0, 0, 0, 0, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11047", "dataset": "MATH"}292{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, -7, -4, 9, 12, -10, -11],\n [0, -11, 15, -15, 12, -16, 16],\n [0, 0, -9, -7, 11, 11, -1],\n [0, 0, 0, 5, 7, -16, 4],\n [0, 0, 0, 0, 10, -6, 7],\n [0, 0, 0, 0, 0, -11, -6],\n [0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1772", "dataset": "MATH"}293{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -11, -3, 2, -9, 6, 3],\n [-15, -15, 11, -17, 10, 17, 2],\n [2, 2, -15, -18, 7, -17, -10],\n [-1, -8, 6, 7, 17, 16, -16],\n [16, 3, -11, -4, -12, 0, -2],\n [-18, 10, -6, 10, -13, -14, 15],\n [-8, -10, -10, -11, -16, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475", "dataset": "MATH"}294{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, -2, -8, 18, 4, 0, 5],\n [-2, -6, -2, 4, 14, -10, -4],\n [-8, -2, -1, -12, -2, -2, 2],\n [18, 4, -12, 1, -8, 2, 0],\n [4, 14, -2, -8, -11, 2, 3],\n [0, -10, -2, 2, 2, 18, -1],\n [5, -4, 2, 0, 3, -1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}295{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[12, -3, -8, 14, -10, -10, 4],\n [-3, -9, 4, -4, 6, -10, 4],\n [-8, 4, -15, 12, -18, 0, -6],\n [14, -4, 12, 17, -14, 11, -8],\n [-10, 6, -18, -14, 7, -8, 0],\n [-10, -10, 0, 11, -8, -6, -10],\n [4, 4, -6, -8, 0, -10, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-72", "dataset": "MATH"}296{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 6, 8, 8, 3, 12, -2],\n [6, -10, 2, 4, 0, 2, -8],\n [8, 2, 2, 6, -2, -1, -4],\n [8, 4, 6, -6, 5, 2, -4],\n [3, 0, -2, 5, -11, 7, 0],\n [12, 2, -1, 2, 7, -1, 12],\n [-2, -8, -4, -4, 0, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}297{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 12, 6, -9, 5, -18, 6],\n [9, 17, -1, -13, -17, -16, -11],\n [12, 0, -13, -5, -16, -18, 11],\n [0, 0, -10, -12, 18, -12, -10],\n [-15, 6, -7, -13, -1, 2, -4],\n [-16, -17, -15, 13, -17, 10, -17],\n [15, 8, -1, 17, 0, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}298{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -4, 1, 0, -1, -4, 0],\n [-4, 0, -1, 2, -8, -3, -10],\n [1, -1, -10, 12, 8, 6, 9],\n [0, 2, 12, 17, 4, 14, 4],\n [-1, -8, 8, 4, 3, -4, 3],\n [-4, -3, 6, 14, -4, -18, 0],\n [0, -10, 9, 4, 3, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}299{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, 3, 8, 18, 13, 0, 9],\n [9, -9, 1, 6, 2, -5, 3],\n [7, -8, -12, -2, -1, -12, 1],\n [-8, -3, 8, -8, -3, 4, -7],\n [-16, -17, 5, 10, 15, 1, -1],\n [-5, -1, -17, -18, 1, 15, -8],\n [8, 4, -16, -7, 11, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838", "dataset": "MATH"}300{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 7) of the inverse. Round your answer to the nearest integer:\n[[-18, -4, -8, -3, 16, -5, 11],\n [-4, 10, -3, -9, 0, 2, 10],\n [-8, -3, 2, -4, -5, 4, -9],\n [-3, -9, -4, -7, 1, -5, 2],\n [16, 0, -5, 1, -12, -10, 2],\n [-5, 2, 4, -5, -10, -16, -4],\n [11, 10, -9, 2, 2, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}301{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, -6, -2, 14, -10, 2, -4],\n [-6, 15, -4, 4, -2, 2, -4],\n [-2, -4, 13, 14, -9, -8, 4],\n [14, 4, 14, 4, 12, 0, -2],\n [-10, -2, -9, 12, 7, -4, 0],\n [2, 2, -8, 0, -4, -10, -10],\n [-4, -4, 4, -2, 0, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}302{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -17, -8, -2, 15, 0, -1],\n [-6, -14, 4, 5, 10, -11, 7],\n [-4, -18, 9, -5, 15, 12, -13],\n [-14, 12, 18, -4, -4, -14, 9],\n [14, -8, -13, 4, -17, -4, 4],\n [3, -10, 11, -3, 11, -10, -18],\n [-11, -1, 8, -1, 13, 13, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}303{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[17, 4, 12, 3, 14, -10, 0],\n [4, 6, 10, 6, -1, -6, -8],\n [12, 10, -17, 2, 2, 4, 15],\n [3, 6, 2, 13, 2, 4, -4],\n [14, -1, 2, 2, 15, -7, 12],\n [-10, -6, 4, 4, -7, 15, -8],\n [0, -8, 15, -4, 12, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706", "dataset": "MATH"}304{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -6, 0, 1, -3, -2, 10],\n [-6, -2, 2, 10, -8, 7, 5],\n [0, 2, 5, -10, 5, 11, 8],\n [1, 10, -10, 2, 0, 9, -2],\n [-3, -8, 5, 0, -6, -4, -16],\n [-2, 7, 11, 9, -4, -7, -14],\n [10, 5, 8, -2, -16, -14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}305{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[14, 1, 14, 16, 15, 17, 8],\n [0, -14, 10, -9, -6, 10, -14],\n [0, 0, 3, -4, -6, -18, -18],\n [0, 0, 0, -13, 9, 12, -11],\n [0, 0, 0, 0, 1, -5, -5],\n [0, 0, 0, 0, 0, 17, 15],\n [0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4372", "dataset": "MATH"}306{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-14, 5, 10, 10, 7, -16, -17],\n [6, 0, -17, 0, -18, 8, 16],\n [-14, -15, -2, 2, 12, 3, -8],\n [15, -4, -9, 13, 12, 18, 9],\n [12, -13, -5, 4, -3, 6, -17],\n [15, 6, 17, -3, -1, -6, 18],\n [8, 15, -8, -18, -6, 11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235", "dataset": "MATH"}307{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, -4, -3, 7, -14, -1, -4],\n [-4, 12, 5, 10, 3, 2, 14],\n [-3, 5, 2, 6, -4, -2, 4],\n [7, 10, 6, -7, 10, 14, 2],\n [-14, 3, -4, 10, -14, -14, -5],\n [-1, 2, -2, 14, -14, -1, 6],\n [-4, 14, 4, 2, -5, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}308{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 6, 10, 10, 9, 2, -12],\n [6, -12, -8, -7, -12, -2, -2],\n [10, -8, 17, -14, -6, -16, 6],\n [10, -7, -14, -7, -2, -1, 6],\n [9, -12, -6, -2, -6, -2, 14],\n [2, -2, -16, -1, -2, -5, 4],\n [-12, -2, 6, 6, 14, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525", "dataset": "MATH"}309{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-14, 0, 9, 7, 4, 11, -16],\n [9, 14, -16, -14, 0, -18, -10],\n [-14, 15, 18, 14, 6, 10, 6],\n [-10, -16, -4, -15, 1, 4, 18],\n [-11, 18, 14, 14, -12, 3, -14],\n [-4, 2, 6, -2, -12, 0, -12],\n [5, -8, -18, 13, -17, -4, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5503", "dataset": "MATH"}310{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[5, -2, -10, 16, 1, 0, -1],\n [1, 11, -18, 5, 5, 0, 11],\n [7, 10, -6, -15, -2, 14, -14],\n [9, 5, -2, -8, -7, -6, -11],\n [-18, -10, 9, -17, -5, -6, -17],\n [-15, -7, -9, -16, -15, -13, 4],\n [-14, -16, -9, 0, -5, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}311{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, 17, 5, -2, 3, 0, -9],\n [0, -17, 14, 12, 16, 18, 17],\n [0, 0, 7, 6, -2, -4, 18],\n [0, 0, 0, 3, -2, -5, -5],\n [0, 0, 0, 0, 11, 3, -3],\n [0, 0, 0, 0, 0, -13, -15],\n [0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2547", "dataset": "MATH"}312{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, -10, 16, -11, -12, -15, -6],\n [0, -12, -9, 6, 16, 6, 10],\n [0, 0, -13, -9, -17, 6, -12],\n [0, 0, 0, 4, -12, 8, -6],\n [0, 0, 0, 0, -6, -7, -12],\n [0, 0, 0, 0, 0, -18, 5],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3045", "dataset": "MATH"}313{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 16, 4, 4, 7, -18, -5],\n [0, -9, -18, -14, -16, 8, 3],\n [0, 0, -17, -6, -3, -11, -11],\n [0, 0, 0, -7, -10, 18, -10],\n [0, 0, 0, 0, -8, 1, 0],\n [0, 0, 0, 0, 0, 15, 10],\n [0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777", "dataset": "MATH"}314{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[8, 8, -2, -4, -17, -12, 4],\n [8, -11, 12, -4, 6, 9, 9],\n [-2, 12, 5, -5, 0, 15, 14],\n [-4, -4, -5, -12, -2, 14, 6],\n [-17, 6, 0, -2, -7, 7, -8],\n [-12, 9, 15, 14, 7, 13, 5],\n [4, 9, 14, 6, -8, 5, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}315{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[18, -10, 0, -12, -14, 5, -12],\n [0, -10, 11, -16, 3, 1, 13],\n [0, 0, 1, 6, 16, 5, -6],\n [0, 0, 0, -18, -2, -17, -13],\n [0, 0, 0, 0, -3, -7, 10],\n [0, 0, 0, 0, 0, 3, -9],\n [0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10199", "dataset": "MATH"}316{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[4, 2, 5, 9, -6, -7, 0],\n [2, 11, 9, 7, 4, -13, -4],\n [5, 9, -16, -10, -5, 8, -1],\n [9, 7, -10, -13, -3, -3, -1],\n [-6, 4, -5, -3, -10, -6, 4],\n [-7, -13, 8, -3, -6, 11, 8],\n [0, -4, -1, -1, 4, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}317{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[13, -18, 15, -10, -7, -9, -9],\n [0, -13, 5, 5, 2, 12, 11],\n [0, 0, -7, 16, -12, 6, -13],\n [0, 0, 0, 10, 9, 3, -11],\n [0, 0, 0, 0, -1, -1, -6],\n [0, 0, 0, 0, 0, -2, 13],\n [0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2052", "dataset": "MATH"}318{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 16, -4, -11, 1, 2, -18],\n [10, 5, 11, 16, 14, 1, -3],\n [-10, 12, -2, 12, 4, -13, 11],\n [-12, -8, 15, -7, 8, -7, -6],\n [-11, -3, 10, 16, 10, 12, -6],\n [-7, -17, 14, -11, 13, 9, -4],\n [4, 5, -6, 2, -7, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}319{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, -5, -2, 5, 15, 3, -9],\n [0, 2, 18, -12, 7, -6, -3],\n [0, 0, -14, 13, -3, -10, 3],\n [0, 0, 0, 1, -4, 7, -10],\n [0, 0, 0, 0, -9, 14, -3],\n [0, 0, 0, 0, 0, -1, 9],\n [0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2702", "dataset": "MATH"}320{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[7, -8, -18, -8, 5, -9, -5],\n [-5, -12, 4, 3, 17, 8, -17],\n [0, -12, -7, -16, -14, -11, -5],\n [17, -12, -12, 13, -11, -7, -9],\n [-5, -10, 11, -14, -18, -18, 1],\n [-8, 7, -16, -13, -8, -11, 10],\n [-9, 15, 5, -2, 13, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-159", "dataset": "MATH"}321{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -14, 10, 15, -3, 6, 18],\n [-11, 10, 6, 4, 15, -16, 11],\n [15, 13, 10, -10, -17, -12, -14],\n [-11, 13, -1, -1, -3, 2, -9],\n [-15, -11, 0, -10, 11, -2, -4],\n [-15, -13, -3, 7, 18, 4, -6],\n [-2, 8, 3, 18, 0, 16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}322{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 12, -17, 18, -5, -10, -9],\n [-12, 9, 6, 9, -17, -2, -15],\n [-6, -1, -16, 18, 14, 5, -11],\n [16, -17, 14, -7, 3, -6, -9],\n [-2, -14, -10, -6, 4, 11, -15],\n [2, -10, -12, -3, 4, 4, 12],\n [-14, -13, -18, 9, -1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}323{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[14, -2, -2, 18, 6, 7, -4],\n [-2, -5, -6, 0, 10, 13, -4],\n [-2, -6, 9, -4, -4, -8, -8],\n [18, 0, -4, 7, -4, 1, -14],\n [6, 10, -4, -4, 17, -11, 8],\n [7, 13, -8, 1, -11, -17, -1],\n [-4, -4, -8, -14, 8, -1, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}324{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, 1, 6, -6, 8, 0, 2],\n [1, -5, 0, 8, -1, 11, 0],\n [6, 0, -1, 2, 4, -3, 9],\n [-6, 8, 2, -2, 2, -4, 9],\n [8, -1, 4, 2, 1, -12, -10],\n [0, 11, -3, -4, -12, -10, 4],\n [2, 0, 9, 9, -10, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936", "dataset": "MATH"}325{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, 13, -10, -5, -6, 14, 13],\n [0, 11, -3, -7, -9, -17, -1],\n [0, 0, 5, -7, 10, 3, 17],\n [0, 0, 0, 14, -15, 11, 1],\n [0, 0, 0, 0, 10, 4, 15],\n [0, 0, 0, 0, 0, -6, 5],\n [0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-504", "dataset": "MATH"}326{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 3, 11, 11, -3, -8, 3],\n [10, 6, -5, -5, -17, -6, -16],\n [11, -1, 17, 2, 0, -3, 9],\n [-15, -4, -18, -3, 1, 14, -2],\n [-14, -14, -6, 17, 11, -15, 4],\n [2, 2, -13, 5, 12, 0, -7],\n [-5, -7, -4, 0, 9, -14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}327{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 4, -16, 18, 14, 2, 1],\n [0, -2, 10, -11, 7, 9, 15],\n [0, 0, 18, -6, 6, 4, 3],\n [0, 0, 0, -15, 14, -7, -10],\n [0, 0, 0, 0, -12, -11, 14],\n [0, 0, 0, 0, 0, -18, 8],\n [0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}328{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[3, 5, 4, 11, 0, -6, 6],\n [5, -16, 4, 4, 9, -2, -3],\n [4, 4, 17, -10, -2, 4, 0],\n [11, 4, -10, 4, 6, -2, 2],\n [0, 9, -2, 6, -13, -14, 12],\n [-6, -2, 4, -2, -14, -14, -10],\n [6, -3, 0, 2, 12, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}329{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[14, 0, -17, -8, 16, -2, -16],\n [0, 16, 2, 6, -17, -18, -12],\n [0, 0, 17, 2, 16, 17, -11],\n [0, 0, 0, -12, -17, -18, -18],\n [0, 0, 0, 0, 9, -1, 5],\n [0, 0, 0, 0, 0, 14, -12],\n [0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}330{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[17, 2, 11, -7, -5, 12, 8],\n [2, 5, -6, 9, -6, 2, -6],\n [11, -6, -16, 0, -6, -1, 16],\n [-7, 9, 0, 5, 0, 8, 0],\n [-5, -6, -6, 0, 8, -10, 4],\n [12, 2, -1, 8, -10, 10, -1],\n [8, -6, 16, 0, 4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}331{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-16, 3, 8, 0, 12, -10, -5],\n [3, -10, 8, -6, -8, -1, -4],\n [8, 8, 16, 14, -8, 10, 13],\n [0, -6, 14, -11, -10, -8, 10],\n [12, -8, -8, -10, -17, 6, -8],\n [-10, -1, 10, -8, 6, -14, -6],\n [-5, -4, 13, 10, -8, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}332{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[-7, -8, -9, -8, 10, 4, 8],\n [-8, 11, -6, -8, -6, -1, 11],\n [-9, -6, -15, -2, 8, -3, 0],\n [-8, -8, -2, -14, 2, 0, 12],\n [10, -6, 8, 2, -12, 0, -6],\n [4, -1, -3, 0, 0, 11, 4],\n [8, 11, 0, 12, -6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}333{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, -15, 12, 10, 17, -6, -10],\n [0, -16, 6, 6, -7, 10, -8],\n [0, 0, -5, -3, -9, 12, 12],\n [0, 0, 0, 1, -10, -4, -10],\n [0, 0, 0, 0, 1, -5, 3],\n [0, 0, 0, 0, 0, 13, 1],\n [0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416", "dataset": "MATH"}334{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -3, 12, -10, -4, 3, 0],\n [-3, -2, 6, 16, 5, -3, 10],\n [12, 6, 15, -3, 1, -4, -3],\n [-10, 16, -3, 1, 6, 1, -6],\n [-4, 5, 1, 6, -5, 3, 9],\n [3, -3, -4, 1, 3, -4, 2],\n [0, 10, -3, -6, 9, 2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1034", "dataset": "MATH"}335{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 2, 2, 0, 9, 12, 4],\n [2, -18, -6, 7, -14, -10, 0],\n [2, -6, -18, 0, -9, 0, -2],\n [0, 7, 0, 6, -1, -3, 1],\n [9, -14, -9, -1, -14, 14, 8],\n [12, -10, 0, -3, 14, 14, 6],\n [4, 0, -2, 1, 8, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}336{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/252 * A where A =\n[[5, 4, 0, -2, -1, 3, 1],\n [4, 12, 8, -9, -3, 4, -12],\n [0, 8, 6, -6, 15, -6, 2],\n [-2, -9, -6, -16, 0, -6, 4],\n [-1, -3, 15, 0, -15, -6, -10],\n [3, 4, -6, -6, -6, 5, 4],\n [1, -12, 2, 4, -10, 4, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}337{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, -18, -11, -16, -5, -2, 15],\n [0, -14, 10, 16, -1, 11, -4],\n [0, 0, 14, -9, 0, 18, -16],\n [0, 0, 0, 14, 9, 13, -3],\n [0, 0, 0, 0, -7, 3, 18],\n [0, 0, 0, 0, 0, -1, -6],\n [0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-271", "dataset": "MATH"}338{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[14, -17, -8, -9, 14, -12, -4],\n [0, -8, 8, -12, -18, -9, 2],\n [0, 0, 11, -11, 5, 0, -16],\n [0, 0, 0, -1, 0, 11, -6],\n [0, 0, 0, 0, -15, 17, -5],\n [0, 0, 0, 0, 0, 2, -11],\n [0, 0, 0, 0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13734", "dataset": "MATH"}339{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 6) of the inverse. Round your answer to the nearest integer:\n[[15, 10, -16, -9, 1, -17, 8],\n [13, -9, -2, 14, -13, -1, -10],\n [-11, 6, 12, -15, 1, 9, -18],\n [4, -6, -3, 7, 12, -18, -2],\n [-3, 18, -9, 12, -9, 15, -13],\n [9, 9, -6, -7, -17, -11, -10],\n [-11, -16, -10, -6, -10, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}340{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-11, 12, 12, -2, 0, -16, 11],\n [0, 10, -1, -7, 4, -8, -10],\n [0, 0, 6, -10, -7, -8, 9],\n [0, 0, 0, 17, -10, -11, -16],\n [0, 0, 0, 0, 9, -4, 0],\n [0, 0, 0, 0, 0, 18, -8],\n [0, 0, 0, 0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370", "dataset": "MATH"}341{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 1, 9, 4, 16, -18, 10],\n [-10, -10, 3, -17, -3, -13, -6],\n [14, 0, -4, 14, -9, -18, -7],\n [10, -2, -15, 10, -12, -6, -14],\n [-13, 15, -12, 9, -9, -15, -16],\n [6, 4, 8, -5, 13, 4, 18],\n [-16, 16, -6, 15, 5, -18, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}342{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-11, 0, -10, 9, -5, 8, -1],\n [0, 14, 18, 6, -6, 4, 17],\n [0, 0, 15, 17, -2, -9, 4],\n [0, 0, 0, -17, 0, -3, 6],\n [0, 0, 0, 0, 11, -9, 0],\n [0, 0, 0, 0, 0, 2, 10],\n [0, 0, 0, 0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1488", "dataset": "MATH"}343{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 9, 17, -9, 16, 16, 18],\n [0, -6, -8, 0, 9, -15, 18],\n [0, 0, -5, 12, 9, 17, 0],\n [0, 0, 0, -15, -1, 6, -1],\n [0, 0, 0, 0, 16, -18, -14],\n [0, 0, 0, 0, 0, -15, 10],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7195", "dataset": "MATH"}344{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[6, 1, 12, 11, -3, -17, -2],\n [0, -12, -10, -2, -10, -10, 18],\n [0, 0, -11, 6, -17, -9, 5],\n [0, 0, 0, -8, -13, -13, 13],\n [0, 0, 0, 0, -16, 15, -7],\n [0, 0, 0, 0, 0, -1, 8],\n [0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4911", "dataset": "MATH"}345{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-13, 4, 0, -12, 0, -4, 10],\n [4, -15, -2, -5, -4, 14, -2],\n [0, -2, 15, -6, 0, -3, 0],\n [-12, -5, -6, -16, 12, 10, 2],\n [0, -4, 0, 12, -9, -4, 14],\n [-4, 14, -3, 10, -4, -9, 10],\n [10, -2, 0, 2, 14, 10, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}346{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 1, 16, -4, 5, -3, 17],\n [0, -11, -16, 0, -16, 17, 6],\n [0, 0, -3, -2, 5, -2, 1],\n [0, 0, 0, -5, -8, -7, -14],\n [0, 0, 0, 0, 14, 11, 5],\n [0, 0, 0, 0, 0, 3, -5],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2464", "dataset": "MATH"}347{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, 14, 10, 0, -10, -5, 3],\n [14, -2, -6, -6, -12, 6, 14],\n [10, -6, -11, -13, 4, 8, 4],\n [0, -6, -13, 3, -4, 0, 6],\n [-10, -12, 4, -4, 3, 0, 0],\n [-5, 6, 8, 0, 0, 14, 4],\n [3, 14, 4, 6, 0, 4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}348{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 4, -14, 17, 5, 17, -14],\n [-13, 17, -15, -9, -18, 2, 18],\n [-16, 12, 8, -2, 4, -6, 8],\n [1, -6, 5, -16, -9, -18, -6],\n [-5, 14, -17, -17, 12, -15, 15],\n [0, 18, -10, 5, -6, 11, 0],\n [-9, -5, 1, -15, -14, 13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287", "dataset": "MATH"}349{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-5, -13, -5, -7, 8, 7, -7],\n [0, -9, -3, 7, -11, 10, 1],\n [0, 0, -2, -18, 10, -5, -2],\n [0, 0, 0, 8, 14, 10, 18],\n [0, 0, 0, 0, -14, 5, 15],\n [0, 0, 0, 0, 0, 7, -1],\n [0, 0, 0, 0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-407", "dataset": "MATH"}350{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, -18, 9, 14, -15, 1, 17],\n [12, 9, -16, -13, 4, -12, 17],\n [-18, -13, 5, 18, 17, 5, 10],\n [18, 13, 6, -9, 16, 6, 8],\n [13, -7, -15, 7, -16, -2, -10],\n [10, -18, -1, 1, 15, 9, 16],\n [-3, 2, -6, 16, 13, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}351{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, -12, 14, 8, -14, -7, 10],\n [-12, -15, 10, 6, 5, 10, -7],\n [14, 10, 2, 16, 11, 6, -14],\n [8, 6, 16, -3, -5, 2, 0],\n [-14, 5, 11, -5, -13, 18, 2],\n [-7, 10, 6, 2, 18, 4, -10],\n [10, -7, -14, 0, 2, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-106", "dataset": "MATH"}352{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -6, 4, 7, 6, 2, 6],\n [-6, -16, -17, -16, 12, -14, -16],\n [4, -17, -15, 12, -18, 4, 2],\n [7, -16, 12, 3, 2, 12, 10],\n [6, 12, -18, 2, 6, -8, 5],\n [2, -14, 4, 12, -8, 6, -6],\n [6, -16, 2, 10, 5, -6, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}353{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[9, 15, -3, 17, -12, -1, -13],\n [9, 15, 10, -15, -5, -14, 6],\n [-11, -4, 0, -8, 1, 17, -1],\n [-5, 6, -3, -1, -18, -18, -18],\n [2, 6, 8, -9, -7, 9, 13],\n [14, -11, 7, -17, 16, 15, -13],\n [12, 4, -7, 9, -4, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}354{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-17, -8, 18, 6, 2, 17, -10],\n [-7, -9, -14, 14, -14, -3, 18],\n [18, 10, -1, 10, -13, -1, 13],\n [12, -8, 7, 9, 8, 0, 8],\n [1, -16, -3, 10, -4, 11, -18],\n [10, 11, 13, -9, 8, -11, 17],\n [16, 17, 17, 6, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}355{"messages": [{"content": "Find the value at position (1, 4) of the inverse of matrix 1/252 * A where A =\n[[6, 10, -2, 6, -10, -4, -10],\n [10, 15, 2, 10, -3, -2, 2],\n [-2, 2, -9, 14, 2, 10, 0],\n [6, 10, 14, -2, 4, 6, -4],\n [-10, -3, 2, 4, 11, -5, 0],\n [-4, -2, 10, 6, -5, -1, 2],\n [-10, 2, 0, -4, 0, 2, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}356{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, 6, -15, 13, -4, 7, -8],\n [0, -8, -17, 8, 7, -11, 2],\n [0, 0, -18, -6, -10, 9, -13],\n [0, 0, 0, -10, -7, 3, -7],\n [0, 0, 0, 0, 15, -11, -9],\n [0, 0, 0, 0, 0, -15, -17],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}357{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-17, -4, -11, 7, 16, 2, -11],\n [0, -11, -9, 4, -15, 11, 4],\n [0, 0, -13, -2, 6, 5, 3],\n [0, 0, 0, 15, 7, 0, 7],\n [0, 0, 0, 0, 3, -12, -15],\n [0, 0, 0, 0, 0, 17, 7],\n [0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}358{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[18, 3, 3, 3, -4, -2, 9],\n [0, 2, -2, -14, -1, -2, -15],\n [0, 0, 18, -10, 0, -10, 4],\n [0, 0, 0, -2, 3, 16, 11],\n [0, 0, 0, 0, 13, 6, -6],\n [0, 0, 0, 0, 0, -5, 11],\n [0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13974", "dataset": "MATH"}359{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -8, -10, -13, 15, 18, 13],\n [-7, 13, -2, -15, 14, -10, 15],\n [11, 1, 4, 16, 4, 4, 18],\n [4, 9, 0, 11, 2, 5, 2],\n [7, 17, 7, 14, 17, -15, -10],\n [-11, -17, 10, 4, -13, 17, 2],\n [3, -10, 15, 7, -18, 17, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}360{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[3, -15, -17, -3, -3, 3, -18],\n [0, 5, -15, -1, -2, -12, -9],\n [0, 0, 3, 13, 10, 16, -2],\n [0, 0, 0, 11, 1, -12, -12],\n [0, 0, 0, 0, -17, 14, -8],\n [0, 0, 0, 0, 0, 1, -11],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-128712", "dataset": "MATH"}361{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -14, -17, -6, -1, 7, 6],\n [0, -14, -17, -15, -7, -8, -15],\n [0, 0, 8, -13, -4, 12, 3],\n [0, 0, 0, 2, 11, 2, 17],\n [0, 0, 0, 0, 12, -6, -1],\n [0, 0, 0, 0, 0, -6, 7],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}362{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[13, -4, 12, -13, 6, -1, 3],\n [12, 17, -10, -16, 14, 8, -18],\n [-10, -14, -4, -10, 9, -6, 5],\n [-9, 3, 3, 18, 1, -9, -9],\n [7, 6, 9, -6, -4, -13, -7],\n [0, 13, -8, 14, -17, -4, 17],\n [-14, -4, -9, -2, 15, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "662", "dataset": "MATH"}363{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, -16, 18, -16, -14, 9, -5],\n [-8, -11, 18, -11, -7, -4, 0],\n [9, -12, -12, 11, -1, 5, -13],\n [-15, -16, -13, 7, -8, 10, 1],\n [-9, 7, 8, -5, 17, -7, 4],\n [2, -11, -10, 5, 12, 6, -2],\n [10, -16, 2, -11, -5, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}364{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -8, 1, -15, 1, 12, 1],\n [-8, -18, -1, 14, 17, -1, 12],\n [16, -4, -13, -11, 3, -18, -6],\n [5, 2, -15, -12, -7, -6, -3],\n [-13, -5, 12, 17, 18, 16, -9],\n [-2, 11, -12, -1, 0, -4, 3],\n [11, 1, 13, 6, 4, -14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6720", "dataset": "MATH"}365{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, 18, -12, -14, -4, -11, -10],\n [0, 3, 15, 16, -6, -8, 13],\n [0, 0, 5, 3, -16, -5, -17],\n [0, 0, 0, 6, 15, -8, 18],\n [0, 0, 0, 0, -13, -18, 15],\n [0, 0, 0, 0, 0, 12, -2],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4553", "dataset": "MATH"}366{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[16, 2, 6, 16, -2, -8, 2],\n [2, -16, 4, 6, 6, 8, 5],\n [6, 4, -9, -4, 8, 16, 8],\n [16, 6, -4, -3, 6, 6, 10],\n [-2, 6, 8, 6, -16, -12, -6],\n [-8, 8, 16, 6, -12, -2, 5],\n [2, 5, 8, 10, -6, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-123", "dataset": "MATH"}367{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, 6, 9, 3, 6, -2, -7],\n [0, 18, -3, -2, 12, -4, -6],\n [0, 0, -17, -11, -12, -9, -15],\n [0, 0, 0, -1, 5, 13, 15],\n [0, 0, 0, 0, -4, -7, -2],\n [0, 0, 0, 0, 0, -3, 13],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3838", "dataset": "MATH"}368{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-15, -12, -1, -15, -8, 1, -8],\n [0, -2, 15, -7, 9, 16, -11],\n [0, 0, 5, -17, 12, 3, -18],\n [0, 0, 0, 17, -16, -14, -18],\n [0, 0, 0, 0, -9, 15, -3],\n [0, 0, 0, 0, 0, 11, 16],\n [0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}369{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-3, -8, 3, 17, 4, 7, 12],\n [0, -14, 6, 15, -7, 3, -10],\n [0, 0, 10, 8, -2, -14, -6],\n [0, 0, 0, -17, 4, -6, -15],\n [0, 0, 0, 0, -10, -13, -9],\n [0, 0, 0, 0, 0, -3, 13],\n [0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}370{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 15, -15, -16, -9, 9, 15],\n [0, 17, -16, 4, -2, -12, 7],\n [-1, -13, 12, 10, -10, 16, -2],\n [-7, 17, 5, -9, 11, 10, -9],\n [9, -1, -2, -8, -18, -2, 17],\n [17, -10, 9, 14, -16, -11, -13],\n [-13, 10, 18, -7, -10, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}371{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 16, -4, -6, -6, -5, -6],\n [16, -11, -6, 2, 0, 4, -2],\n [-4, -6, 7, 2, 13, 1, -4],\n [-6, 2, 2, 18, -7, -10, -16],\n [-6, 0, 13, -7, -5, 8, 0],\n [-5, 4, 1, -10, 8, -2, 6],\n [-6, -2, -4, -16, 0, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-89", "dataset": "MATH"}372{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-2, 14, -2, -8, -6, 6, 0],\n [14, -1, 0, 11, 6, 8, 8],\n [-2, 0, -17, 4, 4, 10, 0],\n [-8, 11, 4, 1, 8, -6, -2],\n [-6, 6, 4, 8, -12, -6, -10],\n [6, 8, 10, -6, -6, 1, 6],\n [0, 8, 0, -2, -10, 6, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}373{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, -1, 6, 3, 16, 10, 2],\n [0, -7, 17, 5, 13, 8, 13],\n [0, 0, 7, -8, -1, -14, -3],\n [0, 0, 0, 4, 15, -2, -9],\n [0, 0, 0, 0, 5, -16, -17],\n [0, 0, 0, 0, 0, 12, 15],\n [0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}374{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -8, -6, -5, -1, 3, -2],\n [-8, -4, 3, -10, 4, -14, 6],\n [-6, 3, -4, 4, 4, 1, 6],\n [-5, -10, 4, -15, 0, 14, -8],\n [-1, 4, 4, 0, 13, -2, -2],\n [3, -14, 1, 14, -2, 5, 2],\n [-2, 6, 6, -8, -2, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}375{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[1, -3, 15, -3, -5, 9, -1],\n [7, -12, 15, -12, 14, 16, 2],\n [9, 13, -3, -9, 4, -4, -13],\n [14, -7, 17, 12, -9, 15, -9],\n [-8, -5, -16, 14, -12, -15, -9],\n [-4, -3, -15, -15, 17, 8, 3],\n [3, -2, 15, 13, -13, 14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}376{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[17, -14, -14, -9, -12, -7, 11],\n [0, 9, -6, 3, -1, 8, -11],\n [0, 0, 10, -14, -12, 3, -15],\n [0, 0, 0, -18, -11, 13, 11],\n [0, 0, 0, 0, 14, -6, 6],\n [0, 0, 0, 0, 0, 1, -12],\n [0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2883", "dataset": "MATH"}377{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, 1, 18, -18, -3, 11, -10],\n [-9, -6, 1, 10, -15, 9, 18],\n [-6, -16, 18, 0, 9, 0, -2],\n [-1, -1, 4, -10, 10, 10, -17],\n [-2, 12, 9, 11, 16, 1, -3],\n [15, -5, 7, 1, 5, -1, -10],\n [0, 1, 11, 7, 12, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}378{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -13, -18, 5, 15, -12, -8],\n [-8, 17, 1, -3, -14, 5, 11],\n [11, 18, 14, 1, 3, 2, 18],\n [8, 16, -13, 13, -3, 9, -3],\n [8, -16, 2, 11, 3, 0, 12],\n [1, 0, -17, 8, -11, 8, -4],\n [-7, -5, -12, -2, 7, 18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}379{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -2, 9, -7, 16, 3, -18],\n [0, 2, -18, -15, 13, -18, -6],\n [0, 0, -12, -16, 7, 12, 17],\n [0, 0, 0, -2, 11, -17, -11],\n [0, 0, 0, 0, -4, -17, 18],\n [0, 0, 0, 0, 0, -3, -6],\n [0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91595", "dataset": "MATH"}380{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, 6, -14, -14, 10, -16, -1],\n [6, 18, -2, 1, 0, 8, -6],\n [-14, -2, -16, -13, 2, -2, 2],\n [-14, 1, -13, -15, 6, 0, -4],\n [10, 0, 2, 6, 8, -4, -1],\n [-16, 8, -2, 0, -4, -12, -1],\n [-1, -6, 2, -4, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3951", "dataset": "MATH"}381{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 5, 1, -4, -9, -2, -8],\n [5, -3, -8, 12, 18, 4, 10],\n [1, -8, -6, 5, -7, -2, -2],\n [-4, 12, 5, 3, -8, -10, 4],\n [-9, 18, -7, -8, -12, -16, -16],\n [-2, 4, -2, -10, -16, 10, -14],\n [-8, 10, -2, 4, -16, -14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"}382{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 5, -9, 4, -3, 18, -3],\n [0, -13, 11, 18, -18, 6, 2],\n [0, 0, -7, -14, -10, -10, 16],\n [0, 0, 0, 18, 16, -2, -6],\n [0, 0, 0, 0, -2, -14, -13],\n [0, 0, 0, 0, 0, 8, -16],\n [0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-181", "dataset": "MATH"}383{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -18, -15, -5, -1, 15, -18],\n [3, -3, 3, -3, 9, 9, 3],\n [-13, 6, -17, -12, -2, 16, 1],\n [-17, -12, 13, 0, -7, -10, 8],\n [-5, -17, 2, -15, 2, 3, -17],\n [-2, 0, 5, 1, -7, 6, 4],\n [15, 13, 5, 6, -16, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}384{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 7, -11, -14, -8, 16, 8],\n [0, 13, 9, 17, -1, -9, 13],\n [-1, -7, -11, 14, -5, -17, -10],\n [-14, 15, 0, -12, -2, 7, 8],\n [9, 1, -13, -11, 13, 0, 13],\n [0, 5, 5, -2, -1, -7, 4],\n [-1, -3, -3, 17, 4, 3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}385{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 1, 14, 12, -11, -9, -18],\n [0, 6, 13, -9, -10, 1, 1],\n [0, 0, 2, 0, -4, -13, -9],\n [0, 0, 0, -11, 9, -16, -17],\n [0, 0, 0, 0, -4, 1, 3],\n [0, 0, 0, 0, 0, -15, -3],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131", "dataset": "MATH"}386{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-16, -4, 14, -1, 4, -16, 11],\n [-2, 13, -12, -5, -4, -7, -11],\n [-3, 15, 5, 10, -3, -14, -14],\n [11, -14, -6, 16, 6, -5, 7],\n [-1, 1, 15, -12, -9, -4, -2],\n [-8, 15, 8, 2, 12, -15, -2],\n [1, 6, 4, -4, 14, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}387{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-14, -3, 13, 3, 13, -6, 7],\n [-2, -14, 14, 8, -14, 18, -12],\n [-1, 12, -13, -17, -6, -8, 7],\n [2, -17, 1, -2, -3, -14, -5],\n [5, -15, 5, -10, -16, -10, -1],\n [17, 0, 5, -15, -10, 14, -18],\n [16, -9, -7, -1, -5, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}388{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, 5, -18, 11, -4, -11, 16],\n [0, -3, 2, -4, -14, -12, -12],\n [0, 0, 3, -6, -2, -6, 7],\n [0, 0, 0, -15, 9, 7, -15],\n [0, 0, 0, 0, 16, 6, -11],\n [0, 0, 0, 0, 0, -7, -8],\n [0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2361", "dataset": "MATH"}389{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-2, -11, 4, -9, 4, 10, 4],\n [-11, -13, 1, 14, 5, -2, 2],\n [4, 1, 1, 16, -10, 4, -1],\n [-9, 14, 16, -10, 4, 10, 2],\n [4, 5, -10, 4, -7, -9, 1],\n [10, -2, 4, 10, -9, 14, -6],\n [4, 2, -1, 2, 1, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}390{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[-1, 6, 6, 4, 8, -10, -3],\n [6, -9, 6, 11, 3, 10, -12],\n [6, 6, 6, 7, 6, -5, 0],\n [4, 11, 7, 6, -2, -16, -3],\n [8, 3, 6, -2, 15, 0, 8],\n [-10, 10, -5, -16, 0, -1, -4],\n [-3, -12, 0, -3, 8, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}391{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[1, 7, 13, 5, 12, -7, 17],\n [0, -13, -12, 12, 8, -11, -16],\n [0, 0, -4, -12, -4, 6, -16],\n [0, 0, 0, 17, -16, -14, 6],\n [0, 0, 0, 0, -17, 9, -9],\n [0, 0, 0, 0, 0, -18, 14],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}392{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -13, 14, 9, 11, -2, -10],\n [9, -12, 9, -2, -14, -14, -5],\n [-13, -12, -2, -10, 12, 3, -10],\n [-3, 17, 15, -6, 0, -7, 17],\n [-9, -3, 9, 0, -13, -15, 11],\n [12, 8, 2, 18, -10, 16, 2],\n [-2, 5, 12, -13, 16, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-310", "dataset": "MATH"}393{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, 14, 0, 4, -4, -10, -2],\n [14, 10, 0, 2, 1, 0, 10],\n [0, 0, 0, -6, -12, 16, 7],\n [4, 2, -6, -13, -2, -8, 0],\n [-4, 1, -12, -2, 5, 3, 1],\n [-10, 0, 16, -8, 3, -2, -1],\n [-2, 10, 7, 0, 1, -1, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}394{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, 15, -7, -14, 8, -6, 7],\n [0, 13, -8, -3, 3, -3, -6],\n [0, 0, 10, -1, -17, -17, -16],\n [0, 0, 0, -7, 13, -15, -10],\n [0, 0, 0, 0, -12, -9, 10],\n [0, 0, 0, 0, 0, 3, 4],\n [0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1322", "dataset": "MATH"}395{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 10, 2, 16, -14, -7, -12],\n [-17, 6, -9, -13, 8, 16, -9],\n [-10, 1, 18, 16, 18, -11, 12],\n [-3, 9, -13, 13, 9, -8, 4],\n [11, -10, 9, 5, 9, 5, -4],\n [14, 15, 3, 10, 15, -9, 11],\n [-8, 15, 2, -6, 6, 2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}396{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-14, 3, -12, -6, 4, 2, -13],\n [1, -7, -10, 9, -8, 13, -8],\n [5, -4, 16, -2, 6, 16, 0],\n [12, -2, 4, -18, -9, -11, 7],\n [15, 0, -5, -11, -18, 6, 5],\n [1, 11, -14, -16, 13, -2, -14],\n [-8, -15, 0, 4, -2, -6, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}397{"messages": [{"content": "Find the value at position (5, 6) of the inverse of matrix 1/252 * A where A =\n[[-18, -17, -1, 17, 14, 17, -17],\n [0, -3, -15, -10, 2, 4, -17],\n [0, 0, 7, -12, 17, 14, 17],\n [0, 0, 0, 7, 9, 9, 2],\n [0, 0, 0, 0, 16, -14, -3],\n [0, 0, 0, 0, 0, 5, 5],\n [0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}398{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-14, 2, 6, 6, 4, -4, 1],\n [2, 15, 0, -4, -5, 1, 6],\n [6, 0, -7, 0, 6, 8, -2],\n [6, -4, 0, -14, 1, 0, 2],\n [4, -5, 6, 1, 18, -14, 4],\n [-4, 1, 8, 0, -14, 8, 1],\n [1, 6, -2, 2, 4, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}399{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[3, -13, -8, -5, 17, -17, 1],\n [0, -15, 10, 5, -18, 5, 11],\n [0, 0, 18, -15, -4, 1, 1],\n [0, 0, 0, 5, -16, 10, -11],\n [0, 0, 0, 0, -15, 16, -7],\n [0, 0, 0, 0, 0, 17, -18],\n [0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}400{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 2, -1, 4, 4, 9, 17],\n [0, -12, -1, 1, -14, -1, 14],\n [0, 0, -18, 2, -11, -12, 11],\n [0, 0, 0, -15, 18, 2, -6],\n [0, 0, 0, 0, -7, -17, 0],\n [0, 0, 0, 0, 0, 4, 12],\n [0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-76", "dataset": "MATH"}401{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 6, -7, -4, 12, 8, 6],\n [6, -15, 16, -14, 0, 0, 6],\n [-7, 16, -10, -4, 4, -4, -11],\n [-4, -14, -4, 8, 3, 6, -17],\n [12, 0, 4, 3, 18, 9, 15],\n [8, 0, -4, 6, 9, -6, 3],\n [6, 6, -11, -17, 15, 3, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}402{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, 14, -10, 12, 2, -9, 2],\n [14, -9, -6, 10, 3, 4, 1],\n [-10, -6, 2, 2, 6, -6, 8],\n [12, 10, 2, 10, 9, 0, -1],\n [2, 3, 6, 9, 4, 4, -10],\n [-9, 4, -6, 0, 4, -6, -1],\n [2, 1, 8, -1, -10, -1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174", "dataset": "MATH"}403{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-12, -8, -9, 4, 12, -7, 12],\n [-8, -2, 2, -6, -4, -5, 4],\n [-9, 2, -10, -4, 4, -13, 12],\n [4, -6, -4, 12, 12, -15, -8],\n [12, -4, 4, 12, -11, -10, -4],\n [-7, -5, -13, -15, -10, 16, -4],\n [12, 4, 12, -8, -4, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}404{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-13, -10, 13, 0, 0, 4, 11],\n [-10, 3, -2, 0, -12, -5, 4],\n [13, -2, -12, -2, 0, 2, -4],\n [0, 0, -2, -13, -1, 2, 6],\n [0, -12, 0, -1, -14, -4, -2],\n [4, -5, 2, 2, -4, 9, 15],\n [11, 4, -4, 6, -2, 15, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-139", "dataset": "MATH"}405{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[10, 5, -4, -13, 13, 15, 17],\n [0, -7, 16, -2, 8, -2, -8],\n [0, 0, 10, 5, 5, -3, 12],\n [0, 0, 0, 6, 3, 16, 14],\n [0, 0, 0, 0, -13, -16, -13],\n [0, 0, 0, 0, 0, -18, 18],\n [0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}406{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[6, 12, -5, -12, 5, 17, -16],\n [7, 7, -18, -4, -8, 18, -12],\n [-7, -16, 7, 11, 13, 17, 18],\n [-1, -18, 2, 9, -3, 9, 3],\n [0, -18, 12, 15, -13, 9, -16],\n [12, -3, -2, 8, 5, 1, 13],\n [16, -6, 1, -17, -15, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}407{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, 13, -2, -18, 14, 11, -14],\n [-7, 13, -2, 13, 5, -7, 12],\n [0, 10, 2, 7, 9, -2, -10],\n [2, 15, -8, 1, -3, 10, -18],\n [-1, 3, -11, -12, 6, 11, 15],\n [-8, -4, 16, 4, 2, 9, -6],\n [15, -13, -15, -14, -13, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15285", "dataset": "MATH"}408{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-16, 2, -10, -4, -6, -4, 10],\n [2, 9, -2, -8, -4, -5, -1],\n [-10, -2, 6, 2, 2, -4, 8],\n [-4, -8, 2, -3, -4, 12, -4],\n [-6, -4, 2, -4, 11, -9, 5],\n [-4, -5, -4, 12, -9, -5, -2],\n [10, -1, 8, -4, 5, -2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-147", "dataset": "MATH"}409{"messages": [{"content": "Find the value at position (1, 5) of the inverse of matrix 1/252 * A where A =\n[[-6, -15, 4, -9, -14, -5, 15],\n [9, -11, -3, 12, -12, -16, 10],\n [17, -15, -10, -2, 1, -5, 10],\n [-6, 17, -2, -15, 1, -8, 3],\n [-11, 9, 11, 14, 14, 17, 8],\n [1, 14, 6, 0, 2, 14, -16],\n [-5, -4, 14, 3, -18, 12, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}410{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, 13, -7, -3, -11, -5, -1],\n [0, 14, 15, 15, -12, -13, -13],\n [0, 0, 18, -4, 7, -16, -9],\n [0, 0, 0, -16, -18, 14, 0],\n [0, 0, 0, 0, -7, -6, -3],\n [0, 0, 0, 0, 0, 13, 15],\n [0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}411{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-16, -4, 15, 3, 3, 3, 16],\n [-4, 2, 13, -4, -12, 6, 1],\n [15, 13, 16, -8, -4, -7, 0],\n [3, -4, -8, 6, 0, -7, 5],\n [3, -12, -4, 0, -2, -11, 4],\n [3, 6, -7, -7, -11, -8, -1],\n [16, 1, 0, 5, 4, -1, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}412{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[11, -4, -6, -12, -2, -2, -13],\n [-4, 11, -10, -10, -8, 10, 0],\n [-6, -10, 17, 3, 4, 14, -4],\n [-12, -10, 3, 17, 0, -6, -2],\n [-2, -8, 4, 0, 12, -2, -3],\n [-2, 10, 14, -6, -2, 0, 10],\n [-13, 0, -4, -2, -3, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}413{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[12, -16, 14, 15, 2, 18, 0],\n [0, 2, -5, -9, -12, 10, -11],\n [0, 0, -8, -17, -13, 10, -14],\n [0, 0, 0, -1, 17, -3, -14],\n [0, 0, 0, 0, 12, 1, -2],\n [0, 0, 0, 0, 0, 11, -14],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}414{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[4, 10, 3, 5, -6, 14, 3],\n [16, -2, 3, -14, 6, -13, -2],\n [12, -2, 14, 18, -15, -5, -6],\n [8, 5, 8, -11, 2, -8, 12],\n [8, 8, -11, 14, -7, 16, 15],\n [-3, 17, -17, -7, 8, -2, 1],\n [2, 11, 1, -11, -1, -1, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}415{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-17, -7, 13, -11, -9, -8, -5],\n [0, 11, -15, -8, 5, 3, -16],\n [0, 0, -7, 2, -14, -12, -15],\n [0, 0, 0, -10, 7, -7, -18],\n [0, 0, 0, 0, 10, -5, -10],\n [0, 0, 0, 0, 0, 10, 6],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}416{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 7) rounded to the nearest integer?\n[[-8, 7, -7, 10, -4, 0, -6],\n [7, 2, 8, 10, 12, -6, -2],\n [-7, 8, -4, -8, -18, 6, 4],\n [10, 10, -8, 17, 9, 2, 8],\n [-4, 12, -18, 9, 5, 13, -9],\n [0, -6, 6, 2, 13, -13, 8],\n [-6, -2, 4, 8, -9, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}417{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[13, -12, 4, 4, -1, -12, 5],\n [0, -14, 3, 3, -9, 7, -4],\n [0, 0, 17, 12, 9, 15, 16],\n [0, 0, 0, -4, -18, 6, 7],\n [0, 0, 0, 0, -18, 3, -8],\n [0, 0, 0, 0, 0, -11, 4],\n [0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}418{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, -16, 10, 18, -3, -3, -12],\n [0, -13, -1, 0, -17, -16, 6],\n [0, 0, 9, 13, 17, 17, 4],\n [0, 0, 0, -11, -4, 10, 9],\n [0, 0, 0, 0, -4, -12, 5],\n [0, 0, 0, 0, 0, -8, 2],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-73", "dataset": "MATH"}419{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-16, 4, 4, 8, 16, 6, 13],\n [3, -11, -1, 9, 9, -8, -7],\n [-17, 18, -15, 15, 4, -6, -12],\n [13, 4, -11, 18, 15, 10, 18],\n [4, 10, -14, -8, -5, -17, 16],\n [16, 9, -11, 13, -15, -12, 8],\n [18, -2, -9, -15, 4, -5, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}420{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-17, 2, 0, -2, 10, -2, -2],\n [2, -15, -1, 4, 12, -11, -6],\n [0, -1, 6, -10, 5, 0, 14],\n [-2, 4, -10, 4, -8, 6, 14],\n [10, 12, 5, -8, 1, 16, -2],\n [-2, -11, 0, 6, 16, 3, -4],\n [-2, -6, 14, 14, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163", "dataset": "MATH"}421{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-16, -12, 8, 9, 12, -4, -11],\n [-13, 9, -15, 11, -2, 15, -13],\n [17, 16, -3, -17, -11, -4, 8],\n [-3, -18, -9, -12, -9, -7, -2],\n [-7, -4, 13, 13, 7, -5, 7],\n [-14, -15, 9, -18, -6, -16, 6],\n [-3, 2, -6, 17, -11, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}422{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, 1, -1, -7, 6, -8, 3],\n [15, -6, -7, 17, 9, 8, -6],\n [8, 12, -17, -1, 7, 12, 3],\n [17, 0, -5, -5, 10, -2, 18],\n [-10, -18, -15, -12, -8, -5, 0],\n [-16, -11, 10, 18, -10, 0, -7],\n [8, 18, 6, -2, 14, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914", "dataset": "MATH"}423{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-1, 14, -4, -8, 17, -4, 11],\n [-4, 4, -4, 10, -8, -1, 12],\n [-10, 3, -8, -2, 14, -8, -11],\n [-15, 17, 0, 5, -1, 14, 17],\n [-9, -5, -12, -7, 3, 8, 18],\n [-8, 17, -6, 13, -11, -12, -2],\n [3, 15, 1, -11, 3, 8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}424{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 0, 2, 8, -2, 5, -8],\n [0, 0, -7, 4, -1, -10, 1],\n [2, -7, 12, 0, 5, 9, 4],\n [8, 4, 0, -15, -8, 8, 8],\n [-2, -1, 5, -8, 0, 14, 2],\n [5, -10, 9, 8, 14, 9, -2],\n [-8, 1, 4, 8, 2, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3436", "dataset": "MATH"}425{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-13, 6, -6, -5, 14, 3, -8],\n [6, -15, 16, 0, 8, -4, -3],\n [-6, 16, -13, -4, 6, -6, -5],\n [-5, 0, -4, 11, -8, -5, 0],\n [14, 8, 6, -8, 5, 8, -6],\n [3, -4, -6, -5, 8, 14, 2],\n [-8, -3, -5, 0, -6, 2, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}426{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 6, 1, -2, 17, 7, 0],\n [0, -16, 9, 3, 0, -3, -13],\n [0, 0, 15, 12, -8, 17, -13],\n [0, 0, 0, -11, 14, -4, 8],\n [0, 0, 0, 0, -17, -4, 8],\n [0, 0, 0, 0, 0, -8, -9],\n [0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}427{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 6) of the inverse. Round your answer to the nearest integer:\n[[-12, -12, 17, -12, 1, -1, -5],\n [-5, 2, 8, 7, 8, 5, -14],\n [9, 13, 5, -13, -9, -16, -12],\n [10, 15, -12, -2, -6, 2, 12],\n [-10, -6, -2, -11, -10, -10, 11],\n [-12, -2, -14, -2, -18, -3, -2],\n [11, 12, 16, -11, 11, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}428{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[15, 1, -14, -10, -3, 2, -8],\n [1, -2, 10, -6, 12, -4, 6],\n [-14, 10, 11, -4, -6, 0, -12],\n [-10, -6, -4, 8, 16, 6, 4],\n [-3, 12, -6, 16, -11, 0, -4],\n [2, -4, 0, 6, 0, -7, 2],\n [-8, 6, -12, 4, -4, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}429{"messages": [{"content": "Find the value at position (4, 4) of the inverse of matrix 1/252 * A where A =\n[[-11, -1, 4, -2, -2, -4, -5],\n [-1, 8, 0, -10, 16, -12, 8],\n [4, 0, -2, 1, -6, 0, 6],\n [-2, -10, 1, 10, -11, -4, -15],\n [-2, 16, -6, -11, -10, -8, 9],\n [-4, -12, 0, -4, -8, -14, 0],\n [-5, 8, 6, -15, 9, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}430{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 3) rounded to the nearest integer?\n[[14, -4, -4, 12, 9, -9, -12],\n [14, -12, -14, 7, -3, -11, 3],\n [15, 9, 17, -12, 9, -17, -10],\n [-13, -18, -16, -9, 18, 4, 14],\n [-10, -6, 9, -12, 7, -3, 7],\n [13, 17, -18, 2, -6, 7, -10],\n [18, 4, -18, -17, 9, 17, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}431{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-14, 18, 6, -11, 15, 13, -8],\n [6, -16, 13, 16, 13, 15, 18],\n [-14, 9, 9, -11, 8, -3, -1],\n [6, -18, -11, 2, 15, 5, 18],\n [7, -5, 10, 11, -16, -12, 17],\n [-8, 13, -7, -4, 5, -18, -1],\n [-12, -17, 12, 14, 11, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}432{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, 6, -3, 3, 17, 8, -2],\n [0, 16, 3, 16, -4, 2, -6],\n [0, 0, 12, 13, 11, -1, -3],\n [0, 0, 0, -9, -7, -11, -16],\n [0, 0, 0, 0, 4, -9, -1],\n [0, 0, 0, 0, 0, -12, -15],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}433{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[15, 7, -14, 6, 15, -15, 15],\n [8, 10, -14, -1, -15, -18, 1],\n [-13, 1, 1, 8, 7, 13, -9],\n [-1, -7, -9, 5, 5, 6, -11],\n [-5, 12, 5, -3, 1, -4, -5],\n [-7, 15, -11, 0, -14, 8, -6],\n [13, 12, 18, -17, -12, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}434{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[4, 12, -11, 13, 2, 12, -18],\n [-6, -8, 10, -15, 17, -4, -16],\n [10, 2, -17, -13, 12, 5, -2],\n [-14, -17, -7, -14, 1, -11, -18],\n [-13, -8, -16, 12, 9, -14, 7],\n [-3, 12, 9, -12, -10, 16, 8],\n [-7, 6, 10, 12, 15, 14, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "314", "dataset": "MATH"}435{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-17, -5, -6, 5, -14, 15, 4],\n [0, 11, -3, 15, -8, -5, -4],\n [16, -12, 10, 3, 4, 5, 16],\n [-9, -11, -7, 10, 10, 4, 7],\n [18, 13, -13, -11, -2, -7, 3],\n [-5, 15, 0, -13, -1, 17, 18],\n [-4, -10, -13, -17, -3, -18, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"}436{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, -1, 4, -2, -8, -6, -2],\n [-1, 12, 2, 6, 1, -6, 4],\n [4, 2, 11, -4, 4, 7, 14],\n [-2, 6, -4, 3, 1, -10, -2],\n [-8, 1, 4, 1, 4, -3, 8],\n [-6, -6, 7, -10, -3, 17, 14],\n [-2, 4, 14, -2, 8, 14, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-183", "dataset": "MATH"}437{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -13, -3, 16, 1, -8, 13],\n [-5, 5, 12, -2, 6, -10, 3],\n [16, 18, -2, 9, -18, -10, -6],\n [13, 9, 12, -11, -11, 15, 4],\n [-9, 18, 6, 14, -15, -12, 14],\n [-17, 13, -14, -2, -7, -7, 16],\n [2, 2, -17, 2, -4, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-78", "dataset": "MATH"}438{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, 4, 12, 7, -17, -12, 5],\n [13, 7, 4, -5, 10, 6, 12],\n [-17, -17, 4, -8, 10, 16, -10],\n [13, 11, -4, -5, -2, 3, 11],\n [-2, -3, -11, 12, -7, 14, -7],\n [6, -1, 0, -16, 16, -14, 16],\n [8, 18, 2, -3, 9, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380", "dataset": "MATH"}439{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-2, 11, -15, -17, -10, 12, 6],\n [0, 17, -14, 5, 5, 10, 12],\n [0, 0, 4, 16, -13, -13, 18],\n [0, 0, 0, 9, 6, 14, -5],\n [0, 0, 0, 0, -15, -6, -12],\n [0, 0, 0, 0, 0, -5, 0],\n [0, 0, 0, 0, 0, 0, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3169", "dataset": "MATH"}440{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[18, 9, 17, -3, -4, 10, -1],\n [0, 10, -13, 8, -12, 8, 0],\n [-2, -8, -14, -17, -7, -8, -9],\n [9, -12, -5, -6, -14, -11, -18],\n [-14, -8, -9, -4, 10, 6, -13],\n [-8, -2, -4, -3, -17, 17, 0],\n [2, -8, -16, 15, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}441{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, 2, -4, 8, 8, -9, -1],\n [2, -5, 13, 2, -6, 6, 6],\n [-4, 13, 16, -6, -16, -1, -2],\n [8, 2, -6, -9, 0, -4, 2],\n [8, -6, -16, 0, 0, 2, -1],\n [-9, 6, -1, -4, 2, -15, -16],\n [-1, 6, -2, 2, -1, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"}442{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, -15, -3, 18, 8, -14, -4],\n [4, -16, -1, 7, -13, -2, 8],\n [1, -13, 16, -7, -16, -15, -15],\n [-15, 2, -17, -3, -12, 0, 14],\n [-10, 18, -2, 8, 14, -7, -8],\n [-6, 12, -6, 7, 12, 3, -13],\n [1, 2, -9, 0, 16, 7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}443{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[18, -11, -14, 17, 9, -16, -11],\n [0, 8, 17, -3, 7, -15, -7],\n [0, 0, 12, -4, 15, 10, -10],\n [0, 0, 0, 18, 5, -2, -6],\n [0, 0, 0, 0, 2, -2, 3],\n [0, 0, 0, 0, 0, -4, 1],\n [0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-345", "dataset": "MATH"}444{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[8, 6, 1, -4, -11, 14, -13],\n [6, 0, -12, -9, 4, -4, -5],\n [1, -12, 16, -6, 8, 0, 6],\n [-4, -9, -6, 12, -8, 12, 2],\n [-11, 4, 8, -8, 0, -7, 6],\n [14, -4, 0, 12, -7, -5, -13],\n [-13, -5, 6, 2, 6, -13, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-190", "dataset": "MATH"}445{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 2, -12, -15, -7, 8, -2],\n [1, 12, 7, 12, 16, -10, -14],\n [-11, 2, -3, -3, -1, 9, -1],\n [-5, 18, -3, 2, -18, -8, -8],\n [-17, 13, 0, -14, -16, 9, 7],\n [4, 11, -11, 17, 10, -6, 6],\n [3, 14, 18, -12, 4, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-337", "dataset": "MATH"}446{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-4, 15, -5, 10, -3, 10, 4],\n [0, -15, -7, 15, -15, 1, 9],\n [0, 0, -5, 16, -18, 0, -18],\n [0, 0, 0, 16, 4, 7, 1],\n [0, 0, 0, 0, 11, -1, -12],\n [0, 0, 0, 0, 0, 5, 11],\n [0, 0, 0, 0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "408", "dataset": "MATH"}447{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[5, 3, -14, -4, 17, 18, 10],\n [-4, 8, -11, 10, 0, 12, -10],\n [-9, 18, -9, 14, 6, -15, -14],\n [4, -14, -11, -2, -18, -7, 16],\n [-5, -1, -9, -4, 14, 0, 15],\n [6, -3, -11, 16, 2, 0, -8],\n [-8, -8, 3, 2, 8, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-65", "dataset": "MATH"}448{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[14, 2, -17, -6, -17, 12, -9],\n [4, 3, 10, 14, 12, -5, -9],\n [-1, -8, -16, -17, -11, 12, -11],\n [-17, 3, -14, -12, 1, 9, -6],\n [-17, 13, 7, -16, -6, 2, 18],\n [4, -12, -2, 9, 11, -14, 5],\n [-12, 15, 14, 8, -5, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}449{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-16, -12, 16, 6, -4, 0, 0],\n [0, -8, 2, 15, -12, 8, 4],\n [0, 0, -11, 18, -16, -17, 3],\n [0, 0, 0, -7, -2, 3, 0],\n [0, 0, 0, 0, -2, 4, -9],\n [0, 0, 0, 0, 0, 1, -15],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-275", "dataset": "MATH"}450{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 6, 3, -10, -5, -4, -6],\n [6, 9, 15, 14, 0, 17, 0],\n [3, 15, 12, -9, -1, -8, -1],\n [-10, 14, -9, 10, 2, 0, 12],\n [-5, 0, -1, 2, -3, 3, 1],\n [-4, 17, -8, 0, 3, -14, -3],\n [-6, 0, -1, 12, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}451{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 4, 8, 0, -10, 2, -2],\n [4, 18, 7, 2, 0, -8, 15],\n [8, 7, 1, -9, 12, 6, 7],\n [0, 2, -9, -1, 10, -8, 4],\n [-10, 0, 12, 10, -18, -7, -6],\n [2, -8, 6, -8, -7, 13, 0],\n [-2, 15, 7, 4, -6, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1402", "dataset": "MATH"}452{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, -18, 2, -16, 8, -12, 14],\n [0, 11, -1, 7, 1, 12, -11],\n [0, 0, -18, -1, 0, -13, -2],\n [0, 0, 0, 8, 17, -13, -13],\n [0, 0, 0, 0, -17, -10, -8],\n [0, 0, 0, 0, 0, 16, -13],\n [0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}453{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -2, 0, 4, 2, -6, 16],\n [-2, 17, -4, -6, 2, -6, -16],\n [0, -4, -11, 4, -6, 1, 0],\n [4, -6, 4, -7, -2, -8, -7],\n [2, 2, -6, -2, -11, 8, -8],\n [-6, -6, 1, -8, 8, 3, 4],\n [16, -16, 0, -7, -8, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-72", "dataset": "MATH"}454{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -1, -7, 8, -13, 5, 14],\n [-3, -7, 12, 18, -6, -11, -16],\n [1, -15, -17, 17, 4, 0, -11],\n [-3, -1, 17, 5, -18, -18, 17],\n [-8, -1, -3, -2, 5, 15, -15],\n [16, -4, -17, 12, -10, -9, 6],\n [-14, -5, -17, -1, 10, 1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-159", "dataset": "MATH"}455{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, 10, 17, -1, 6, 0, 0],\n [10, 9, -2, -9, -17, -8, 2],\n [17, -2, -9, -13, -5, -4, 15],\n [-1, -9, -13, 9, 2, -3, 1],\n [6, -17, -5, 2, -10, -10, 12],\n [0, -8, -4, -3, -10, -10, -5],\n [0, 2, 15, 1, 12, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}456{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, -12, 8, -7, 1, -5, -9],\n [0, 11, 12, -9, 0, 0, 4],\n [0, 0, -15, 14, -18, -6, -16],\n [0, 0, 0, 17, -17, 3, 3],\n [0, 0, 0, 0, -10, 13, 8],\n [0, 0, 0, 0, 0, -10, -12],\n [0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1775", "dataset": "MATH"}457{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, 6, 18, -4, -15, -5, -2],\n [2, -3, 7, -10, -17, -4, 16],\n [5, -5, 18, 18, -13, -1, 3],\n [-1, -17, 13, -2, -18, -10, -6],\n [17, 18, 11, 12, 4, 9, -9],\n [6, 17, 7, 7, -6, -2, -15],\n [4, 16, -8, -7, -10, -4, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}458{"messages": [{"content": "Find the value at position (4, 6) of the inverse of matrix 1/252 * A where A =\n[[-15, -8, 13, -15, -18, 7, 14],\n [0, 8, -14, -12, 6, -11, 15],\n [0, 0, 12, -8, 18, 17, 3],\n [0, 0, 0, -11, 6, 9, 17],\n [0, 0, 0, 0, -16, 13, -18],\n [0, 0, 0, 0, 0, 4, 12],\n [0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}459{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -12, 0, 4, 17, 13, -15],\n [0, -14, -16, 3, 9, 3, 3],\n [0, 0, -6, -12, -9, 9, -15],\n [0, 0, 0, 1, -13, -10, 9],\n [0, 0, 0, 0, 18, 5, -11],\n [0, 0, 0, 0, 0, 10, 4],\n [0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}460{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, 13, 13, -6, 3, -4, 0],\n [13, 7, 2, -10, -13, 7, 14],\n [13, 2, -7, -14, 2, 6, -4],\n [-6, -10, -14, 9, -6, 6, 16],\n [3, -13, 2, -6, 18, 1, -6],\n [-4, 7, 6, 6, 1, -4, 6],\n [0, 14, -4, 16, -6, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}461{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[18, 4, -4, -10, -2, -4, 0],\n [4, 5, -4, 0, 6, -5, 11],\n [-4, -4, -15, -10, 14, 1, 4],\n [-10, 0, -10, -9, -8, 10, 3],\n [-2, 6, 14, -8, 3, -1, 0],\n [-4, -5, 1, 10, -1, 13, 4],\n [0, 11, 4, 3, 0, 4, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}462{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-18, 13, 2, -15, -10, 3, -7],\n [0, 11, 13, 17, -12, -2, -18],\n [0, 0, 8, -3, -12, 13, 6],\n [0, 0, 0, 6, 11, -12, -7],\n [0, 0, 0, 0, -12, -3, 13],\n [0, 0, 0, 0, 0, 18, -13],\n [0, 0, 0, 0, 0, 0, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-237", "dataset": "MATH"}463{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[17, -12, 14, -4, 13, 3, 10],\n [0, -14, -5, 16, -17, 6, -3],\n [0, 0, 16, 4, -14, 16, 10],\n [0, 0, 0, 4, -17, -1, 11],\n [0, 0, 0, 0, 7, 14, 8],\n [0, 0, 0, 0, 0, 3, -7],\n [0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-145", "dataset": "MATH"}464{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-5, 12, -13, 4, 11, -2, -12],\n [12, -15, 0, 2, 14, -3, 14],\n [-13, 0, 18, 2, -3, 10, -2],\n [4, 2, 2, -1, 6, 3, 14],\n [11, 14, -3, 6, -8, 8, 4],\n [-2, -3, 10, 3, 8, 5, 2],\n [-12, 14, -2, 14, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-82", "dataset": "MATH"}465{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[18, 8, -1, 5, -17, -3, -5],\n [-2, -13, 16, -2, -13, 2, 16],\n [4, -7, 10, 8, -13, 2, -12],\n [-3, -14, -4, 2, -15, -14, -12],\n [16, 17, -4, 9, -17, -14, -12],\n [3, 12, 13, -11, -8, -18, 0],\n [18, -12, 6, 3, 8, -4, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}466{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, -13, 1, 8, 4, -2, -6],\n [-15, 1, 6, 3, -2, -8, 6],\n [-14, 2, 7, -3, 2, 13, -15],\n [-11, -10, -2, -6, -10, -13, 8],\n [18, 5, -10, -8, 16, 10, -11],\n [-2, -12, -7, -4, 10, 5, 18],\n [-5, -8, 16, -2, 8, -16, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-59", "dataset": "MATH"}467{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 7) of the inverse. Round your answer to the nearest integer:\n[[-15, 3, -6, -6, 4, -8, -18],\n [3, 0, 2, 14, -8, -4, 12],\n [-6, 2, -10, 7, -2, 10, -10],\n [-6, 14, 7, 8, 1, 2, 2],\n [4, -8, -2, 1, 9, -12, -2],\n [-8, -4, 10, 2, -12, -13, 13],\n [-18, 12, -10, 2, -2, 13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}468{"messages": [{"content": "Find the value at position (6, 2) of the inverse of matrix 1/252 * A where A =\n[[-8, -2, -12, 11, -13, 2, 7],\n [-2, -16, 5, 7, 12, 0, 8],\n [-12, 5, 8, -6, -8, -14, -6],\n [11, 7, -6, 15, 0, -6, 0],\n [-13, 12, -8, 0, -4, 2, -4],\n [2, 0, -14, -6, 2, -2, -7],\n [7, 8, -6, 0, -4, -7, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}469{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, -15, 12, 7, 8, 15, 12],\n [0, -11, -7, 16, 15, -6, 8],\n [0, 0, -8, 3, 2, 9, -16],\n [0, 0, 0, -10, -12, -7, 0],\n [0, 0, 0, 0, 2, 15, -6],\n [0, 0, 0, 0, 0, -11, 7],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-190", "dataset": "MATH"}470{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-16, 11, 17, 4, -1, -9, -7],\n [-11, 13, -2, -5, 18, -10, 7],\n [5, 4, 12, -17, -1, -3, 10],\n [-8, -17, -5, -15, 15, -10, -12],\n [-2, 4, -8, 3, -1, 9, -3],\n [-15, 17, 3, -8, 2, -3, -10],\n [16, 15, -10, -6, -13, -15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-189", "dataset": "MATH"}471{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 4, 9, -4, 1, -4, -2],\n [4, -15, -2, -12, -6, 7, -6],\n [9, -2, 9, 3, 14, 7, -4],\n [-4, -12, 3, 15, 1, 1, -2],\n [1, -6, 14, 1, 5, 0, 3],\n [-4, 7, 7, 1, 0, -10, 5],\n [-2, -6, -4, -2, 3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-180", "dataset": "MATH"}472{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, -1, -5, -3, 5, 13, -8],\n [-8, -15, 7, -14, 17, 14, -5],\n [13, -12, -9, -17, -9, 16, 2],\n [-11, -1, -10, 11, -15, 16, -5],\n [-5, 18, 1, 10, 4, 2, 12],\n [13, -12, -6, 4, -11, -7, 17],\n [-3, 7, 10, 10, -13, 18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "286", "dataset": "MATH"}473{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 5, 0, 0, 16, -9, -12],\n [5, 14, 4, 12, 5, 5, 12],\n [0, 4, -15, -10, 2, -1, 2],\n [0, 12, -10, 7, 9, -8, 5],\n [16, 5, 2, 9, 1, -5, 6],\n [-9, 5, -1, -8, -5, -14, 10],\n [-12, 12, 2, 5, 6, 10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}474{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-4, 10, -9, 10, 12, 12, -16],\n [10, -10, -6, 2, 10, -7, -8],\n [-9, -6, -12, 3, 14, 1, 3],\n [10, 2, 3, 11, 10, 2, 4],\n [12, 10, 14, 10, 2, -6, 2],\n [12, -7, 1, 2, -6, -18, -4],\n [-16, -8, 3, 4, 2, -4, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}475{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[10, 3, -2, 9, -7, 7, 0],\n [3, -4, -2, -16, -6, -8, -2],\n [-2, -2, 9, -8, 6, -6, -16],\n [9, -16, -8, -5, 2, 12, -2],\n [-7, -6, 6, 2, -17, -4, -10],\n [7, -8, -6, 12, -4, -16, 2],\n [0, -2, -16, -2, -10, 2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}476{"messages": [{"content": "Find the value at position (1, 7) of the inverse of matrix 1/252 * A where A =\n[[10, -15, -10, 2, -7, -7, -15],\n [0, -10, 13, -6, 15, 0, -5],\n [0, 0, 9, 7, -9, 5, -2],\n [0, 0, 0, 2, 3, -14, 17],\n [0, 0, 0, 0, -1, 16, -4],\n [0, 0, 0, 0, 0, 2, 18],\n [0, 0, 0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23087", "dataset": "MATH"}477{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, -17, 16, -4, -16, 12, 4],\n [-7, -11, 2, 2, 13, -2, 18],\n [5, -11, -1, -8, -9, 7, -13],\n [-2, 4, 18, 9, -3, -7, 2],\n [5, 9, 18, 2, 14, -17, 18],\n [0, 9, -4, -18, 9, 16, 13],\n [9, -10, 5, -15, -16, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}478{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[3, 15, 1, 17, 18, 8, 13],\n [0, 13, 5, -16, 8, -10, 4],\n [0, 0, 18, -12, 11, -6, -1],\n [0, 0, 0, -1, 16, -2, 0],\n [0, 0, 0, 0, -3, 14, 6],\n [0, 0, 0, 0, 0, -14, -13],\n [0, 0, 0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14790", "dataset": "MATH"}479{"messages": [{"content": "Find the value at position (7, 2) of the inverse of matrix 1/252 * A where A =\n[[-16, 2, -11, 2, -16, -2, 1],\n [2, 18, 2, -10, -2, 12, -16],\n [-11, 2, 4, 0, 0, -1, 6],\n [2, -10, 0, 9, -12, 6, -8],\n [-16, -2, 0, -12, -14, 2, -2],\n [-2, 12, -1, 6, 2, 5, 12],\n [1, -16, 6, -8, -2, 12, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}480{"messages": [{"content": "Find the value at position (6, 2) of the inverse of matrix 1/252 * A where A =\n[[16, 17, -5, -13, 13, 7, -4],\n [12, 18, 18, 0, -5, 17, 18],\n [-8, 8, -17, 3, -17, 1, -2],\n [-15, -5, -12, -4, 11, -3, -17],\n [0, -18, 12, -15, 8, 6, 3],\n [-9, 14, 11, 11, -3, -10, -2],\n [16, -4, 9, 1, 14, 14, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}481{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -2, 5, -13, -7, -3, 8],\n [-2, 6, 5, -2, 8, 4, -1],\n [5, 5, -13, -8, -9, 9, 7],\n [-13, -2, -8, -18, 8, -4, 6],\n [-7, 8, -9, 8, 17, 12, 10],\n [-3, 4, 9, -4, 12, -14, -5],\n [8, -1, 7, 6, 10, -5, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}482{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[4, 2, -6, -11, -14, 6, 18],\n [0, -11, -15, 3, -5, 0, -6],\n [0, 0, 14, 3, -18, -8, -3],\n [0, 0, 0, -10, -11, -5, -4],\n [0, 0, 0, 0, -18, 1, 17],\n [0, 0, 0, 0, 0, 1, -14],\n [0, 0, 0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}483{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-2, 2, 4, -9, -2, -18, 18],\n [0, -7, -18, 1, 12, -15, 7],\n [0, 0, -18, -18, -16, -7, 2],\n [0, 0, 0, 14, -13, 6, 4],\n [0, 0, 0, 0, 16, -8, 17],\n [0, 0, 0, 0, 0, 4, 16],\n [0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-773", "dataset": "MATH"}484{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 6) rounded to the nearest integer?\n[[0, 2, 3, -17, -13, 2, 14],\n [0, 8, 18, 10, 9, 15, -18],\n [6, 2, 15, 7, 17, 16, 4],\n [-2, -7, 1, 8, 18, 1, -8],\n [9, -17, 5, -3, -7, -3, 17],\n [-17, 6, 10, 9, -9, 4, 13],\n [12, 0, -4, 14, -2, 17, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}485{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, -16, -17, -1, 4, 0, -12],\n [0, 1, 1, 0, -3, 2, 10],\n [0, 0, 10, 12, -7, 11, -15],\n [0, 0, 0, 8, -15, -11, -11],\n [0, 0, 0, 0, 2, 5, 10],\n [0, 0, 0, 0, 0, -6, -18],\n [0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494", "dataset": "MATH"}486{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, 0, 0, 2, 3, -11, 5],\n [0, -7, 12, 4, 12, 4, 3],\n [0, 12, 2, 6, -12, 6, 7],\n [2, 4, 6, 2, 0, 8, 4],\n [3, 12, -12, 0, -8, -5, 6],\n [-11, 4, 6, 8, -5, 2, 8],\n [5, 3, 7, 4, 6, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}487{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-18, 9, -1, 1, -12, 18, -3],\n [4, 13, -2, 0, 15, -5, -16],\n [6, -8, -4, 0, -4, -4, -4],\n [-10, -14, 0, 5, 10, -14, 3],\n [-6, 10, -3, 17, -2, 1, -5],\n [-13, 3, -10, 13, 5, 14, -6],\n [16, -13, 11, -3, -18, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}488{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -5, 18, -5, 7, 17, 4],\n [-17, -12, 3, 9, 1, -1, 5],\n [14, 7, 0, -6, -9, -5, -10],\n [-8, -16, -7, 16, 13, -5, -18],\n [8, 18, -18, 10, 5, -2, 16],\n [12, 13, 0, 12, 1, 9, -16],\n [13, 3, -4, 0, 12, 7, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2421", "dataset": "MATH"}489{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[1, -17, 2, 17, 9, 1, 18],\n [17, -8, -16, 18, 1, 13, 6],\n [2, -3, -18, 4, 5, 6, -12],\n [16, -5, -10, -16, 1, 14, 13],\n [17, 7, -14, 11, -2, -13, -4],\n [-18, -6, 15, 11, 0, -17, -7],\n [5, -8, -17, -18, 9, -15, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}490{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 5) of the inverse. Round your answer to the nearest integer:\n[[-12, 3, 7, 10, 6, -9, 1],\n [-5, 14, -14, -13, 3, -2, -4],\n [9, -17, -1, 8, 2, 4, -12],\n [0, -10, -7, 11, -12, -17, -2],\n [-8, -7, -16, 2, -5, -4, -9],\n [17, -9, -2, 6, 8, 14, -8],\n [-6, -18, 12, 14, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}491{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 14, 3, -13, 17, -9, -3],\n [0, 1, -15, 1, 3, 10, -3],\n [0, 0, 11, -16, 5, 18, -6],\n [0, 0, 0, -11, 5, -3, 13],\n [0, 0, 0, 0, -17, 7, -2],\n [0, 0, 0, 0, 0, -14, -10],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}492{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -16, 4, -10, 11, 0, -16],\n [0, 15, -17, 8, 4, 13, 16],\n [0, 0, -8, 0, 6, -12, 12],\n [0, 0, 0, -1, 17, -15, 5],\n [0, 0, 0, 0, -14, 5, 16],\n [0, 0, 0, 0, 0, 15, -10],\n [0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-306", "dataset": "MATH"}493{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -4, 2, -16, -11, -13, 10],\n [0, -2, -9, 14, -6, 8, -7],\n [-17, -9, 2, 4, -18, 14, 7],\n [-4, 3, 6, -18, 7, 2, 5],\n [-3, 13, -3, -6, 13, 5, -6],\n [-8, -4, -9, -16, -3, -2, 6],\n [11, 16, 18, -6, 5, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708", "dataset": "MATH"}494{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, -18, -8, 7, 0, 0, -7],\n [0, -1, -14, 5, -5, -16, -13],\n [0, 0, 7, -18, -3, -10, -14],\n [0, 0, 0, 1, 3, -6, -8],\n [0, 0, 0, 0, -18, 17, -13],\n [0, 0, 0, 0, 0, 6, -4],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-131136", "dataset": "MATH"}495{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 10, 0, -2, 8, 4, 10],\n [10, 9, -2, -10, 4, 2, 7],\n [0, -2, -9, -4, -3, 8, 0],\n [-2, -10, -4, 14, -6, -1, -6],\n [8, 4, -3, -6, 5, 4, 3],\n [4, 2, 8, -1, 4, 9, -4],\n [10, 7, 0, -6, 3, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189", "dataset": "MATH"}496{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 7) rounded to the nearest integer?\n[[-4, 3, 0, -12, -4, 0, -12],\n [3, -16, -4, -1, 1, 10, 0],\n [0, -4, 0, 4, -6, -8, 8],\n [-12, -1, 4, -13, -6, 0, -2],\n [-4, 1, -6, -6, 12, -8, 12],\n [0, 10, -8, 0, -8, 14, -14],\n [-12, 0, 8, -2, 12, -14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}497{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[13, 8, 15, 9, -10, -11, 2],\n [11, 10, -10, -6, -1, 3, 12],\n [16, -9, -10, 12, 5, -11, 1],\n [-2, 9, -13, 14, 9, -18, 16],\n [5, -13, -12, -10, 18, -3, 15],\n [16, 16, 1, 4, 16, 4, -15],\n [-9, -8, -10, -7, -2, 13, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}498{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, 9, -14, -1, 2, -4, -16],\n [7, -4, 1, 2, 7, 4, 6],\n [-15, -9, 3, -16, 0, 12, -10],\n [10, 18, -12, 5, -11, 15, 7],\n [9, 9, -12, -16, 3, -1, -7],\n [12, -14, 10, 17, -5, -1, -12],\n [4, 14, -3, 18, 6, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}499{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, -4, 4, 11, 10, 9, -12],\n [-4, 13, 0, -6, -2, 8, 8],\n [4, 0, 9, -7, -8, -2, 0],\n [11, -6, -7, -5, 4, 1, -6],\n [10, -2, -8, 4, 8, 6, 8],\n [9, 8, -2, 1, 6, 5, -2],\n [-12, 8, 0, -6, 8, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}500{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 9, 0, 4, -11, 6, 16],\n [0, -16, -17, -14, 1, -7, -3],\n [0, 0, 10, 16, 18, 2, 2],\n [0, 0, 0, 17, -6, -8, 5],\n [0, 0, 0, 0, 18, -16, 15],\n [0, 0, 0, 0, 0, -3, 15],\n [0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}501{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[9, -4, -6, 16, 5, -18, 5],\n [0, -1, 7, 10, -11, 7, -14],\n [0, 0, 17, -6, -2, -6, 6],\n [0, 0, 0, 6, 15, -7, 0],\n [0, 0, 0, 0, 7, -4, 9],\n [0, 0, 0, 0, 0, 13, 11],\n [0, 0, 0, 0, 0, 0, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4546", "dataset": "MATH"}502{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[5, -8, 16, -18, -11, 4, 1],\n [13, -8, -12, 11, -6, -16, -12],\n [-6, 18, 6, 4, 14, -14, 13],\n [11, 12, -6, -14, 4, -18, -9],\n [8, -11, -16, 0, -17, 12, -9],\n [-3, 18, 1, -16, 16, 15, 2],\n [17, 13, -1, 15, -16, -16, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}503{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, -16, -2, 0, 0, -14, -14],\n [0, 8, 17, 16, 2, -14, 5],\n [0, 0, -18, -9, -17, -3, 18],\n [0, 0, 0, -3, 8, 11, 14],\n [0, 0, 0, 0, -13, 11, -4],\n [0, 0, 0, 0, 0, 4, -8],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}504{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 17, 4, 8, 8, 6, 5],\n [17, 10, 13, 2, 8, 17, 6],\n [4, 13, -16, -3, -5, -7, -8],\n [8, 2, -3, -6, 2, -16, 6],\n [8, 8, -5, 2, -10, 11, 4],\n [6, 17, -7, -16, 11, -9, -5],\n [5, 6, -8, 6, 4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}505{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 0, -14, -4, 5, -4, -4],\n [0, 5, 6, -2, 4, 0, 7],\n [-14, 6, -4, 0, 13, -11, 10],\n [-4, -2, 0, -15, -9, -12, 10],\n [5, 4, 13, -9, -18, -6, -5],\n [-4, 0, -11, -12, -6, -16, 2],\n [-4, 7, 10, 10, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}506{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -3, -3, -2, -11, 0, -9],\n [-3, 8, 5, 4, 4, 2, 4],\n [-3, 5, 9, -2, -9, -2, 2],\n [-2, 4, -2, 14, -6, -4, 4],\n [-11, 4, -9, -6, -3, -8, -4],\n [0, 2, -2, -4, -8, 16, -7],\n [-9, 4, 2, 4, -4, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}507{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, -8, 10, -2, 8, -6, -15],\n [-8, 0, -8, 10, 1, -6, 2],\n [10, -8, -17, -2, -3, 6, -5],\n [-2, 10, -2, 4, 1, 1, -6],\n [8, 1, -3, 1, -11, 10, 1],\n [-6, -6, 6, 1, 10, -1, 5],\n [-15, 2, -5, -6, 1, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-538", "dataset": "MATH"}508{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[3, 0, -10, -1, -2, 8, -10],\n [0, -11, -14, -4, -5, 12, 3],\n [-10, -14, 18, -6, 6, 16, -3],\n [-1, -4, -6, 1, 2, -11, 2],\n [-2, -5, 6, 2, -15, -10, -7],\n [8, 12, 16, -11, -10, 16, 9],\n [-10, 3, -3, 2, -7, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-246", "dataset": "MATH"}509{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 4, -15, 18, -12, -13, -4],\n [0, 13, -5, 16, -8, -9, -2],\n [0, 0, -14, -9, 13, -7, -6],\n [0, 0, 0, -7, 16, 17, 9],\n [0, 0, 0, 0, 10, -6, 16],\n [0, 0, 0, 0, 0, 14, 8],\n [0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}510{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-5, 2, 2, 12, -13, 10, -10],\n [2, 18, -15, 10, 3, 6, 4],\n [2, -15, 2, -13, 0, 0, -11],\n [12, 10, -13, 12, -9, 10, 5],\n [-13, 3, 0, -9, -9, 3, 5],\n [10, 6, 0, 10, 3, 16, -1],\n [-10, 4, -11, 5, 5, -1, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}511{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[0, -9, -13, 5, -10, 8, -12],\n [-13, 14, 2, -2, 12, 18, -8],\n [9, -14, -7, -16, -17, 7, -17],\n [-7, -17, -3, 11, 17, -15, -8],\n [5, -1, 8, 18, -17, -4, -8],\n [8, 4, 16, 11, 5, 0, 10],\n [-6, 4, -7, 10, -13, 4, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}512{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 5, -11, -10, 3, -15, -6],\n [15, -16, 18, 9, 7, 15, -4],\n [-11, 16, 5, 18, -15, -7, 0],\n [-4, 11, 18, -7, 0, 15, -12],\n [9, 9, 10, 18, 1, -8, 4],\n [1, 1, -8, -17, -6, -6, -4],\n [12, 4, 3, -3, 10, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-82", "dataset": "MATH"}513{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[8, 10, -14, -17, 1, -6, 7],\n [16, -11, 9, -4, -11, -8, 10],\n [-14, -12, -1, 9, -7, -7, 17],\n [10, -8, -13, 2, -9, 13, 14],\n [-2, -16, -1, -9, -11, 15, 18],\n [14, -9, -1, 6, 17, -17, 0],\n [-9, -16, 0, 7, 6, -2, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}514{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, 4, -4, -2, 6, 4, 6],\n [4, -2, -6, -5, -7, 4, -4],\n [-4, -6, -3, 12, -10, -1, -4],\n [-2, -5, 12, 14, 7, -4, -1],\n [6, -7, -10, 7, -15, 11, -7],\n [4, 4, -1, -4, 11, 14, 12],\n [6, -4, -4, -1, -7, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1467", "dataset": "MATH"}515{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[2, 4, 10, 12, -9, -10, -5],\n [4, 8, 8, -4, -10, -12, 5],\n [10, 8, 5, -14, 4, 3, -14],\n [12, -4, -14, -2, -8, 6, 7],\n [-9, -10, 4, -8, -7, 2, 2],\n [-10, -12, 3, 6, 2, -7, -2],\n [-5, 5, -14, 7, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}516{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 2, -6, 4, 1, -17, 1],\n [2, -6, 8, -9, 8, 0, 11],\n [-6, 8, 17, -2, -12, 0, -3],\n [4, -9, -2, 15, 3, 16, 12],\n [1, 8, -12, 3, 9, -7, -4],\n [-17, 0, 0, 16, -7, 13, -9],\n [1, 11, -3, 12, -4, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770", "dataset": "MATH"}517{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[5, 9, -7, -8, 8, 4, 14],\n [0, 9, 9, -13, 10, 15, -16],\n [0, 0, 17, -4, -13, 14, -7],\n [0, 0, 0, 17, -14, 6, -2],\n [0, 0, 0, 0, -13, 0, -18],\n [0, 0, 0, 0, 0, 8, 7],\n [0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}518{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-16, -9, 2, 14, 9, -8, -9],\n [-9, -7, -8, -6, -12, 2, -12],\n [2, -8, -18, 2, -2, 3, -2],\n [14, -6, 2, -5, -3, 4, -12],\n [9, -12, -2, -3, -18, 15, -11],\n [-8, 2, 3, 4, 15, 8, 7],\n [-9, -12, -2, -12, -11, 7, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}519{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 9, -9, -12, -16, -12, -10],\n [16, 7, -14, -6, 11, -9, 4],\n [-8, -7, -6, -3, -10, -9, 10],\n [-10, 14, 5, 16, -8, -6, 4],\n [6, -3, 2, -9, 0, 16, 9],\n [-17, 11, -14, -4, 17, -16, 5],\n [-7, -11, -5, -1, 1, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}520{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-18, -8, 7, -10, 0, -2, -10],\n [-8, 3, -3, -2, 13, -12, -14],\n [7, -3, -2, 4, -13, -2, -14],\n [-10, -2, 4, 18, 1, 6, -2],\n [0, 13, -13, 1, 3, 2, -8],\n [-2, -12, -2, 6, 2, -18, 6],\n [-10, -14, -14, -2, -8, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}521{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -8, -2, 0, 14, -8, 12],\n [-8, 17, -4, -6, 8, 8, 6],\n [-2, -4, 1, 6, 10, 3, -3],\n [0, -6, 6, 1, 16, 8, 0],\n [14, 8, 10, 16, -10, 9, 10],\n [-8, 8, 3, 8, 9, 4, 8],\n [12, 6, -3, 0, 10, 8, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}522{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-4, -3, 4, 18, -18, 0, 18],\n [0, 11, -2, 7, -6, 3, 4],\n [0, 0, 16, -7, -10, 15, -5],\n [0, 0, 0, -12, 14, 16, -8],\n [0, 0, 0, 0, 18, -8, -6],\n [0, 0, 0, 0, 0, 13, 18],\n [0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1898", "dataset": "MATH"}523{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-11, -1, 12, 1, 11, 8, 2],\n [-1, 6, 4, -2, 9, -1, 8],\n [12, 4, 10, 2, 2, -4, -6],\n [1, -2, 2, 15, 0, -5, -8],\n [11, 9, 2, 0, -11, -4, 12],\n [8, -1, -4, -5, -4, 18, 0],\n [2, 8, -6, -8, 12, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}524{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[14, -1, 0, 13, 3, -18, 6],\n [1, 16, -13, -13, 18, -16, 18],\n [12, 16, -4, -2, -4, -14, 3],\n [-8, 9, -5, -16, -8, 11, -14],\n [3, -6, 2, 18, 6, 2, 9],\n [-15, 10, 16, 4, -12, -10, 4],\n [-16, -10, -15, 6, -13, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}525{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[16, 12, 13, 16, 9, -14, 11],\n [0, -2, -9, -12, -15, 8, -12],\n [0, 0, -11, -11, 18, -14, -12],\n [0, 0, 0, 5, -17, -7, 7],\n [0, 0, 0, 0, -5, -1, 13],\n [0, 0, 0, 0, 0, 3, 9],\n [0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}526{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 7) of the inverse. Round your answer to the nearest integer:\n[[10, 6, -2, -6, -3, 16, 17],\n [0, -10, 10, -14, -16, -9, 12],\n [0, 0, -11, -17, -15, -3, 2],\n [0, 0, 0, -4, -13, -3, 4],\n [0, 0, 0, 0, -6, -17, 1],\n [0, 0, 0, 0, 0, 10, 0],\n [0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}527{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-7, 10, 4, 4, 3, 6, 6],\n [10, 12, -17, 8, 4, -10, 14],\n [4, -17, -13, 14, -8, -6, 4],\n [4, 8, 14, 10, -2, -2, 4],\n [3, 4, -8, -2, -18, -5, -3],\n [6, -10, -6, -2, -5, 6, 0],\n [6, 14, 4, 4, -3, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}528{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[8, -11, 4, 4, 14, -6, 16],\n [0, -7, 12, -14, 6, 2, -16],\n [0, 0, -2, 16, 6, -17, 8],\n [0, 0, 0, 13, 10, 3, -6],\n [0, 0, 0, 0, -4, -5, 16],\n [0, 0, 0, 0, 0, -8, 7],\n [0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "795", "dataset": "MATH"}529{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[12, 5, -10, 0, 12, -16, -3],\n [5, -1, -5, 11, 10, 10, 3],\n [-10, -5, 3, -12, -16, 7, -1],\n [0, 11, -12, 3, -9, 2, -2],\n [12, 10, -16, -9, -11, 12, -2],\n [-16, 10, 7, 2, 12, -1, -3],\n [-3, 3, -1, -2, -2, -3, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-132", "dataset": "MATH"}530{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 3, 6, 2, 17, 1, -3],\n [9, 10, 7, -17, -9, -6, -4],\n [-10, 8, -11, -13, 17, 5, -16],\n [7, 17, 2, -6, -8, -11, -5],\n [14, -17, -18, -8, -13, 13, -4],\n [-7, 18, 10, 3, -5, 0, -14],\n [16, 6, -10, -12, -1, -17, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}531{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-17, -11, -12, 16, 4, -11, 2],\n [0, -18, -7, -8, 11, -15, 15],\n [0, 0, -16, 9, -15, -7, 5],\n [0, 0, 0, 11, -13, 11, -11],\n [0, 0, 0, 0, 9, 13, 6],\n [0, 0, 0, 0, 0, 2, -18],\n [0, 0, 0, 0, 0, 0, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}532{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-15, -13, -10, 7, -17, -17, 2],\n [3, -16, 16, 14, -4, -8, -9],\n [17, -5, -17, 18, 10, 16, 1],\n [2, 15, 14, 0, -11, 12, -8],\n [-11, 6, 1, -12, -6, -9, -11],\n [1, -2, -8, -3, 18, 13, 7],\n [18, -10, 16, -16, 12, -12, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-116", "dataset": "MATH"}533{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 10, 0, -13, -14, -14, -11],\n [0, 18, 18, -1, 7, -3, 3],\n [0, 0, -16, -7, 4, -8, 10],\n [0, 0, 0, 18, -8, -8, 6],\n [0, 0, 0, 0, 16, -13, 2],\n [0, 0, 0, 0, 0, -17, 17],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-188", "dataset": "MATH"}534{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -18, 1, -11, -16, 13, 6],\n [0, -5, 8, 13, 8, -15, -8],\n [0, 0, 5, -10, -11, 12, -2],\n [0, 0, 0, 18, -11, -13, -10],\n [0, 0, 0, 0, 4, -14, 8],\n [0, 0, 0, 0, 0, 12, -8],\n [0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1474", "dataset": "MATH"}535{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 16, 9, 10, 2, 6, 12],\n [0, 16, 3, -14, -6, 13, -16],\n [0, 0, 8, 11, -13, 6, 9],\n [0, 0, 0, 7, -1, -10, -15],\n [0, 0, 0, 0, -10, -12, 10],\n [0, 0, 0, 0, 0, -1, 6],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5600", "dataset": "MATH"}536{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-3, -14, 16, 8, -18, 15, 13],\n [14, 12, -6, -17, 11, -9, 4],\n [14, 10, 11, 15, -2, 3, -14],\n [-8, 3, 13, 5, -8, -8, -2],\n [13, 0, 8, 13, 6, 9, 8],\n [-5, -17, -2, -18, 13, 0, -5],\n [12, -1, -5, -5, 5, -14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}537{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 2, 6, -2, 8, -8, 6],\n [2, 4, -2, -6, 0, 2, 0],\n [6, -2, -1, -2, 0, 6, 12],\n [-2, -6, -2, 15, -6, 4, 7],\n [8, 0, 0, -6, -18, 11, -2],\n [-8, 2, 6, 4, 11, -17, -6],\n [6, 0, 12, 7, -2, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "681", "dataset": "MATH"}538{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-14, 2, 8, -14, 2, -11, 3],\n [-1, -15, -15, 18, -4, 8, 2],\n [-15, -8, 0, 0, 8, 9, -14],\n [6, -16, 7, -9, 5, 10, -12],\n [4, 8, -10, -16, -6, -13, 2],\n [0, 6, -15, 3, -14, -18, -2],\n [-10, -10, 5, -9, 1, -2, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}539{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 7) rounded to the nearest integer?\n[[10, 0, 2, -1, -2, -2, -2],\n [0, -12, 4, -4, -2, -4, 4],\n [2, 4, -2, -8, -2, 4, -3],\n [-1, -4, -8, 4, -10, -6, -10],\n [-2, -2, -2, -10, 7, -3, -8],\n [-2, -4, 4, -6, -3, 14, 4],\n [-2, 4, -3, -10, -8, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}540{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -10, -2, -9, -6, -8, 1],\n [-10, 4, -4, 10, -8, 12, -2],\n [-2, -4, 8, 17, 0, -8, 9],\n [-9, 10, 17, 14, 0, -4, -12],\n [-6, -8, 0, 0, 2, 2, 12],\n [-8, 12, -8, -4, 2, 14, -6],\n [1, -2, 9, -12, 12, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-65", "dataset": "MATH"}541{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, -4, 0, -15, 6, -11, 0],\n [-4, -1, -12, 1, 10, -2, -3],\n [0, -12, -13, -4, -4, 1, -10],\n [-15, 1, -4, 1, -10, 2, 2],\n [6, 10, -4, -10, 3, 8, 6],\n [-11, -2, 1, 2, 8, 9, 12],\n [0, -3, -10, 2, 6, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}542{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[4, 4, -1, -8, 17, 7, -11],\n [0, -1, -6, 17, -7, 3, -17],\n [0, 0, 14, -16, 15, 4, 13],\n [0, 0, 0, -16, 11, 6, 11],\n [0, 0, 0, 0, -2, 5, 9],\n [0, 0, 0, 0, 0, -5, 9],\n [0, 0, 0, 0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-384", "dataset": "MATH"}543{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, 2, -10, -7, 10, 5, 14],\n [-5, -1, -14, -4, -12, 6, -5],\n [17, 16, 5, -4, -8, 5, -8],\n [-2, -13, 2, -11, -4, 13, -9],\n [9, -4, -7, -1, 18, 5, 18],\n [10, -9, -5, -3, 18, -8, 7],\n [0, -1, 11, 13, 4, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-68", "dataset": "MATH"}544{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -2, 6, 4, 9, 11, 2],\n [-2, 0, -2, 8, -3, 5, 0],\n [6, -2, -8, 3, 5, -2, 4],\n [4, 8, 3, -14, 17, -4, 2],\n [9, -3, 5, 17, 10, 16, 12],\n [11, 5, -2, -4, 16, -10, -4],\n [2, 0, 4, 2, 12, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}545{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-12, -8, 2, 4, 0, 10, -5],\n [-8, 16, -2, -6, -9, -1, 5],\n [2, -2, 7, 14, 7, 0, 2],\n [4, -6, 14, -2, 5, 3, 5],\n [0, -9, 7, 5, -8, 7, -16],\n [10, -1, 0, 3, 7, 15, 9],\n [-5, 5, 2, 5, -16, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4232", "dataset": "MATH"}546{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-5, -6, 6, -6, -6, 18, -13],\n [0, -5, -11, 5, 3, 2, 7],\n [0, 0, -5, -10, -12, 12, -3],\n [0, 0, 0, -4, 6, -12, 7],\n [0, 0, 0, 0, -16, -18, -6],\n [0, 0, 0, 0, 0, 6, -14],\n [0, 0, 0, 0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38780", "dataset": "MATH"}547{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-16, -13, -6, 12, -2, 2, -3],\n [0, 13, -18, -11, -18, -17, 18],\n [0, 0, 1, 2, 18, 16, -4],\n [0, 0, 0, 4, -4, 7, -7],\n [0, 0, 0, 0, 9, -4, 0],\n [0, 0, 0, 0, 0, -14, -12],\n [0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}548{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-13, 10, -9, -3, 15, 12, 17],\n [0, 14, 0, 13, 4, -16, -18],\n [0, 0, -14, -6, -8, 3, 4],\n [0, 0, 0, -14, 5, 11, -11],\n [0, 0, 0, 0, 5, -1, 18],\n [0, 0, 0, 0, 0, 12, 12],\n [0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}549{"messages": [{"content": "Find the value at position (7, 2) of the inverse of matrix 1/252 * A where A =\n[[11, -4, 2, 11, -8, -12, -8],\n [-4, -5, -8, -10, -12, 2, 8],\n [2, -8, -4, 2, 8, 0, -13],\n [11, -10, 2, -12, -4, -2, -14],\n [-8, -12, 8, -4, -11, -2, -2],\n [-12, 2, 0, -2, -2, -18, -8],\n [-8, 8, -13, -14, -2, -8, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}550{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[14, -12, 4, -7, 6, 8, 12],\n [-12, -14, -10, 1, 3, 8, -2],\n [4, -10, -15, 10, 2, -4, 15],\n [-7, 1, 10, 0, -6, -3, 6],\n [6, 3, 2, -6, -3, -10, -4],\n [8, 8, -4, -3, -10, -10, -1],\n [12, -2, 15, 6, -4, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-101", "dataset": "MATH"}551{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[14, 10, -6, 4, 2, 4, -4],\n [10, -7, -4, -4, -4, 2, 0],\n [-6, -4, -13, -4, 0, -8, 4],\n [4, -4, -4, -9, -10, 6, 0],\n [2, -4, 0, -10, 12, 4, 8],\n [4, 2, -8, 6, 4, 5, -10],\n [-4, 0, 4, 0, 8, -10, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}552{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 5, 9, -1, 10, -4, 8],\n [5, 6, 5, 4, 0, 9, 12],\n [9, 5, 6, 12, 2, 11, -3],\n [-1, 4, 12, 12, -12, 15, 2],\n [10, 0, 2, -12, 12, 9, 0],\n [-4, 9, 11, 15, 9, 6, 13],\n [8, 12, -3, 2, 0, 13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}553{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-18, -7, 7, 4, 3, 9, -2],\n [0, -5, -2, -14, -6, -10, 7],\n [0, 0, -2, -3, 11, 13, -5],\n [0, 0, 0, -8, -14, -8, 15],\n [0, 0, 0, 0, 12, 0, 1],\n [0, 0, 0, 0, 0, -18, -17],\n [0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-263", "dataset": "MATH"}554{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[18, -6, -4, -2, 3, -16, 2],\n [-6, -9, -4, 14, -6, -15, 4],\n [-4, -4, 17, -8, -10, -9, -4],\n [-2, 14, -8, 9, 8, 9, 0],\n [3, -6, -10, 8, -7, 0, 4],\n [-16, -15, -9, 9, 0, -6, -2],\n [2, 4, -4, 0, 4, -2, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-528", "dataset": "MATH"}555{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[13, 9, 5, 9, 11, 10, 15],\n [0, 6, -5, -9, -9, -11, -5],\n [0, 0, -16, 1, -6, 4, 0],\n [0, 0, 0, -12, 18, -11, 6],\n [0, 0, 0, 0, -8, 16, 8],\n [0, 0, 0, 0, 0, 16, -6],\n [0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}556{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 18, 11, -8, 4, 9, 10],\n [0, -16, -10, -11, 14, 15, -10],\n [0, 0, -14, 11, -8, 9, -2],\n [0, 0, 0, 8, 6, -14, 0],\n [0, 0, 0, 0, -5, 8, -11],\n [0, 0, 0, 0, 0, -1, 4],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2667", "dataset": "MATH"}557{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-14, 16, -18, 17, -1, -13, 4],\n [0, -12, -11, -6, 11, -1, -5],\n [0, 0, 14, -6, 6, 5, 10],\n [0, 0, 0, 9, -14, -1, 18],\n [0, 0, 0, 0, 5, -10, -7],\n [0, 0, 0, 0, 0, 14, 5],\n [0, 0, 0, 0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}558{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -15, -1, 2, -11, -13, 1],\n [0, 3, 2, -13, 13, -13, -6],\n [0, 0, 5, 11, 3, -7, 7],\n [0, 0, 0, -7, 14, 2, 17],\n [0, 0, 0, 0, 13, 9, -9],\n [0, 0, 0, 0, 0, -14, -16],\n [0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5658", "dataset": "MATH"}559{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 7) rounded to the nearest integer?\n[[-8, 10, 8, -10, 16, -10, -1],\n [2, 17, -18, 8, 10, 0, 5],\n [-18, 17, 4, -6, 11, 18, -8],\n [-12, 16, -8, 2, -16, 11, 5],\n [-16, 18, 14, 3, 12, -7, -5],\n [-7, 8, -6, 5, -10, -11, 18],\n [-4, -12, 5, -3, 5, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}560{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, 15, -16, -18, 12, 4, 1],\n [-3, 13, -2, -1, -15, 16, 17],\n [4, -4, -6, -5, -5, 18, -14],\n [3, 9, -15, 10, 18, 16, 1],\n [16, 16, 1, -17, -1, 11, 10],\n [3, 10, -9, 1, -3, -13, -2],\n [-13, 3, -1, 13, 9, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}561{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[9, -4, 10, -12, 15, 13, -17],\n [7, -8, 6, 0, 1, 14, -2],\n [11, -1, 13, -15, 13, 0, -16],\n [9, -13, -2, -14, 0, 16, 3],\n [5, -9, -17, 9, 18, -2, -13],\n [-14, -12, 13, -15, 2, 13, -1],\n [14, -5, -13, -8, 1, 10, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}562{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -14, 12, 11, 0, 12, -5],\n [-14, 3, 2, -12, -9, 2, 8],\n [12, 2, -9, 2, -4, 8, 0],\n [11, -12, 2, 15, 6, -6, 4],\n [0, -9, -4, 6, -6, 2, -3],\n [12, 2, 8, -6, 2, 11, -4],\n [-5, 8, 0, 4, -3, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}563{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-6, 6, 6, -2, -7, -8, -9],\n [0, -3, 1, -14, 13, 8, -15],\n [0, 0, 5, -1, -18, -2, 7],\n [0, 0, 0, 2, 14, 11, -11],\n [0, 0, 0, 0, 12, -16, -8],\n [0, 0, 0, 0, 0, 16, -6],\n [0, 0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1303", "dataset": "MATH"}564{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, 11, 8, 0, -6, -8, 1],\n [11, 7, 6, -4, 10, -2, 3],\n [8, 6, 0, 2, -12, -8, -8],\n [0, -4, 2, -12, -2, 6, -6],\n [-6, 10, -12, -2, -1, -4, -1],\n [-8, -2, -8, 6, -4, 15, -14],\n [1, 3, -8, -6, -1, -14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}565{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[14, -18, -12, 3, 13, -5, 5],\n [0, 8, 4, 2, 10, -18, 12],\n [0, 0, 8, -4, 6, -4, 0],\n [0, 0, 0, -7, -17, 2, -5],\n [0, 0, 0, 0, 2, -5, 2],\n [0, 0, 0, 0, 0, -17, 10],\n [0, 0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1619", "dataset": "MATH"}566{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-13, 5, 8, -2, -4, 2, -10],\n [5, 14, -2, -5, -14, 0, -2],\n [8, -2, 0, 0, 14, -2, 6],\n [-2, -5, 0, -7, 4, -14, 9],\n [-4, -14, 14, 4, -13, 0, -4],\n [2, 0, -2, -14, 0, 15, -14],\n [-10, -2, 6, 9, -4, -14, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}567{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 18, -12, 16, 11, -3, -4],\n [1, 9, 18, -16, 10, 18, -10],\n [8, 13, 12, 7, -16, -8, 10],\n [8, -9, 16, 4, -13, -8, 8],\n [12, 11, -16, -6, 2, -8, -16],\n [12, 5, -7, 8, 2, 6, 11],\n [11, -9, -16, -6, 8, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}568{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -15, -3, -9, 18, 8, -18],\n [0, -6, -16, -2, 0, 18, -14],\n [0, 0, 2, -16, -15, 13, 5],\n [0, 0, 0, 7, 5, -18, 15],\n [0, 0, 0, 0, -16, 9, 6],\n [0, 0, 0, 0, 0, 15, 7],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25583", "dataset": "MATH"}569{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-5, 16, -3, 5, -2, -1, -2],\n [0, 2, 5, 15, 17, 8, -2],\n [0, 0, -15, 6, 11, 14, 7],\n [0, 0, 0, -14, -6, 11, -12],\n [0, 0, 0, 0, -14, 5, -12],\n [0, 0, 0, 0, 0, -15, 11],\n [0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1067", "dataset": "MATH"}570{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, -11, -2, 10, 10, 2, -5],\n [-11, 15, 11, -12, 9, 7, 4],\n [-2, 11, 16, 6, 14, -3, -2],\n [10, -12, 6, 8, 0, -1, -6],\n [10, 9, 14, 0, -9, 6, 3],\n [2, 7, -3, -1, 6, -15, 4],\n [-5, 4, -2, -6, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}571{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[-6, -6, 6, -14, 10, 14, 5],\n [-9, 6, -9, -3, 9, -7, 13],\n [10, 8, 7, -16, 7, -18, 16],\n [8, -15, 0, 3, -13, -10, -8],\n [3, -10, 10, -9, 15, 12, 3],\n [-15, -17, -14, -4, 0, -4, -11],\n [1, -7, -15, 17, -4, -18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-271", "dataset": "MATH"}572{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 4, 7, -1, 14, -5, -18],\n [-6, -4, 18, -14, -5, -5, -14],\n [-8, 13, -14, 17, -4, -12, -14],\n [11, -4, 11, -5, 5, 5, 16],\n [-14, -7, 1, -14, 17, 2, -16],\n [10, 6, 8, 17, 3, 16, -18],\n [-16, 5, -11, -1, -16, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}573{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -18, 7, -7, 2, -6, -7],\n [-6, -1, 0, 0, -13, -12, -12],\n [9, 9, 0, -3, -2, 3, 0],\n [10, 0, 16, 6, 1, 18, 0],\n [-6, -7, -4, -15, -4, -2, 8],\n [-8, 4, -4, 12, 7, -12, -6],\n [-6, 1, 15, -9, 18, 8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}574{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[17, -3, 2, -3, -2, -4, -6],\n [0, -14, 8, -18, 11, 4, -4],\n [0, 0, 11, -3, -1, 7, -2],\n [0, 0, 0, -2, 8, 18, 3],\n [0, 0, 0, 0, -11, 8, 13],\n [0, 0, 0, 0, 0, -4, -6],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "814", "dataset": "MATH"}575{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[4, 15, 11, -9, -18, 3, 14],\n [0, 3, -3, 11, -1, 5, -14],\n [0, 0, 8, -7, -9, 15, 14],\n [0, 0, 0, 8, -12, 17, 8],\n [0, 0, 0, 0, -16, 10, -5],\n [0, 0, 0, 0, 0, 9, -12],\n [0, 0, 0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205", "dataset": "MATH"}576{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, 17, 13, 9, 9, 13, -11],\n [0, 1, 14, 11, 18, -3, 6],\n [0, 0, -11, 14, 18, -18, 12],\n [0, 0, 0, -5, 4, -10, -11],\n [0, 0, 0, 0, -17, -10, -18],\n [0, 0, 0, 0, 0, 14, 9],\n [0, 0, 0, 0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154171", "dataset": "MATH"}577{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 4, 8, 2, 6, -8, 4],\n [4, 9, -9, -7, 10, -2, 8],\n [8, -9, 8, -3, -14, -2, -4],\n [2, -7, -3, 7, -2, 0, 2],\n [6, 10, -14, -2, -14, -6, 0],\n [-8, -2, -2, 0, -6, -16, -9],\n [4, 8, -4, 2, 0, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1046", "dataset": "MATH"}578{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 1, 0, -4, -6, -10, -10],\n [1, -11, -6, -6, 0, 10, 0],\n [0, -6, 10, 10, 12, 8, 10],\n [-4, -6, 10, -1, -6, 11, -8],\n [-6, 0, 12, -6, 3, -4, -9],\n [-10, 10, 8, 11, -4, 4, -2],\n [-10, 0, 10, -8, -9, -2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}579{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[16, -16, 9, -4, -6, 0, -1],\n [12, 18, 2, -14, -2, 0, -15],\n [7, 5, 0, 11, 7, -8, -16],\n [3, -2, -8, 8, 10, -7, -6],\n [-8, 12, -8, 17, -17, 4, 17],\n [-5, 18, 8, -7, 10, -13, 4],\n [-9, 15, -7, 13, 7, -12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2363", "dataset": "MATH"}580{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[14, -1, 16, 1, 12, -14, 13],\n [0, -18, -12, 3, 15, -9, 7],\n [13, 8, -7, 4, -5, 15, -2],\n [-13, 8, -11, 14, 16, -2, 7],\n [-12, 5, 6, 16, 7, -14, 16],\n [11, 6, 5, 11, 1, -16, 13],\n [-11, 4, -3, 16, 6, -4, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49", "dataset": "MATH"}581{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[15, -6, -8, -9, -7, 4, 6],\n [-6, 4, -12, 10, -6, 10, -16],\n [-8, -12, -13, 4, 13, -4, 5],\n [-9, 10, 4, 15, 12, -6, 10],\n [-7, -6, 13, 12, 11, 4, -8],\n [4, 10, -4, -6, 4, 10, 0],\n [6, -16, 5, 10, -8, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}582{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 18, -14, 7, -13, -3, -18],\n [-10, 2, -12, -4, 5, -14, 10],\n [-8, -15, -9, 15, -15, -9, 14],\n [-1, -7, 4, 6, 18, -15, -6],\n [-1, 10, 11, 9, -12, 5, -9],\n [18, 8, 2, 17, 10, -12, -6],\n [4, 6, -6, 18, 11, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}583{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-18, -1, 2, 5, -2, -10, 9],\n [0, -6, 9, -2, -10, 2, 11],\n [0, 0, 17, 6, -12, 1, 16],\n [0, 0, 0, -5, -14, 15, 5],\n [0, 0, 0, 0, 2, 18, 13],\n [0, 0, 0, 0, 0, 12, 7],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}584{"messages": [{"content": "Find the value at position (1, 2) of the inverse of matrix 1/252 * A where A =\n[[16, 10, -10, 4, 10, -9, 2],\n [10, 7, -12, -10, 0, -10, -8],\n [-10, -12, 12, -2, 3, -1, 7],\n [4, -10, -2, -14, 9, 6, -3],\n [10, 0, 3, 9, 10, 6, 15],\n [-9, -10, -1, 6, 6, -17, -2],\n [2, -8, 7, -3, 15, -2, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}585{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-18, 8, 5, 3, -5, -11, 8],\n [0, 14, 2, 13, 13, 5, -8],\n [0, 0, -1, -8, 8, -18, 10],\n [0, 0, 0, -12, 12, 8, 13],\n [0, 0, 0, 0, 1, 18, -2],\n [0, 0, 0, 0, 0, 3, -5],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-607", "dataset": "MATH"}586{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -9, -16, 4, 0, 6, -16],\n [-9, -7, -2, 3, -4, 4, -10],\n [-16, -2, 18, 1, -4, 4, -6],\n [4, 3, 1, 13, -10, -10, -5],\n [0, -4, -4, -10, 17, -8, 7],\n [6, 4, 4, -10, -8, 5, -10],\n [-16, -10, -6, -5, 7, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}587{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-13, -16, -13, -2, 16, 18, 16],\n [4, -11, -12, -9, 7, -9, 0],\n [4, 12, 14, -17, 9, 13, 14],\n [-10, 10, -4, -1, -1, -12, -5],\n [10, 0, -14, -14, -4, 7, 5],\n [0, 1, -10, 9, -3, -8, 15],\n [6, 2, -14, -8, -10, -8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}588{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 7, -9, 0, -3, 18, -15],\n [-5, 11, -12, -7, 5, 3, 11],\n [1, 7, -14, -13, 15, -14, -9],\n [9, -16, -6, -17, 16, 9, 18],\n [4, 4, 16, 13, -17, -3, -3],\n [-16, 9, 10, 1, 17, 14, 3],\n [-11, 5, 18, 1, -7, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}589{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 11, 12, 3, -4, 18, 9],\n [-8, -5, -8, -10, 5, -9, 18],\n [13, 1, -5, -15, 5, 13, -9],\n [-3, 13, -1, 6, -12, -1, -1],\n [-16, -18, 14, -12, -9, -11, 13],\n [4, -2, -5, -2, 6, 2, -13],\n [1, 1, 7, 13, -11, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}590{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 7) of the inverse. Round your answer to the nearest integer:\n[[-1, -8, -11, 3, 3, 12, -17],\n [-8, 16, -11, 1, 0, -4, 2],\n [-11, -11, -11, 14, 10, 8, 18],\n [3, 1, 14, 6, 14, -4, -4],\n [3, 0, 10, 14, -4, -10, -10],\n [12, -4, 8, -4, -10, 0, 1],\n [-17, 2, 18, -4, -10, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}591{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-14, 8, -2, 2, 2, -13, -2],\n [8, 15, -5, -7, -12, 8, 8],\n [-2, -5, -13, -3, 14, -6, 0],\n [2, -7, -3, -14, 2, 4, -2],\n [2, -12, 14, 2, 16, 6, -2],\n [-13, 8, -6, 4, 6, 11, -14],\n [-2, 8, 0, -2, -2, -14, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5378", "dataset": "MATH"}592{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-9, 3, 5, -11, -13, -12, 1],\n [-2, 17, -11, -6, 5, 12, 4],\n [-2, 5, -9, 12, 1, -3, -5],\n [-16, 11, -1, -13, 1, 16, 0],\n [7, 16, -7, -11, 18, -9, 2],\n [10, 12, -12, 15, 15, 11, -15],\n [11, 6, -5, 5, 12, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}593{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 2, 3, -2, -14, -13, -9],\n [0, -12, -15, 18, 0, 9, 1],\n [0, 0, -16, 6, -17, -4, -16],\n [0, 0, 0, 8, -14, -2, -7],\n [0, 0, 0, 0, 11, 3, 13],\n [0, 0, 0, 0, 0, 1, -12],\n [0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2374", "dataset": "MATH"}594{"messages": [{"content": "Find the value at position (6, 5) of the inverse of matrix 1/252 * A where A =\n[[-5, 12, 7, 0, -14, -13, 16],\n [-3, 12, -1, -5, 6, -4, 7],\n [17, -8, 18, 18, -12, -1, 1],\n [-17, 7, 4, 13, -6, -6, -2],\n [6, 3, 8, -2, 7, -5, -5],\n [-7, -14, 18, -15, 10, 6, -15],\n [-3, -17, 4, -15, 1, -2, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}595{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 1, 15, 5, -1, 11, -18],\n [0, 10, 13, -17, 17, -2, -17],\n [0, 0, -18, 4, -13, -3, -17],\n [0, 0, 0, 9, 16, -15, -12],\n [0, 0, 0, 0, 18, -17, 5],\n [0, 0, 0, 0, 0, -18, -10],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-393", "dataset": "MATH"}596{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-15, -11, -18, 17, -12, 6, 10],\n [-18, -1, -15, 1, -11, 8, 16],\n [6, -5, 12, -14, -2, -9, -3],\n [-15, -14, 1, -13, -8, -2, -16],\n [-3, 17, 7, 5, 15, 1, -2],\n [1, -3, -15, -1, 17, 16, 11],\n [-1, 2, 13, -14, 4, 11, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}597{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -5, 2, 15, 7, 6, 12],\n [0, -15, 5, 12, 0, -8, 10],\n [0, 0, -16, -8, 2, 11, 0],\n [0, 0, 0, 7, -14, 0, 8],\n [0, 0, 0, 0, -1, 10, -16],\n [0, 0, 0, 0, 0, -15, 9],\n [0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7529", "dataset": "MATH"}598{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[13, 11, -18, 13, 1, 2, 0],\n [0, 9, 13, 11, 4, 8, 18],\n [0, 0, 12, -17, -9, 0, 12],\n [0, 0, 0, -2, 4, -1, -8],\n [0, 0, 0, 0, 9, 16, 2],\n [0, 0, 0, 0, 0, 3, -10],\n [0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2461", "dataset": "MATH"}599{"messages": [{"content": "Find the value at position (3, 6) of the inverse of matrix 1/252 * A where A =\n[[15, -17, -2, -5, -2, 11, 10],\n [0, -10, 4, 17, -5, 1, -2],\n [0, 0, 11, 8, 8, 12, 7],\n [0, 0, 0, -4, 11, 6, -8],\n [0, 0, 0, 0, -11, 7, -13],\n [0, 0, 0, 0, 0, 15, 4],\n [0, 0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}600{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, 8, 8, 8, -9, -12, 1],\n [8, 12, 0, 4, 3, -14, 3],\n [8, 0, 10, 3, -9, -1, 2],\n [8, 4, 3, -10, 0, 0, 10],\n [-9, 3, -9, 0, 7, -9, 8],\n [-12, -14, -1, 0, -9, -1, -2],\n [1, 3, 2, 10, 8, -2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1279", "dataset": "MATH"}601{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[13, 12, 8, -14, 2, 6, 6],\n [12, -12, 0, -2, 0, 12, 6],\n [8, 0, -18, -10, -12, 2, -9],\n [-14, -2, -10, 11, 4, -11, 11],\n [2, 0, -12, 4, -4, 8, -10],\n [6, 12, 2, -11, 8, -5, 11],\n [6, 6, -9, 11, -10, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-77", "dataset": "MATH"}602{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 11, -16, -5, -8, 4, 13],\n [0, -18, -10, -10, -7, -18, -3],\n [0, 0, -9, 14, 3, -3, 0],\n [0, 0, 0, 7, 1, 1, -14],\n [0, 0, 0, 0, 15, -6, 6],\n [0, 0, 0, 0, 0, -3, -5],\n [0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-361", "dataset": "MATH"}603{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, 8, 8, 6, -10, 0, -8],\n [8, 1, 6, -14, 2, 14, -2],\n [8, 6, 12, 8, 4, 3, 2],\n [6, -14, 8, -6, -10, -6, -10],\n [-10, 2, 4, -10, 5, -14, 2],\n [0, 14, 3, -6, -14, -17, 4],\n [-8, -2, 2, -10, 2, 4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}604{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[6, 1, 2, 6, 2, 8, -10],\n [1, 3, -4, 8, 0, 8, 0],\n [2, -4, -16, -12, 10, -6, 0],\n [6, 8, -12, 14, -3, 10, 2],\n [2, 0, 10, -3, -16, -8, -8],\n [8, 8, -6, 10, -8, 3, -6],\n [-10, 0, 0, 2, -8, -6, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1634", "dataset": "MATH"}605{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-7, 9, 15, -13, 0, -7, 6],\n [0, -2, -7, -16, 5, -11, 17],\n [0, 0, 13, 13, -18, -16, -18],\n [0, 0, 0, -4, 18, 2, 4],\n [0, 0, 0, 0, 7, 3, 17],\n [0, 0, 0, 0, 0, 8, -15],\n [0, 0, 0, 0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9884", "dataset": "MATH"}606{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-3, -9, -9, 17, 2, -5, -11],\n [0, -3, 7, -13, -17, -10, -14],\n [0, 0, -14, -14, -2, -10, 15],\n [0, 0, 0, -4, -18, -12, 4],\n [0, 0, 0, 0, -6, -6, -17],\n [0, 0, 0, 0, 0, 15, -3],\n [0, 0, 0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-292", "dataset": "MATH"}607{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[0, -6, -2, 2, 5, -1, -1],\n [-6, 11, -2, 12, 0, 7, -10],\n [-2, -2, 18, -8, -8, 6, 10],\n [2, 12, -8, -1, 3, 0, 0],\n [5, 0, -8, 3, 16, 6, 11],\n [-1, 7, 6, 0, 6, -16, -6],\n [-1, -10, 10, 0, 11, -6, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1695", "dataset": "MATH"}608{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -1, -14, -14, -11, -10, 13],\n [0, -6, -1, -15, 3, 1, -4],\n [0, 0, 15, 11, -14, -18, 12],\n [0, 0, 0, -9, 10, 12, -8],\n [0, 0, 0, 0, 4, 14, 18],\n [0, 0, 0, 0, 0, 6, -6],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}609{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-15, -1, 0, 0, 15, 4, 6],\n [-1, 2, -6, -2, -8, -12, -4],\n [0, -6, -7, 2, -4, -10, 3],\n [0, -2, 2, 9, -1, 2, 13],\n [15, -8, -4, -1, -1, -12, 2],\n [4, -12, -10, 2, -12, 11, 10],\n [6, -4, 3, 13, 2, 10, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}610{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -6, 4, 12, -3, 7, -1],\n [-6, -6, -4, -11, -4, 2, 3],\n [4, -4, 9, -14, -13, -14, 6],\n [12, -11, -14, -18, -2, 11, 2],\n [-3, -4, -13, -2, 15, 4, 4],\n [7, 2, -14, 11, 4, -15, 0],\n [-1, 3, 6, 2, 4, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}611{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[10, 6, -1, -16, -1, -12, 9],\n [-2, 6, -1, -16, 6, -12, -9],\n [0, -4, 2, 2, 18, 9, 13],\n [8, 4, -9, -13, 5, -1, -9],\n [-4, 15, -11, 16, 8, 6, -16],\n [2, 13, 2, -10, -18, -15, -15],\n [7, 15, 8, -4, 13, -12, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}612{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -18, 9, 1, -8, -4, 14],\n [-18, 13, -12, -2, 0, 12, -2],\n [9, -12, -4, -8, -1, -1, -1],\n [1, -2, -8, -11, 2, 2, -3],\n [-8, 0, -1, 2, -9, -10, 0],\n [-4, 12, -1, 2, -10, -16, 15],\n [14, -2, -1, -3, 0, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}613{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -2, 0, 4, 2, 10, -8],\n [-2, -7, 0, 0, 14, 0, -6],\n [0, 0, 3, 9, 8, -9, 0],\n [4, 0, 9, -13, 9, 4, 12],\n [2, 14, 8, 9, -13, -16, 4],\n [10, 0, -9, 4, -16, -2, 8],\n [-8, -6, 0, 12, 4, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}614{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, -2, 6, 11, 10, 10, -1],\n [12, 0, -2, -13, -7, -16, 16],\n [14, 10, -16, -14, -5, 17, 9],\n [13, -1, -6, -17, 6, 1, -12],\n [-8, -14, 10, -1, -11, 8, -17],\n [16, 7, 4, -14, -3, -8, 0],\n [-3, 13, -7, -17, 3, 7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}615{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, -14, 6, 0, -8, -2, -8],\n [-14, -6, -7, 3, -18, 10, 10],\n [6, -7, 13, 0, -15, 0, 12],\n [0, 3, 0, -11, -16, 8, 3],\n [-8, -18, -15, -16, -16, -1, 2],\n [-2, 10, 0, 8, -1, 1, -2],\n [-8, 10, 12, 3, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}616{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, 18, 6, 10, 12, -17, -7],\n [-14, 8, 15, -5, -12, 18, 17],\n [-9, 10, -3, 2, 14, 10, -2],\n [-6, -13, -17, -11, 13, 17, -10],\n [4, -12, 12, 2, -18, -17, -8],\n [18, -1, 5, 0, -14, 10, -17],\n [-2, -8, 18, -6, 10, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-119", "dataset": "MATH"}617{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -11, 18, -17, -2, -6, -5],\n [0, 8, 1, -7, 3, 18, 12],\n [0, 0, -10, -9, 10, 11, -17],\n [0, 0, 0, 5, -5, 6, 6],\n [0, 0, 0, 0, 5, 16, 11],\n [0, 0, 0, 0, 0, -15, 11],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-662", "dataset": "MATH"}618{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-16, -4, -9, 3, 4, -8, -3],\n [-3, -5, -13, -2, 12, -9, 1],\n [-10, -4, -17, -15, 5, -1, -8],\n [18, 7, -11, 3, -14, -17, -14],\n [16, 13, 0, -15, 4, 0, 7],\n [7, -12, 13, 14, 7, 5, 4],\n [7, 12, -13, 12, -7, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}619{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-16, -10, -2, 5, 14, 12, 0],\n [-10, -12, -8, -4, 3, -18, -2],\n [-2, -8, -14, 12, -4, 3, 4],\n [5, -4, 12, 13, -2, -5, 8],\n [14, 3, -4, -2, -5, -8, 4],\n [12, -18, 3, -5, -8, -12, -6],\n [0, -2, 4, 8, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42", "dataset": "MATH"}620{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 7) of the inverse. Round your answer to the nearest integer:\n[[-1, 8, 14, 4, 10, 2, -5],\n [8, 0, 2, -6, -6, -3, -12],\n [14, 2, -9, -2, -1, 12, 4],\n [4, -6, -2, -7, 10, 3, -4],\n [10, -6, -1, 10, -10, -12, -6],\n [2, -3, 12, 3, -12, 16, -10],\n [-5, -12, 4, -4, -6, -10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}621{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-17, -4, 5, -10, 0, -6, -6],\n [-4, -9, -2, 6, 7, -10, 4],\n [5, -2, -3, -7, 2, 4, 8],\n [-10, 6, -7, -2, 9, -4, 16],\n [0, 7, 2, 9, -17, -2, -18],\n [-6, -10, 4, -4, -2, -14, 8],\n [-6, 4, 8, 16, -18, 8, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}622{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-18, -8, -1, 8, -9, 17, 2],\n [0, -18, -5, 1, -10, 8, -15],\n [0, 0, 12, -9, -10, 9, 9],\n [0, 0, 0, -11, 4, -14, -12],\n [0, 0, 0, 0, 14, 2, -2],\n [0, 0, 0, 0, 0, -16, 15],\n [0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}623{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, -8, 7, -6, 0, 6, 2],\n [-8, -4, 1, -12, 6, -2, 2],\n [7, 1, -9, 5, -2, -16, 5],\n [-6, -12, 5, 0, -11, -12, 3],\n [0, 6, -2, -11, -4, 2, -14],\n [6, -2, -16, -12, 2, 14, -13],\n [2, 2, 5, 3, -14, -13, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-737", "dataset": "MATH"}624{"messages": [{"content": "Find the value at position (5, 2) of the inverse of matrix 1/252 * A where A =\n[[-16, -16, -13, -9, -6, -7, 8],\n [-11, -14, 17, 11, 18, 10, 3],\n [-5, -9, -8, 16, 4, -11, 2],\n [18, 9, 12, 9, 8, 2, -10],\n [10, -4, 14, 18, 17, 9, -9],\n [4, 9, 15, -14, -1, -13, 4],\n [9, -6, 6, -12, -17, -3, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}625{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, -17, -9, -5, 8, -4, 2],\n [0, 14, 3, -1, -17, 10, -12],\n [0, 0, -10, -11, 14, -14, -5],\n [0, 0, 0, 4, 8, -4, 11],\n [0, 0, 0, 0, -11, 10, -7],\n [0, 0, 0, 0, 0, 9, 7],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}626{"messages": [{"content": "Find the value at position (4, 7) of the inverse of matrix 1/252 * A where A =\n[[-18, -4, 1, 8, 6, 3, 0],\n [-4, -15, -12, 1, 0, 0, -16],\n [1, -12, -5, 10, -12, 3, 8],\n [8, 1, 10, -5, -8, 5, 6],\n [6, 0, -12, -8, 0, -1, 2],\n [3, 0, 3, 5, -1, 11, 0],\n [0, -16, 8, 6, 2, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}627{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[4, 2, 17, 11, 2, 4, 2],\n [0, -6, 3, -12, 5, -14, 7],\n [0, 0, -8, 11, -15, -17, -6],\n [0, 0, 0, -6, 10, -3, -16],\n [0, 0, 0, 0, -13, 9, 17],\n [0, 0, 0, 0, 0, 6, 10],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}628{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-11, 5, 12, 0, -9, -2, 2],\n [5, 9, -1, 0, -5, -8, -2],\n [12, -1, -13, 10, 1, -2, 2],\n [0, 0, 10, -10, 1, -7, 6],\n [-9, -5, 1, 1, 5, 14, 6],\n [-2, -8, -2, -7, 14, 5, 3],\n [2, -2, 2, 6, 6, 3, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}629{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 13, 6, -16, 7, 17, -2],\n [0, 3, 16, -12, -16, -13, -6],\n [0, 0, 14, -4, -5, 0, 9],\n [0, 0, 0, -9, -12, -18, -4],\n [0, 0, 0, 0, 17, -3, 10],\n [0, 0, 0, 0, 0, 4, 3],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166", "dataset": "MATH"}630{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[-12, -15, 18, -14, -17, -14, -16],\n [-11, 7, -9, 15, 17, -7, 1],\n [10, -5, -14, 8, -15, 10, -16],\n [14, 11, 17, -10, -18, 4, -16],\n [13, 5, -13, -6, -4, 11, -7],\n [16, 9, -15, -12, -3, 3, 6],\n [-16, 3, 12, 18, 3, 8, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}631{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -2, 1, 5, 12, -11, -14],\n [-17, -15, 16, 15, -16, 1, -10],\n [-13, -14, 16, 12, -6, 7, 3],\n [13, -4, -8, -3, -13, -8, -9],\n [-3, -7, -12, 8, 5, -4, -13],\n [0, -11, 17, -6, 14, 13, 9],\n [-9, 14, -18, 2, -14, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-110", "dataset": "MATH"}632{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, 1, -10, -3, 9, 17, 5],\n [0, -5, 15, 5, -8, 17, -18],\n [0, 0, -10, -16, -3, -15, 7],\n [0, 0, 0, 8, -17, -9, 6],\n [0, 0, 0, 0, -2, -3, -1],\n [0, 0, 0, 0, 0, -4, 10],\n [0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-163", "dataset": "MATH"}633{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 15, -5, 6, -7, 1, -12],\n [0, -10, -15, 12, 4, -13, 9],\n [0, 0, 5, 15, 0, 5, 1],\n [0, 0, 0, -18, 17, -12, 1],\n [0, 0, 0, 0, 8, 9, 6],\n [0, 0, 0, 0, 0, -4, 2],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2193", "dataset": "MATH"}634{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/252 * A where A =\n[[-12, -4, -2, -10, -6, 13, -17],\n [0, 1, 0, 8, 17, 11, -8],\n [0, 0, 11, -17, 15, 3, 12],\n [0, 0, 0, 7, -1, -4, 15],\n [0, 0, 0, 0, 16, -6, -6],\n [0, 0, 0, 0, 0, -3, 11],\n [0, 0, 0, 0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}635{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[0, -2, -16, -16, 9, 12, -11],\n [-2, 16, 17, 8, 14, -8, 2],\n [-13, 2, 9, -2, -1, -8, 6],\n [11, 6, -12, 18, 8, 7, -6],\n [5, -7, -5, -10, 12, -15, 0],\n [-18, 10, -13, -18, 6, 8, 3],\n [-2, 10, -16, -2, -17, 13, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}636{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[14, 3, -15, -6, 4, -6, 1],\n [0, 15, 10, 13, -8, -1, 2],\n [0, 0, -12, 8, -12, -17, 14],\n [0, 0, 0, -7, -6, -16, -11],\n [0, 0, 0, 0, 13, -13, 8],\n [0, 0, 0, 0, 0, -7, 6],\n [0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}637{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[-14, -15, -11, -3, -18, -4, 5],\n [0, -13, -17, -14, 15, 13, 10],\n [0, 0, 12, 5, -4, -7, 1],\n [0, 0, 0, 4, -12, -7, -4],\n [0, 0, 0, 0, -12, 11, -1],\n [0, 0, 0, 0, 0, 10, 15],\n [0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}638{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, 1, -12, 4, -4, -4, -5],\n [1, 15, 8, -1, -6, 0, 10],\n [-12, 8, -10, -16, 8, 4, 2],\n [4, -1, -16, -4, 2, 8, -8],\n [-4, -6, 8, 2, -3, -6, -2],\n [-4, 0, 4, 8, -6, -11, -8],\n [-5, 10, 2, -8, -2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}639{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (3, 7) of the inverse. Round your answer to the nearest integer:\n[[13, -1, -8, -8, 0, 4, -12],\n [-1, 11, -8, 0, -2, 3, -4],\n [-8, -8, 11, 2, 2, 2, 1],\n [-8, 0, 2, -11, 12, 0, -14],\n [0, -2, 2, 12, 3, 14, -12],\n [4, 3, 2, 0, 14, -8, -12],\n [-12, -4, 1, -14, -12, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}640{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[3, -7, 16, -2, -16, -8, -13],\n [0, -2, 3, -18, -16, -3, 16],\n [0, 0, 7, 12, 5, 0, 18],\n [0, 0, 0, -1, -18, 10, -6],\n [0, 0, 0, 0, -3, 6, -9],\n [0, 0, 0, 0, 0, -7, -11],\n [0, 0, 0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39889", "dataset": "MATH"}641{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 2) of the inverse. Round your answer to the nearest integer:\n[[-16, -17, 10, 15, -5, 14, -1],\n [0, -17, -8, 12, -6, 7, 15],\n [0, 0, 3, 12, 0, 5, 6],\n [0, 0, 0, 3, 9, -7, 14],\n [0, 0, 0, 0, 7, -6, 4],\n [0, 0, 0, 0, 0, -16, 11],\n [0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}642{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, -9, -17, 17, -17, -4, 1],\n [0, 11, 5, -17, 3, 10, -5],\n [0, 0, 7, -17, 15, 4, 16],\n [0, 0, 0, -2, 8, 0, 2],\n [0, 0, 0, 0, 1, -4, 16],\n [0, 0, 0, 0, 0, 1, -8],\n [0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14706", "dataset": "MATH"}643{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 7) rounded to the nearest integer?\n[[7, -5, 6, 7, 6, 6, 8],\n [0, 1, -3, 6, 8, -1, -9],\n [0, 0, -15, 4, -12, 11, 7],\n [0, 0, 0, 7, -2, 12, -11],\n [0, 0, 0, 0, -12, 8, 16],\n [0, 0, 0, 0, 0, 11, -12],\n [0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "252", "dataset": "MATH"}644{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 0, -6, -3, -4, -8, -7],\n [3, 6, -16, 5, 6, -10, 9],\n [11, -12, -8, -9, -16, 0, -17],\n [-2, 10, -17, -3, -9, -15, 7],\n [5, -7, 2, -3, 17, 16, -10],\n [-13, -18, -5, 5, -9, -1, -10],\n [8, 0, 17, -16, -10, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}645{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 1, -12, -15, -9, 2, -5],\n [0, -2, 9, -5, -6, 15, -16],\n [0, 0, 1, -11, -14, -17, 9],\n [0, 0, 0, -18, 17, -17, 7],\n [0, 0, 0, 0, -16, -13, -12],\n [0, 0, 0, 0, 0, -6, 2],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1579", "dataset": "MATH"}646{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[10, 12, -5, 6, 7, 3, -10],\n [14, 4, 16, 1, 14, 16, 11],\n [11, 3, -18, -4, 6, 1, -12],\n [-3, 4, 2, -18, 1, 0, -13],\n [13, -18, 11, -3, 8, -1, -6],\n [9, -9, -5, 10, -8, 8, -2],\n [-16, 12, 2, 14, -18, -13, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-251", "dataset": "MATH"}647{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[3, -4, 6, 12, -14, -10, 2],\n [-4, 5, 10, 15, -10, 5, -4],\n [6, 10, -17, -3, 0, 5, -3],\n [12, 15, -3, 12, 14, 3, 1],\n [-14, -10, 0, 14, 17, 0, 0],\n [-10, 5, 5, 3, 0, -9, -14],\n [2, -4, -3, 1, 0, -14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "423", "dataset": "MATH"}648{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, -8, -12, -7, -11, 9, -3],\n [0, 18, 13, 2, -1, -8, -11],\n [0, 0, 3, -10, -5, -4, -8],\n [0, 0, 0, 18, -13, 18, 14],\n [0, 0, 0, 0, 12, 7, -8],\n [0, 0, 0, 0, 0, 9, 3],\n [0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1223", "dataset": "MATH"}649{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 7) of the inverse. Round your answer to the nearest integer:\n[[-3, 6, -1, -3, 0, -3, -14],\n [0, -13, 15, -3, 4, 13, 4],\n [0, 0, 10, -11, 10, -1, -14],\n [0, 0, 0, -2, 13, -15, 12],\n [0, 0, 0, 0, 13, 1, -6],\n [0, 0, 0, 0, 0, 7, 4],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-311", "dataset": "MATH"}650{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -14, 18, -15, 1, 3, 5],\n [0, -13, 8, -9, -9, 7, 18],\n [0, 0, 9, 17, 6, 17, -6],\n [0, 0, 0, 9, 17, 11, -10],\n [0, 0, 0, 0, -14, -18, -14],\n [0, 0, 0, 0, 0, -10, -6],\n [0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3183", "dataset": "MATH"}651{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, -8, 0, 1, 8, 10, -1],\n [0, 6, 1, -13, 17, -4, -1],\n [0, 0, 3, -7, 14, 10, -17],\n [0, 0, 0, 11, 0, -9, 6],\n [0, 0, 0, 0, -11, -17, -1],\n [0, 0, 0, 0, 0, -17, 17],\n [0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}652{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-12, 2, 10, 18, -5, 18, -15],\n [0, -8, 15, -3, -10, -3, -3],\n [0, 0, -6, -14, -1, 1, -17],\n [0, 0, 0, 10, -3, 9, -2],\n [0, 0, 0, 0, 17, 7, -8],\n [0, 0, 0, 0, 0, -13, -7],\n [0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-213", "dataset": "MATH"}653{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[5, 18, 0, -14, 11, 6, 11],\n [6, -10, 8, 5, -4, 7, 11],\n [-8, 10, -4, -10, 10, -4, -2],\n [-3, 3, -8, 6, 11, -17, -18],\n [18, -10, -14, 5, 8, 11, -4],\n [-10, 18, 11, -4, 1, 6, -10],\n [3, -6, 18, 9, -5, 11, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}654{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-7, 16, -18, -18, 1, 15, 15],\n [0, 9, -8, -11, 16, -3, -3],\n [0, 0, -8, -11, 1, 13, 14],\n [0, 0, 0, -5, -16, -17, 3],\n [0, 0, 0, 0, -13, -11, 5],\n [0, 0, 0, 0, 0, 6, -6],\n [0, 0, 0, 0, 0, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}655{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 18, 4, 7, -7, -18, 15],\n [0, 4, -12, -12, -18, -1, -11],\n [0, 0, 4, 10, -18, -4, -4],\n [0, 0, 0, -6, 2, -10, 1],\n [0, 0, 0, 0, 16, 2, 3],\n [0, 0, 0, 0, 0, 8, -2],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4408", "dataset": "MATH"}656{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-3, -1, 6, 15, -15, -14, -5],\n [-18, 3, 2, -6, 17, 10, -10],\n [14, 3, -2, 4, 17, -13, 10],\n [8, -14, -10, 5, 0, 14, 11],\n [-15, 13, -18, 15, 2, 12, -5],\n [7, 3, 15, 14, -6, 13, -11],\n [3, 1, 2, 15, 11, -13, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}657{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[8, 1, -5, -9, -4, -16, -4],\n [12, -8, 0, -4, 1, 3, -12],\n [-5, -15, -10, 6, 16, 18, 8],\n [9, 5, 14, 14, -3, 4, -8],\n [0, 15, 4, -9, 18, -18, -17],\n [3, -2, 5, 2, 10, -5, -11],\n [11, 3, 4, -6, 9, 11, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}658{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, -10, -5, -9, 14, -8, -13],\n [0, 17, -13, -9, -14, 0, -12],\n [0, 0, -8, -16, 11, -13, 16],\n [0, 0, 0, 8, 10, -11, 4],\n [0, 0, 0, 0, -11, 14, -14],\n [0, 0, 0, 0, 0, -5, 1],\n [0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1055", "dataset": "MATH"}659{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-10, -12, 0, -2, 12, -10, -15],\n [-12, 12, -15, 0, 9, -5, -12],\n [0, -15, -4, -10, -8, -9, 4],\n [-2, 0, -10, -6, -4, -4, -4],\n [12, 9, -8, -4, 16, -10, 6],\n [-10, -5, -9, -4, -10, -9, 10],\n [-15, -12, 4, -4, 6, 10, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}660{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[13, -10, -2, 16, -3, -17, 12],\n [0, 14, 2, -2, 16, -12, 10],\n [0, 0, -1, -3, -13, -17, -9],\n [0, 0, 0, 5, -14, 16, -15],\n [0, 0, 0, 0, -18, -8, 7],\n [0, 0, 0, 0, 0, 11, -13],\n [0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-136", "dataset": "MATH"}661{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 5) rounded to the nearest integer?\n[[-7, -15, 13, 16, -3, -4, -17],\n [-13, -5, 10, 7, -1, -15, 18],\n [6, 10, 15, -3, 18, 11, 4],\n [17, 9, -18, -11, -4, 15, 0],\n [11, -9, 8, 1, 6, -10, 15],\n [2, 5, -12, -15, -11, -6, 2],\n [16, -14, -11, -17, 5, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}662{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 5, 12, 4, 4, -11, 4],\n [5, -2, -11, 6, -6, 12, -10],\n [12, -11, -15, 4, 2, 0, 16],\n [4, 6, 4, -14, -8, -6, 6],\n [4, -6, 2, -8, 15, -9, 9],\n [-11, 12, 0, -6, -9, 15, -10],\n [4, -10, 16, 6, 9, -10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}663{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[1, -6, 5, -16, 8, -8, 0],\n [-6, -5, -7, -8, 8, -6, -8],\n [5, -7, 7, -14, 0, -13, 2],\n [-16, -8, -14, 17, 0, 3, -6],\n [8, 8, 0, 0, 18, 1, 6],\n [-8, -6, -13, 3, 1, -12, -10],\n [0, -8, 2, -6, 6, -10, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}664{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-9, 13, -18, 5, 10, -12, 12],\n [0, 11, 6, 9, 17, -12, 16],\n [0, 0, 11, -18, 6, 15, -11],\n [0, 0, 0, 2, 8, -9, 4],\n [0, 0, 0, 0, -15, 4, -14],\n [0, 0, 0, 0, 0, 4, 4],\n [0, 0, 0, 0, 0, 0, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1448", "dataset": "MATH"}665{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, 2, -11, 2, 0, -4, -5],\n [2, 8, -3, 4, 3, 2, -12],\n [-11, -3, 0, 0, 10, 2, -9],\n [2, 4, 0, 9, 3, 10, -10],\n [0, 3, 10, 3, -9, -10, 0],\n [-4, 2, 2, 10, -10, 8, 0],\n [-5, -12, -9, -10, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-662", "dataset": "MATH"}666{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[3, 4, -14, 18, -12, 18, 7],\n [9, -15, 13, -10, 17, 7, -8],\n [1, -4, 16, -10, 14, -8, 3],\n [-13, 18, 2, -7, -12, -17, 5],\n [7, 6, 1, -17, 16, 14, -2],\n [3, -18, 18, 11, -13, -5, 17],\n [14, -13, 7, 5, 14, -11, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1148", "dataset": "MATH"}667{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 2, -10, -9, -9, 11, 14],\n [0, 13, -2, 9, -2, -5, -9],\n [0, 0, -2, 18, 3, -1, 16],\n [0, 0, 0, -13, -4, 16, 7],\n [0, 0, 0, 0, -5, 4, -10],\n [0, 0, 0, 0, 0, -6, -10],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-223", "dataset": "MATH"}668{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 18, -14, 13, 12, -4, -16],\n [-4, -1, 2, -9, 2, 7, -16],\n [-18, 2, -8, -3, 16, 2, -8],\n [12, -18, 13, -16, 13, -14, 18],\n [-7, -5, -10, -12, -3, 9, -12],\n [-5, 13, -11, 8, -16, 8, 11],\n [15, 7, 18, 3, 13, -17, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36", "dataset": "MATH"}669{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 0, 14, -17, -16, 9, -5],\n [-4, 2, -5, -1, 1, -18, -10],\n [-10, 10, -4, 1, 11, 7, -13],\n [-2, -13, 9, -10, 8, 16, -13],\n [-15, -3, 4, 4, 10, -15, 5],\n [-13, -13, -5, -5, 16, -13, 4],\n [1, -2, 1, -13, 9, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}670{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[1, -2, 16, 18, 4, -1, 17],\n [0, -12, 17, -18, 18, 16, -16],\n [0, 0, -10, 18, 6, -7, -12],\n [0, 0, 0, -9, 4, 7, 4],\n [0, 0, 0, 0, -13, 10, 5],\n [0, 0, 0, 0, 0, 18, 9],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3733", "dataset": "MATH"}671{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-5, 10, -13, 15, -11, -17, 7],\n [-2, 5, 12, -3, 2, 7, -2],\n [-15, -15, 0, 6, -11, -1, -1],\n [-12, -2, -16, 3, -4, 12, 17],\n [7, -5, -2, -10, -12, 8, 9],\n [-7, -2, -10, -11, 8, -7, 18],\n [1, -18, -10, 5, 15, 17, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-478", "dataset": "MATH"}672{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, 4, 16, -3, -11, 8, -7],\n [0, 6, -13, -16, 5, 2, -13],\n [0, 0, 14, -16, -17, 5, 2],\n [0, 0, 0, -8, -16, 4, -18],\n [0, 0, 0, 0, -2, 1, -10],\n [0, 0, 0, 0, 0, -11, 10],\n [0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1522", "dataset": "MATH"}673{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -2, 7, -13, -2, -15, 6],\n [0, -2, 3, 9, -13, 11, -9],\n [0, 0, 7, -9, -17, -16, -8],\n [0, 0, 0, 11, -6, 11, -8],\n [0, 0, 0, 0, 7, 6, -2],\n [0, 0, 0, 0, 0, -10, -1],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1264", "dataset": "MATH"}674{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, 15, -17, -5, -1, -10, -15],\n [0, -8, 11, 8, 10, 13, 11],\n [0, 0, -9, -7, 14, 15, -1],\n [0, 0, 0, 9, -1, -10, 3],\n [0, 0, 0, 0, -6, 6, 10],\n [0, 0, 0, 0, 0, 13, -9],\n [0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1583", "dataset": "MATH"}675{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-17, 15, 1, -17, 9, -1, 16],\n [0, -16, 0, 4, 0, -1, 11],\n [0, 0, -6, 15, 5, -1, -15],\n [0, 0, 0, 17, -6, 3, 10],\n [0, 0, 0, 0, 18, -16, -15],\n [0, 0, 0, 0, 0, 15, -11],\n [0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42", "dataset": "MATH"}676{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, 16, 3, 13, 7, -13, -8],\n [0, 2, 3, -18, 2, 1, -10],\n [0, 0, 14, -18, -16, 13, 1],\n [0, 0, 0, 10, 13, -6, 12],\n [0, 0, 0, 0, 18, 14, 18],\n [0, 0, 0, 0, 0, 18, -7],\n [0, 0, 0, 0, 0, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2372", "dataset": "MATH"}677{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-2, -3, 0, -10, -3, 10, 4],\n [-3, 13, 5, -6, 12, 4, 8],\n [0, 5, 11, 8, 6, -8, 1],\n [-10, -6, 8, -15, 15, 5, 11],\n [-3, 12, 6, 15, -11, -14, 3],\n [10, 4, -8, 5, -14, 9, 0],\n [4, 8, 1, 11, 3, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131", "dataset": "MATH"}678{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[-11, -4, -11, 10, 16, -5, 13],\n [-12, 14, 16, 8, -18, -13, -17],\n [-12, -11, 10, -3, 10, 12, 3],\n [-9, -15, 6, -6, -2, -11, 4],\n [-12, 13, 5, -18, 17, 8, -13],\n [12, -7, 7, 6, -15, -13, -6],\n [6, 12, 3, 16, 2, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}679{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[18, 7, -2, 16, -11, -8, 5],\n [-11, 11, -18, 15, 1, 17, 15],\n [15, -6, -13, 17, 6, 8, 12],\n [-16, 9, -15, -2, 15, 1, -6],\n [-14, 5, -2, 12, 9, -18, -17],\n [14, 10, -15, -1, 5, 13, -10],\n [-3, 2, 11, -16, 14, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}680{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-13, -14, 10, 18, 17, 2, -7],\n [4, -5, -9, 8, -17, -5, -12],\n [-2, 1, -11, 1, 17, -14, -6],\n [-2, -13, 0, 6, -16, 9, 7],\n [-11, -4, -18, 4, 17, -3, -15],\n [-11, 17, -9, 11, 17, -3, 11],\n [-9, -8, 15, -3, 0, -15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}681{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[16, 15, 7, -13, 14, 8, -7],\n [-11, -10, -18, -14, -12, -1, 5],\n [7, -9, -7, 3, 8, -16, -1],\n [-14, -5, 6, 12, 2, 1, -5],\n [1, 18, 11, 1, -12, -14, 12],\n [10, -4, 6, -6, 5, -4, 5],\n [7, 0, 5, 0, -2, -14, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}682{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, -9, 2, 6, -13, 11, 10],\n [-8, -8, 8, 0, 3, 9, -15],\n [18, 0, -2, 17, 4, 9, -8],\n [-5, -6, 5, -3, 9, 11, 8],\n [-2, 7, -12, 16, -4, -3, 2],\n [-2, 7, 16, 1, 1, 4, -14],\n [-10, 4, -1, 10, -8, -11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}683{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-17, -2, 9, -12, -2, 0, 14],\n [-2, -5, -2, 0, 8, 6, 4],\n [9, -2, -7, 12, -9, 8, 5],\n [-12, 0, 12, -18, -8, 8, -4],\n [-2, 8, -9, -8, -10, -9, 9],\n [0, 6, 8, 8, -9, -1, -3],\n [14, 4, 5, -4, 9, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}684{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -5, 0, 7, -9, -2, 15],\n [0, 7, 15, 0, 5, 12, -13],\n [0, 0, 3, -12, 14, -13, -3],\n [0, 0, 0, -5, 17, -4, -14],\n [0, 0, 0, 0, 5, -1, -15],\n [0, 0, 0, 0, 0, 2, -13],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}685{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-9, -17, 12, 9, -3, -18, 3],\n [0, 12, 3, 15, -7, 4, 9],\n [0, 0, 4, -18, -17, 12, -17],\n [0, 0, 0, -13, 0, -2, -13],\n [0, 0, 0, 0, 4, -14, -9],\n [0, 0, 0, 0, 0, -14, -6],\n [0, 0, 0, 0, 0, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393", "dataset": "MATH"}686{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[7, -9, -10, -18, -3, -6, -5],\n [4, -1, 9, 1, -18, -7, 8],\n [-6, -15, 6, -13, 3, 17, -16],\n [-4, -8, 15, 8, 4, -2, 4],\n [15, 2, 14, -14, -2, -18, -12],\n [-16, 7, -3, -3, -5, 7, 8],\n [-2, -15, -2, 14, 11, 2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-177", "dataset": "MATH"}687{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-8, 11, -1, 1, 15, 9, -10],\n [12, -3, 12, 10, -6, 4, -5],\n [-17, -7, 9, 13, 5, 18, 10],\n [-1, -16, -6, -6, 10, -17, 9],\n [-15, -14, -14, -11, 15, 6, 8],\n [-12, 17, 13, 2, -1, -17, -14],\n [9, 12, 5, 14, -7, -10, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-41", "dataset": "MATH"}688{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[4, 3, 17, -9, 9, 16, 10],\n [0, -15, -4, 11, 7, 4, 10],\n [0, 0, -1, 16, 14, -12, 15],\n [0, 0, 0, 8, -13, -11, 2],\n [0, 0, 0, 0, 9, -13, -7],\n [0, 0, 0, 0, 0, 16, -17],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25478", "dataset": "MATH"}689{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-15, -17, 9, -5, 10, -17, 15],\n [0, 1, 11, 7, 1, -18, -18],\n [0, 0, 4, -8, -4, -5, -18],\n [0, 0, 0, 7, -16, -13, 6],\n [0, 0, 0, 0, 4, -3, 13],\n [0, 0, 0, 0, 0, -1, 2],\n [0, 0, 0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}690{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, 2, -12, 1, -16, 17, 0],\n [0, -8, -6, 14, -17, 4, 1],\n [0, 0, -17, 11, 6, -15, -18],\n [0, 0, 0, 5, 5, 13, 6],\n [0, 0, 0, 0, -7, -7, 15],\n [0, 0, 0, 0, 0, -16, -18],\n [0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1315", "dataset": "MATH"}691{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, 16, 9, 14, -1, -5, -10],\n [0, -16, 15, 14, 8, -10, -6],\n [0, 0, 7, -14, 8, -4, 9],\n [0, 0, 0, -13, -8, -3, 14],\n [0, 0, 0, 0, -9, -6, -18],\n [0, 0, 0, 0, 0, -14, 13],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "633", "dataset": "MATH"}692{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-14, -15, 17, 2, 14, 7, -8],\n [0, 3, 18, -12, -6, 1, -4],\n [0, 0, 6, 10, 9, -5, -15],\n [0, 0, 0, 10, -2, 17, 0],\n [0, 0, 0, 0, 4, -1, 7],\n [0, 0, 0, 0, 0, 7, -7],\n [0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}693{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 6, 6, 4, -1, 7, -6],\n [6, 7, -11, 7, 11, -6, 7],\n [6, -11, 10, -3, -1, 4, -4],\n [4, 7, -3, 8, -4, -3, 0],\n [-1, 11, -1, -4, 5, -7, 6],\n [7, -6, 4, -3, -7, 7, 6],\n [-6, 7, -4, 0, 6, 6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}694{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[18, -8, 4, -10, -1, 17, 17],\n [9, 0, 11, -4, -7, -17, -10],\n [16, -18, 12, 9, 18, -12, -3],\n [-5, 14, -13, 2, -9, 13, -13],\n [-17, 8, -5, 4, 2, 11, 6],\n [5, -8, 16, -15, 18, 17, -6],\n [-10, 9, -3, -13, 8, -9, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}695{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[2, 7, -16, 16, -12, 8, 14],\n [-15, 7, -11, 1, -2, -14, -10],\n [-11, -12, 18, 17, -16, -11, -14],\n [-14, -2, 8, -7, 9, -15, 9],\n [6, 17, -16, 12, 18, -7, 18],\n [18, -15, 11, 8, 3, -18, 1],\n [-1, -13, -7, -2, 3, -1, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}696{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, -1, 2, -1, 1, 12, 6],\n [-1, -14, -2, -4, -10, -4, 2],\n [2, -2, -9, -1, -2, 2, -4],\n [-1, -4, -1, 12, -8, -6, 6],\n [1, -10, -2, -8, -4, -3, -5],\n [12, -4, 2, -6, -3, -17, 4],\n [6, 2, -4, 6, -5, 4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}697{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[11, -14, 1, 8, 10, -8, -2],\n [-14, 9, -4, -5, -10, 0, 9],\n [1, -4, -17, 6, -13, 3, 14],\n [8, -5, 6, -5, -12, -6, 4],\n [10, -10, -13, -12, 5, 0, 5],\n [-8, 0, 3, -6, 0, -1, 0],\n [-2, 9, 14, 4, 5, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}698{"messages": [{"content": "Find the value at position (1, 3) of the inverse of matrix 1/252 * A where A =\n[[16, -15, -1, 5, 8, 14, 6],\n [0, -1, 1, 16, -13, 8, 9],\n [0, 0, 9, 0, 2, 12, -12],\n [0, 0, 0, 17, -2, 7, 9],\n [0, 0, 0, 0, 15, 4, 11],\n [0, 0, 0, 0, 0, 18, -15],\n [0, 0, 0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}699{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 6, 5, 18, 12, 15, -5],\n [0, -15, 4, -14, 8, -5, -12],\n [0, 0, -17, 1, 10, 7, -18],\n [0, 0, 0, -10, 11, 0, -11],\n [0, 0, 0, 0, 13, 18, 15],\n [0, 0, 0, 0, 0, 4, -18],\n [0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2442", "dataset": "MATH"}700{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, -10, -16, -2, 15, 13, -10],\n [0, 1, -14, 2, -14, -15, -11],\n [0, 0, 18, 13, -2, 9, -13],\n [0, 0, 0, -18, -16, -6, 12],\n [0, 0, 0, 0, -18, 18, 13],\n [0, 0, 0, 0, 0, 18, -17],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1648", "dataset": "MATH"}701{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-15, -1, 11, -8, -2, -5, 0],\n [-1, 4, -13, -6, 4, 2, -10],\n [11, -13, 9, -7, 8, 5, -2],\n [-8, -6, -7, 12, 0, 10, 4],\n [-2, 4, 8, 0, -15, 5, 1],\n [-5, 2, 5, 10, 5, -2, -2],\n [0, -10, -2, 4, 1, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2657", "dataset": "MATH"}702{"messages": [{"content": "Find the value at position (6, 7) of the inverse of matrix 1/252 * A where A =\n[[17, 12, 18, -5, -13, -12, 5],\n [0, 6, -16, 9, 4, 17, -6],\n [0, 0, 5, 18, 14, -5, 5],\n [0, 0, 0, -13, 0, -7, 7],\n [0, 0, 0, 0, -12, 2, -18],\n [0, 0, 0, 0, 0, 12, 9],\n [0, 0, 0, 0, 0, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}703{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-13, -15, 11, -1, 3, -9, 10],\n [0, -15, 0, 7, -12, -6, -16],\n [0, 0, 1, 4, 4, 13, -16],\n [0, 0, 0, -8, 14, -4, 18],\n [0, 0, 0, 0, 17, -1, 8],\n [0, 0, 0, 0, 0, -13, 9],\n [0, 0, 0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1451", "dataset": "MATH"}704{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -10, -10, -8, 4, 4, -3],\n [-10, 18, -14, 2, 3, -7, -6],\n [-10, -14, 12, 8, -6, 0, 1],\n [-8, 2, 8, -10, -2, -2, -4],\n [4, 3, -6, -2, -15, -6, -6],\n [4, -7, 0, -2, -6, 11, 2],\n [-3, -6, 1, -4, -6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}705{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-16, 6, 11, -7, -10, -14, 16],\n [6, -7, 14, -4, -2, 6, -10],\n [11, 14, -5, 6, 4, 4, 10],\n [-7, -4, 6, -2, 2, -16, 0],\n [-10, -2, 4, 2, 5, 17, 4],\n [-14, 6, 4, -16, 17, 14, -6],\n [16, -10, 10, 0, 4, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "306", "dataset": "MATH"}706{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[-4, 13, -3, 9, -13, -13, -17],\n [0, 8, 9, -3, -10, -4, 15],\n [0, 0, -8, 11, -16, -17, -5],\n [0, 0, 0, -11, 10, 8, -3],\n [0, 0, 0, 0, -2, -4, 3],\n [0, 0, 0, 0, 0, -10, 4],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}707{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 12, 16, 9, 7, -13, 15],\n [0, -10, 10, 15, -7, -3, -12],\n [0, 0, -12, -16, 1, -14, -16],\n [0, 0, 0, 14, -17, 17, 2],\n [0, 0, 0, 0, 11, 17, 1],\n [0, 0, 0, 0, 0, 11, 17],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2778", "dataset": "MATH"}708{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 7) of the inverse. Round your answer to the nearest integer:\n[[-6, -10, -2, 12, 5, 0, 11],\n [0, -11, 18, 17, 6, -14, 14],\n [0, 0, 10, 11, 11, 12, 15],\n [0, 0, 0, 14, -2, -8, -12],\n [0, 0, 0, 0, 7, -13, -2],\n [0, 0, 0, 0, 0, 4, 14],\n [0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}709{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[16, -2, 12, -17, -3, 2, 11],\n [0, -5, -3, -10, -11, -10, 15],\n [0, 0, 11, -12, -1, 2, -14],\n [0, 0, 0, 5, 18, 0, -3],\n [0, 0, 0, 0, -4, -3, -11],\n [0, 0, 0, 0, 0, 13, -8],\n [0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-460", "dataset": "MATH"}710{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 14, -3, -13, 6, 1, 17],\n [4, -3, -18, 11, 8, -17, 2],\n [-10, 5, -12, 11, -17, -7, -6],\n [-16, -1, -13, 8, -4, -4, 0],\n [1, 1, -1, 15, 18, 16, -18],\n [-7, -14, 8, 1, 0, -4, -13],\n [-10, 17, 4, -9, -18, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}711{"messages": [{"content": "Find the value at position (2, 2) of the inverse of matrix 1/252 * A where A =\n[[9, 3, 1, -3, -17, 6, 8],\n [0, 4, 13, -2, 1, 11, 9],\n [0, 0, 6, 5, -18, 9, 10],\n [0, 0, 0, 18, -12, 7, 4],\n [0, 0, 0, 0, 2, 2, 17],\n [0, 0, 0, 0, 0, -18, -6],\n [0, 0, 0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}712{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-17, -5, 10, -18, -6, 13, 15],\n [0, -4, -13, 10, 18, 0, -18],\n [0, 0, 8, 9, -11, 12, -7],\n [0, 0, 0, 11, 0, -1, 5],\n [0, 0, 0, 0, -5, -7, 10],\n [0, 0, 0, 0, 0, -12, -5],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-621", "dataset": "MATH"}713{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-10, -17, -5, 12, 11, 8, 17],\n [0, -13, -1, -5, 1, -8, 18],\n [0, 0, 4, -11, 11, 17, -8],\n [0, 0, 0, -17, -17, -11, 11],\n [0, 0, 0, 0, 5, 0, 11],\n [0, 0, 0, 0, 0, 12, -13],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1563", "dataset": "MATH"}714{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 7) of the inverse. Round your answer to the nearest integer:\n[[-11, 12, 7, 10, -15, 9, 6],\n [13, 17, -8, 18, -9, 17, 8],\n [-2, -12, -10, 16, -10, 17, 11],\n [12, 0, 4, 1, -13, 5, 3],\n [-13, 5, 3, -1, -3, 17, -6],\n [18, 5, 0, 1, 8, -2, -3],\n [-18, 2, 8, -18, 11, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}715{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -4, 3, 2, 4, -4, -2],\n [-4, -16, -12, 2, -2, 4, -1],\n [3, -12, 3, 18, 8, -1, 12],\n [2, 2, 18, 1, -6, 12, -11],\n [4, -2, 8, -6, -3, 2, -5],\n [-4, 4, -1, 12, 2, -13, 0],\n [-2, -1, 12, -11, -5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "423", "dataset": "MATH"}716{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[-12, -8, 6, 10, -14, -8, -2],\n [-8, 9, -6, -10, -8, 6, -12],\n [6, -6, 15, -8, -10, -2, -4],\n [10, -10, -8, -3, -8, -1, 12],\n [-14, -8, -10, -8, -17, 13, -16],\n [-8, 6, -2, -1, 13, 5, 0],\n [-2, -12, -4, 12, -16, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}717{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -3, 8, -17, 1, 1, 1],\n [0, -1, -6, -2, 14, 9, -14],\n [0, 0, 1, 2, -6, -13, 10],\n [0, 0, 0, 11, 13, 4, -9],\n [0, 0, 0, 0, 16, 6, -4],\n [0, 0, 0, 0, 0, 10, 2],\n [0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}718{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, 8, 2, 10, 11, -16, 4],\n [8, 7, 12, -11, -4, -10, 2],\n [2, 12, -18, 7, -16, 0, -2],\n [10, -11, 7, -7, 5, 2, -2],\n [11, -4, -16, 5, -4, 11, 5],\n [-16, -10, 0, 2, 11, -3, -4],\n [4, 2, -2, -2, 5, -4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1340", "dataset": "MATH"}719{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[17, -11, -16, 10, -10, -11, 11],\n [0, 9, -9, -6, -17, -18, 3],\n [0, 0, 10, -9, -12, -18, 7],\n [0, 0, 0, 8, -7, 11, 13],\n [0, 0, 0, 0, -12, -18, -16],\n [0, 0, 0, 0, 0, 12, 14],\n [0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1440", "dataset": "MATH"}720{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[6, 3, 3, -8, -8, -15, 14],\n [-1, 12, 9, 3, -16, -12, 1],\n [-12, -12, 10, 7, -16, -2, 1],\n [15, 14, -3, 4, -15, 14, -11],\n [-14, 14, 6, -12, -12, 14, 14],\n [10, 13, 18, 10, 3, -17, -10],\n [10, 14, -9, 9, -7, 3, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}721{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, 15, -3, -9, 2, -9, -8],\n [0, 6, 15, 12, 8, 6, 13],\n [0, 0, 17, 18, 14, 14, 17],\n [0, 0, 0, -18, -14, 11, -1],\n [0, 0, 0, 0, -3, -8, 14],\n [0, 0, 0, 0, 0, -3, 11],\n [0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-427", "dataset": "MATH"}722{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, -3, 2, 9, -11, 10, -13],\n [11, -17, 12, 6, 4, 2, -3],\n [-15, -11, -13, 8, 17, 17, 5],\n [-13, 14, -17, -3, -10, -14, -9],\n [11, -12, 10, -17, 1, -15, 9],\n [-11, 16, -17, 9, -8, 17, -10],\n [-18, 8, -16, -10, 9, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}723{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 8, -10, -5, 10, -12, 3],\n [8, -10, -8, -7, -4, -7, 0],\n [-10, -8, 16, 6, -3, -10, -8],\n [-5, -7, 6, -12, 12, 12, 0],\n [10, -4, -3, 12, 13, 0, 2],\n [-12, -7, -10, 12, 0, -15, -6],\n [3, 0, -8, 0, 2, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}724{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[7, 15, -8, 2, 5, -4, -16],\n [-17, -12, -14, 10, 13, 11, -11],\n [13, -17, -9, 18, -16, 4, 15],\n [-1, 14, 14, -2, -13, -6, 2],\n [12, 2, 14, 9, -13, -11, -6],\n [15, 3, -18, -6, -18, -9, -14],\n [1, -6, 18, -9, -16, 15, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}725{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[11, 4, 0, 2, 14, -2, -2],\n [4, 5, 8, 10, -14, 14, 4],\n [0, 8, 0, 8, 18, 8, -1],\n [2, 10, 8, 13, 0, -10, 10],\n [14, -14, 18, 0, 8, 12, 7],\n [-2, 14, 8, -10, 12, -10, 8],\n [-2, 4, -1, 10, 7, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}726{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -14, 0, 1, 13, -14, -12],\n [-14, -6, 1, -9, 8, -10, -3],\n [0, 1, 3, -4, 8, -4, 10],\n [1, -9, -4, 15, -6, 16, -2],\n [13, 8, 8, -6, -1, 10, 1],\n [-14, -10, -4, 16, 10, 12, 12],\n [-12, -3, 10, -2, 1, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}727{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, -11, 3, -15, 16, -11, 15],\n [0, 6, 6, -2, -3, -4, -2],\n [0, 0, -1, 11, 4, 18, -12],\n [0, 0, 0, 4, 15, -1, 4],\n [0, 0, 0, 0, -17, 10, -10],\n [0, 0, 0, 0, 0, 12, 16],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-149", "dataset": "MATH"}728{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, 6, 2, 17, -6, -10, 16],\n [17, -9, -14, 12, 5, 13, -16],\n [-3, 1, 5, 15, 4, -17, -14],\n [-1, 10, -9, -3, 4, 11, -13],\n [17, 1, -3, 9, 7, 3, -8],\n [-18, -14, 17, -17, -13, 8, 7],\n [16, -6, -7, -1, -13, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}729{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[6, -14, -4, -10, -17, -10, 7],\n [0, 9, -13, -15, 11, -1, 11],\n [0, 0, 11, 18, -7, -2, 15],\n [0, 0, 0, -5, -6, -16, 2],\n [0, 0, 0, 0, -13, 6, 5],\n [0, 0, 0, 0, 0, 14, 14],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3341", "dataset": "MATH"}730{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, -8, -11, -14, -11, -14, -9],\n [-4, -16, -9, -12, 5, 7, 15],\n [-11, -14, 17, 7, -9, 14, 17],\n [12, 6, -6, -18, 17, 17, 5],\n [8, -1, -4, -2, 10, -14, -8],\n [-3, 15, -2, 14, 12, -1, 6],\n [-14, 11, 4, -1, 13, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}731{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[17, -10, 4, -16, 3, 12, 3],\n [0, -16, -5, 0, 12, 17, 13],\n [0, 0, -17, -13, -5, 9, 14],\n [0, 0, 0, -7, 8, 5, 14],\n [0, 0, 0, 0, 16, -6, -10],\n [0, 0, 0, 0, 0, 3, -9],\n [0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}732{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 0, 17, -18, 10, 17, 13],\n [-5, 13, -10, 0, -8, -15, 6],\n [-2, -11, -18, -17, -9, 8, 8],\n [-6, -8, -5, 13, -3, 10, 15],\n [7, -14, 0, 9, 9, -2, 18],\n [0, 8, -7, -16, -15, -8, 15],\n [-1, 16, -1, -13, 15, 14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1120", "dataset": "MATH"}733{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[1, 8, -4, 6, 2, -13, -2],\n [8, -6, 7, -2, -7, -5, -14],\n [-4, 7, 14, 0, 0, 6, -11],\n [6, -2, 0, -10, 6, -4, -11],\n [2, -7, 0, 6, 11, -8, -11],\n [-13, -5, 6, -4, -8, 12, 10],\n [-2, -14, -11, -11, -11, 10, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}734{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -1, 4, -1, 16, -16, -18],\n [-2, -13, -8, -5, 9, 17, -8],\n [-15, -13, 0, 12, -17, 6, -8],\n [2, -16, -17, -8, 5, 5, 2],\n [6, -15, 4, 5, 2, -17, 4],\n [-4, 7, 7, 9, 7, -17, 16],\n [13, 11, 1, -6, 8, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}735{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[12, -7, 14, 13, -17, 4, 13],\n [0, -11, 3, 15, -18, -9, -3],\n [0, 0, -5, 7, -1, 1, 17],\n [0, 0, 0, 3, -8, -8, -16],\n [0, 0, 0, 0, -9, -13, -2],\n [0, 0, 0, 0, 0, 8, 7],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-232", "dataset": "MATH"}736{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[7, -2, 10, 1, 11, -14, -13],\n [-9, -13, -9, 2, -15, -6, -9],\n [-3, 0, -13, 7, -10, -9, -16],\n [0, 16, -13, 10, 0, -4, 2],\n [4, 1, -17, 13, 9, -15, -12],\n [-16, 6, -10, 4, 4, 7, -1],\n [5, 8, -17, -18, -3, 5, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "397", "dataset": "MATH"}737{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 4) of the inverse. Round your answer to the nearest integer:\n[[-8, 7, -13, 7, 10, -18, -10],\n [8, -12, -16, -10, -17, -9, -2],\n [12, -18, -1, -13, -15, -15, 16],\n [-15, -18, 12, 0, 2, 11, -12],\n [-14, -17, -16, -4, 18, -9, -10],\n [4, -5, 14, -3, 1, -11, 15],\n [12, -11, 6, -6, -1, 15, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}738{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-2, -7, -3, -6, -8, -5, 9],\n [5, -2, -10, 11, 18, -16, -11],\n [-1, 11, -16, 15, 9, 18, 6],\n [11, -12, 10, -17, 7, -12, -1],\n [-13, 8, 5, 14, 12, 15, 3],\n [5, 17, 9, 1, -1, 13, 14],\n [-9, -10, 6, -6, -14, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}739{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 4, -12, -7, -4, -6, -8],\n [4, -10, 10, 10, 5, 6, -4],\n [-12, 10, 0, -10, 5, 0, 9],\n [-7, 10, -10, 7, -2, 2, -17],\n [-4, 5, 5, -2, -10, 10, 8],\n [-6, 6, 0, 2, 10, -10, 2],\n [-8, -4, 9, -17, 8, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "686", "dataset": "MATH"}740{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-10, -8, 10, -3, 10, -6, 16],\n [-8, 16, -11, -12, -14, -13, 16],\n [11, -8, 8, 2, -5, 16, 10],\n [5, 17, 13, -13, -9, 1, 1],\n [7, 2, 4, -7, -6, -9, -12],\n [18, -7, 6, -17, 7, -14, -11],\n [-10, 1, -8, 3, -3, -9, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1252", "dataset": "MATH"}741{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/252 * A where A =\n[[0, -15, 0, -16, -2, -5, -9],\n [-13, 12, 12, -10, -7, 7, -17],\n [-15, 13, 9, -13, 11, 9, -6],\n [17, -9, -9, -14, 10, 17, -7],\n [3, -17, -5, -9, -16, -11, -2],\n [-15, 2, 11, 0, -4, 1, 11],\n [-9, 4, 5, -7, -10, -4, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-62", "dataset": "MATH"}742{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 1, -18, -16, -11, 12, -11],\n [-4, 3, 13, -14, -10, -4, 18],\n [14, 3, -8, -13, -2, -14, -10],\n [10, 4, 17, 12, 1, 4, -12],\n [17, -15, 5, -5, 6, -12, -4],\n [-6, 0, -7, 7, 14, -4, 18],\n [-13, 6, -2, 17, -10, 9, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}743{"messages": [{"content": "Find the value at position (2, 4) of the inverse of matrix 1/252 * A where A =\n[[-16, -8, 1, 4, 11, 18, 17],\n [0, 17, 16, 15, -15, 5, 17],\n [0, 0, -14, 9, -6, 17, -10],\n [0, 0, 0, 9, -1, 15, 2],\n [0, 0, 0, 0, -10, -11, 11],\n [0, 0, 0, 0, 0, 17, 12],\n [0, 0, 0, 0, 0, 0, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42", "dataset": "MATH"}744{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, -1, 6, 7, -14, 0, 10],\n [-1, 17, -4, 5, -3, 10, 9],\n [6, -4, -9, -13, -12, -4, -3],\n [7, 5, -13, 8, -5, -9, -4],\n [-14, -3, -12, -5, -15, -16, 3],\n [0, 10, -4, -9, -16, 18, -1],\n [10, 9, -3, -4, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}745{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[15, 1, 12, -4, 9, -13, -16],\n [0, -16, -11, -17, -12, -2, -12],\n [0, 0, -15, -3, 2, -1, 9],\n [0, 0, 0, 11, 9, -2, 17],\n [0, 0, 0, 0, -17, 10, 11],\n [0, 0, 0, 0, 0, 12, -10],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-195", "dataset": "MATH"}746{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, -11, 11, -13, -17, 15, 10],\n [1, -16, 16, -11, -7, 13, 10],\n [2, -16, 8, -16, -18, 1, -12],\n [-18, -9, -7, -15, -12, -9, 3],\n [6, 10, -4, 0, -1, -16, -13],\n [3, 12, 2, -11, -18, -16, 10],\n [-13, 14, -1, -18, 3, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-186", "dataset": "MATH"}747{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, -15, 13, 1, 10, 12, -2],\n [0, -3, 1, -9, 4, 14, -6],\n [0, 0, 17, 5, -13, -4, 15],\n [0, 0, 0, 9, 10, -1, 1],\n [0, 0, 0, 0, 14, -7, 18],\n [0, 0, 0, 0, 0, 4, -11],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}748{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[12, 6, -2, -2, 8, -17, -2],\n [6, 15, 2, 0, 5, 0, -1],\n [-2, 2, -3, -3, 0, -4, 7],\n [-2, 0, -3, 2, -6, -2, -14],\n [8, 5, 0, -6, 9, 3, -6],\n [-17, 0, -4, -2, 3, 14, -16],\n [-2, -1, 7, -14, -6, -16, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417", "dataset": "MATH"}749{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-7, 10, 7, -10, -12, 8, -4],\n [10, -5, 0, 16, 8, 7, -17],\n [7, 0, -15, -5, 0, 5, -12],\n [-10, 16, -5, -3, 6, -2, 0],\n [-12, 8, 0, 6, 3, -4, -4],\n [8, 7, 5, -2, -4, 4, -6],\n [-4, -17, -12, 0, -4, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804", "dataset": "MATH"}750{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-5, 3, -2, 7, 16, 17, 11],\n [2, 1, 7, -7, -11, 16, 10],\n [-12, -9, 1, 9, -5, -7, -11],\n [-12, -14, -18, -10, -1, -9, -18],\n [1, 10, -17, 7, -8, 6, 15],\n [-18, 12, 3, -17, -18, 5, 17],\n [17, 15, -10, -7, 1, -15, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "405", "dataset": "MATH"}751{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-15, -14, -9, 17, 16, -18, -1],\n [0, -13, -13, 0, 13, 11, 7],\n [0, 0, 12, 1, -15, 13, -1],\n [0, 0, 0, -15, 18, -12, -11],\n [0, 0, 0, 0, -10, -3, 18],\n [0, 0, 0, 0, 0, 12, 0],\n [0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838", "dataset": "MATH"}752{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -17, 16, -7, -2, -15, -5],\n [2, -11, 14, 9, -16, -5, 0],\n [-13, 17, 1, -18, -9, -6, -7],\n [-8, 17, -2, 10, -16, 10, -9],\n [0, -15, -7, 12, -17, -18, -2],\n [6, -14, -5, -9, 2, 6, 16],\n [-16, -1, 17, 14, -2, -13, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}753{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[7, 12, 1, 4, -4, -3, -1],\n [12, -3, 15, 2, 3, 3, -4],\n [1, 15, -15, 6, 1, 3, 10],\n [4, 2, 6, -8, 10, -5, 9],\n [-4, 3, 1, 10, 3, -14, 2],\n [-3, 3, 3, -5, -14, -12, 6],\n [-1, -4, 10, 9, 2, 6, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749", "dataset": "MATH"}754{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, -7, 4, 10, -18, 1, -9],\n [0, 4, 2, 16, 13, -9, -17],\n [17, -13, -2, -4, 17, 5, 10],\n [-5, -17, 3, -13, -10, -7, -14],\n [-18, -9, -8, 8, 4, 1, -14],\n [-6, -9, 17, -3, -12, 13, 6],\n [7, 17, 9, -7, 7, -15, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}755{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 0, 13, -6, -4, -2, -1],\n [0, -11, -2, 4, -8, 2, -4],\n [13, -2, -11, 12, -3, 2, 0],\n [-6, 4, 12, 13, -8, 2, -2],\n [-4, -8, -3, -8, 17, -12, 1],\n [-2, 2, 2, 2, -12, -1, 5],\n [-1, -4, 0, -2, 1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}756{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, -10, 0, 7, -18, -16, 15],\n [0, 11, -18, -1, 14, -10, -12],\n [0, 0, -2, -6, -6, 18, -9],\n [0, 0, 0, 16, 4, -14, 9],\n [0, 0, 0, 0, -12, -15, 13],\n [0, 0, 0, 0, 0, -16, -17],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4018", "dataset": "MATH"}757{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-7, -7, 4, 2, 8, 0, -4],\n [-7, -17, 2, -12, -8, 10, -4],\n [4, 2, -8, -6, -5, -1, 4],\n [2, -12, -6, -1, 8, 9, 14],\n [8, -8, -5, 8, -5, 4, -2],\n [0, 10, -1, 9, 4, 17, -12],\n [-4, -4, 4, 14, -2, -12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}758{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -7, -2, -1, 5, -11, 18],\n [11, 1, 4, 18, -9, 14, 5],\n [17, -3, 9, -7, 1, -1, 18],\n [7, -12, 2, 13, -12, 4, 1],\n [1, 13, 7, 17, 5, -18, 9],\n [7, 15, 7, 17, -14, -17, 13],\n [15, 11, 5, 9, -16, -9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378", "dataset": "MATH"}759{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[15, 6, -8, -8, -2, -4, 6],\n [6, 10, -4, 4, -1, 2, 3],\n [-8, -4, 4, 10, -8, -2, -5],\n [-8, 4, 10, -15, 5, -10, 10],\n [-2, -1, -8, 5, -1, 0, -12],\n [-4, 2, -2, -10, 0, -11, -13],\n [6, 3, -5, 10, -12, -13, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "788", "dataset": "MATH"}760{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 0, 8, 12, 1, 11, 5],\n [0, -10, -2, 8, -12, -4, 2],\n [8, -2, 8, 7, -6, 10, 10],\n [12, 8, 7, -7, 14, -2, 1],\n [1, -12, -6, 14, -18, 8, -2],\n [11, -4, 10, -2, 8, 11, -4],\n [5, 2, 10, 1, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}761{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, -16, 11, 5, -16, -17, 0],\n [5, 1, 12, 12, 18, 10, -15],\n [-9, 17, 16, 2, -18, -7, 5],\n [-17, 1, -3, 15, -6, -1, 10],\n [-5, 11, 16, -10, 18, -7, 2],\n [-1, -8, 8, 5, 15, 1, -6],\n [-11, 18, -14, -12, -7, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}762{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 2) rounded to the nearest integer?\n[[-18, -6, 6, 15, 16, -2, 7],\n [2, -7, -3, 1, -9, 4, 11],\n [-11, -14, -7, -5, -7, 5, -2],\n [-18, 18, -8, -13, -4, 4, 4],\n [-7, -12, 18, -3, 16, 10, -2],\n [7, 1, 6, 18, 0, 2, 13],\n [9, -7, -4, 9, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}763{"messages": [{"content": "Find the value at position (3, 7) of the inverse of matrix 1/252 * A where A =\n[[7, -4, 18, -7, -15, 16, 12],\n [8, 13, 14, -6, 18, -17, 18],\n [-14, -1, -2, -17, 16, -5, -7],\n [14, -12, -10, -14, -15, 13, -14],\n [-11, -6, -15, -8, -4, -1, 1],\n [-18, -18, -8, 10, 10, 5, 1],\n [11, -14, -9, -13, -15, -15, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}764{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[14, -12, 10, -8, 10, 8, 5],\n [-12, 2, 9, -12, 4, 10, 3],\n [10, 9, 4, -2, 4, 6, 2],\n [-8, -12, -2, 13, 10, -11, -2],\n [10, 4, 4, 10, -12, -2, -6],\n [8, 10, 6, -11, -2, 7, 14],\n [5, 3, 2, -2, -6, 14, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}765{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-7, -8, 8, -2, 0, 5, 2],\n [-8, -5, -3, 10, -10, 11, 8],\n [8, -3, 12, -4, 16, -8, -6],\n [-2, 10, -4, -12, 8, 7, -8],\n [0, -10, 16, 8, 9, -6, 2],\n [5, 11, -8, 7, -6, 7, -6],\n [2, 8, -6, -8, 2, -6, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}766{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[16, 12, 10, -13, 17, 12, 13],\n [0, 3, -16, -11, 0, 12, 13],\n [0, 0, -16, 13, -9, 9, 8],\n [0, 0, 0, -8, -12, -11, -2],\n [0, 0, 0, 0, -15, -6, -14],\n [0, 0, 0, 0, 0, 7, -13],\n [0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-252", "dataset": "MATH"}767{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-9, -14, 18, -11, 11, -2, -16],\n [2, -3, 13, 8, -13, -3, -16],\n [1, -12, -8, 10, -16, 2, 13],\n [11, -8, -2, 6, 6, -10, 10],\n [-4, 0, -4, 16, -6, -3, -16],\n [12, -18, 16, -3, -18, -5, -12],\n [4, 16, 10, 3, -3, 10, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}768{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-1, 10, 6, -17, 13, 17, 13],\n [1, 18, 14, -14, -13, 3, 2],\n [0, -4, 15, -12, -2, -14, -17],\n [8, 5, 9, -18, 2, 9, -16],\n [11, -18, -1, 14, -4, 5, 17],\n [15, 7, 3, -3, -3, -14, -13],\n [5, 11, 18, 13, 0, 9, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}769{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, -10, 0, 2, 2, -2, 10],\n [-10, 8, 2, -5, 12, 8, -7],\n [0, 2, -9, 4, -4, 8, 4],\n [2, -5, 4, -5, -5, -7, 1],\n [2, 12, -4, -5, 2, -1, 8],\n [-2, 8, 8, -7, -1, 16, 0],\n [10, -7, 4, 1, 8, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-148", "dataset": "MATH"}770{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 9, 13, 5, -12, -1, -16],\n [0, 15, 11, -10, -9, -13, -2],\n [0, 0, -6, 3, -3, 15, -16],\n [0, 0, 0, -1, 4, -18, -17],\n [0, 0, 0, 0, 10, 16, 6],\n [0, 0, 0, 0, 0, 9, 8],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4052", "dataset": "MATH"}771{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (5, 5) rounded to the nearest integer?\n[[-18, -14, -6, 12, 4, -4, 0],\n [-14, -14, -10, 6, 2, 2, -6],\n [-6, -10, 5, 6, 4, -3, -3],\n [12, 6, 6, -11, -3, 2, 8],\n [4, 2, 4, -3, 17, 9, -10],\n [-4, 2, -3, 2, 9, -13, 3],\n [0, -6, -3, 8, -10, 3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}772{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 7, 6, -4, 3, -2, -5],\n [7, -14, -6, 9, 1, 12, -8],\n [6, -6, 0, -6, -10, 0, -8],\n [-4, 9, -6, -8, 0, -3, 1],\n [3, 1, -10, 0, 9, 5, -18],\n [-2, 12, 0, -3, 5, -18, 0],\n [-5, -8, -8, 1, -18, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5967", "dataset": "MATH"}773{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -17, -6, -4, 10, 2, 0],\n [-17, 11, -16, 2, 4, -4, -10],\n [-6, -16, 8, 6, 2, -15, 5],\n [-4, 2, 6, 14, -4, -3, 3],\n [10, 4, 2, -4, 7, 0, 2],\n [2, -4, -15, -3, 0, -11, 2],\n [0, -10, 5, 3, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "379", "dataset": "MATH"}774{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-15, 0, 15, -13, -4, -9, 17],\n [0, -13, -4, 10, 6, 0, -5],\n [0, 0, 2, -8, -9, -4, 11],\n [0, 0, 0, 14, 2, -5, -9],\n [0, 0, 0, 0, -10, 4, -12],\n [0, 0, 0, 0, 0, 6, 3],\n [0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4402", "dataset": "MATH"}775{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-6, 15, 15, 16, 13, -7, 14],\n [0, -14, 0, 12, 8, -4, -15],\n [0, 0, -18, 1, 3, -6, -18],\n [0, 0, 0, -14, -13, 12, 7],\n [0, 0, 0, 0, -12, -15, -18],\n [0, 0, 0, 0, 0, -9, -16],\n [0, 0, 0, 0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-169", "dataset": "MATH"}776{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, 3, -8, 6, -2, 0, -6],\n [3, 6, 13, -1, -6, 8, -4],\n [-8, 13, -15, 9, 5, 11, -6],\n [6, -1, 9, 9, -7, 1, 8],\n [-2, -6, 5, -7, 3, 2, 6],\n [0, 8, 11, 1, 2, -1, 10],\n [-6, -4, -6, 8, 6, 10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-857", "dataset": "MATH"}777{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 2, 3, 6, 3, 9, 14],\n [-17, -15, -3, -7, -2, 17, -3],\n [4, -11, -10, -5, -10, 7, 17],\n [-16, -9, 6, -15, 11, -8, 0],\n [-6, 17, -16, -5, -9, 8, 5],\n [-3, -9, 8, -12, 9, 7, -1],\n [-6, -11, 8, -5, -13, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}778{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[4, -7, 5, 3, 7, 3, -12],\n [-4, 11, -15, -13, -17, 12, 5],\n [16, 12, 6, -11, -7, -17, -4],\n [13, -8, -2, 2, 3, 14, 10],\n [-4, 2, -17, -16, 6, -6, 5],\n [12, -4, -13, -9, -10, -14, 0],\n [1, 14, 18, 12, -6, -13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}779{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -15, -5, -15, 5, 2, -9],\n [0, -13, -3, 9, 17, 14, 11],\n [0, 0, -6, -4, 11, -5, -15],\n [0, 0, 0, -15, -5, 6, -16],\n [0, 0, 0, 0, -2, 7, -15],\n [0, 0, 0, 0, 0, -16, -7],\n [0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-945", "dataset": "MATH"}780{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -12, 9, -6, -3, 2, -15],\n [0, -4, 7, -12, -1, 6, 18],\n [0, 0, 1, -1, 0, -16, -1],\n [0, 0, 0, 3, -11, -8, -7],\n [0, 0, 0, 0, 12, -11, 1],\n [0, 0, 0, 0, 0, 3, 7],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6157", "dataset": "MATH"}781{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, -7, -3, 7, -1, -7, -16],\n [-7, -18, 17, 3, -6, 13, 3],\n [-3, 17, 5, 0, -10, 4, 2],\n [7, 3, 0, 5, -5, 12, 6],\n [-1, -6, -10, -5, 5, -10, -2],\n [-7, 13, 4, 12, -10, 9, 10],\n [-16, 3, 2, 6, -2, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416", "dataset": "MATH"}782{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, -14, 10, -13, 16, 2, 4],\n [16, -17, -10, -6, 15, -3, -14],\n [-18, 3, 7, 15, 2, -12, 6],\n [-7, 12, 8, 3, 15, -2, -8],\n [10, 15, 18, 7, 13, 18, -14],\n [1, -12, 4, -18, -16, -16, -13],\n [12, 8, 10, -4, 17, -14, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}783{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[6, 13, 2, -2, -10, 7, 3],\n [4, -8, -9, 4, -14, 7, -15],\n [8, 15, -16, 13, 7, -1, -12],\n [-6, -13, 16, 12, 18, -15, -15],\n [-11, -8, -17, -1, -1, 3, -7],\n [-2, -2, 17, 10, -3, -8, 3],\n [11, -11, -1, -3, 1, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}784{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 6) rounded to the nearest integer?\n[[10, -6, -2, -2, -10, -17, 5],\n [0, -17, -14, -2, 5, -11, 11],\n [0, 0, 7, -11, -7, -5, 11],\n [0, 0, 0, 8, 17, -18, -5],\n [0, 0, 0, 0, 8, -8, 18],\n [0, 0, 0, 0, 0, 18, 17],\n [0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}785{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-18, -2, 17, -10, 4, 10, -17],\n [-1, 9, -12, -8, -12, 5, -4],\n [12, 0, -9, -11, -18, -17, 10],\n [-9, -10, 12, 13, -17, 5, 18],\n [-13, -11, 6, 6, -8, 16, -18],\n [4, -16, -18, -7, 12, 10, 16],\n [9, 2, -8, 7, -8, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-196", "dataset": "MATH"}786{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[12, -11, 8, 2, 11, -5, -18],\n [5, -13, -13, -14, 16, -4, 16],\n [-11, 16, -14, 12, 12, 18, -11],\n [-13, 4, -3, -11, -15, 13, -16],\n [-3, 15, -6, 14, 3, 12, 5],\n [-16, 14, 11, 7, 15, 3, 11],\n [16, 6, 9, 14, 4, 7, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}787{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-11, 18, 14, -4, -11, 2, -16],\n [0, -5, 8, 1, -15, 5, 8],\n [0, 0, 16, 5, 12, -16, 11],\n [0, 0, 0, -1, 16, 8, -2],\n [0, 0, 0, 0, 16, 9, 3],\n [0, 0, 0, 0, 0, -6, 5],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-351", "dataset": "MATH"}788{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -3, -1, 15, -9, -6, 13],\n [0, -12, -2, 8, -11, 10, 18],\n [0, 0, 5, -3, 7, 12, 8],\n [0, 0, 0, 4, 6, -15, 17],\n [0, 0, 0, 0, -12, -7, -18],\n [0, 0, 0, 0, 0, -16, -15],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}789{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -12, -18, 15, 4, -16, -1],\n [-7, -5, 9, 5, 5, -16, -10],\n [5, -17, 9, -12, -10, 14, 15],\n [2, 10, 8, -2, 4, 2, -11],\n [-10, 14, -15, -1, 13, 11, 6],\n [14, 16, 15, -17, -6, 4, 4],\n [12, -17, -17, -14, -5, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}790{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-18, -4, 11, 2, -11, -12, 15],\n [18, 13, 14, -13, -9, 7, 7],\n [0, 16, -15, 6, -11, -7, 5],\n [5, -2, 6, 14, 8, -17, -10],\n [14, 0, -14, 1, 5, 12, -15],\n [13, 16, -5, 17, -13, -2, -1],\n [-11, -7, -2, 12, -18, -8, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1103", "dataset": "MATH"}791{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[18, 6, -6, 2, 2, -14, -17],\n [6, 4, 0, 8, -6, -2, 8],\n [-6, 0, 15, -4, -1, 14, 10],\n [2, 8, -4, -16, 7, 2, 2],\n [2, -6, -1, 7, 7, -16, 8],\n [-14, -2, 14, 2, -16, 13, 12],\n [-17, 8, 10, 2, 8, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}792{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, -5, 5, 16, 0, 6, -8],\n [-10, -13, 17, 18, 10, -10, 14],\n [4, -4, -8, 4, 7, -18, 11],\n [-2, 4, 17, -14, 16, -10, -15],\n [-12, -18, -3, 6, -13, -5, 18],\n [-8, -18, -18, 17, -11, 13, 14],\n [-11, -5, 5, 10, 6, -13, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}793{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 11, -10, 7, 4, -6, -12],\n [11, -11, -7, -6, 4, 3, 0],\n [-10, -7, 17, -8, -6, -12, -1],\n [7, -6, -8, -4, -2, -12, -6],\n [4, 4, -6, -2, -8, 11, 6],\n [-6, 3, -12, -12, 11, -16, 12],\n [-12, 0, -1, -6, 6, 12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}794{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, -1, 11, 3, 3, 6, 0],\n [-1, -8, -1, -10, 3, 3, -7],\n [11, -1, 11, -10, -1, 12, 6],\n [3, -10, -10, 17, 11, 6, -10],\n [3, 3, -1, 11, -4, 4, 10],\n [6, 3, 12, 6, 4, -1, 10],\n [0, -7, 6, -10, 10, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-86", "dataset": "MATH"}795{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[15, -12, -8, -11, -6, 13, 15],\n [-1, -4, 5, 2, -1, -5, 0],\n [-6, -3, -17, 15, 7, 3, 1],\n [10, -1, 10, 8, 16, 10, -13],\n [18, 6, 2, 12, -3, -5, -13],\n [-8, 8, -14, -4, -3, -1, 14],\n [16, 5, 16, -12, -5, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}796{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-4, 6, 1, 4, -2, -10, 1],\n [6, -1, 2, 16, -4, 2, -2],\n [1, 2, -15, -7, 4, -8, 4],\n [4, 16, -7, -3, -1, 14, 3],\n [-2, -4, 4, -1, -1, 2, -3],\n [-10, 2, -8, 14, 2, 0, -2],\n [1, -2, 4, 3, -3, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}797{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -12, -18, -18, -2, 3, 17],\n [0, -13, 11, 14, 1, -3, -15],\n [0, 0, -6, -11, 3, -15, 15],\n [0, 0, 0, 5, 8, -6, -14],\n [0, 0, 0, 0, 5, -6, 2],\n [0, 0, 0, 0, 0, -6, 12],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3081", "dataset": "MATH"}798{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-9, 14, -1, -4, -6, 1, -10],\n [14, 4, -1, -2, 14, -14, 0],\n [-1, -1, -5, 0, -10, -4, 3],\n [-4, -2, 0, 17, 16, -4, -3],\n [-6, 14, -10, 16, -4, -10, -10],\n [1, -14, -4, -4, -10, -13, 16],\n [-10, 0, 3, -3, -10, 16, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-349", "dataset": "MATH"}799{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, 14, -3, 10, -13, 18, 4],\n [0, -18, -7, 8, 6, 3, 15],\n [0, 0, 10, 11, 11, 1, 3],\n [0, 0, 0, -5, -11, 18, -14],\n [0, 0, 0, 0, -6, 0, -16],\n [0, 0, 0, 0, 0, -12, 1],\n [0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1402", "dataset": "MATH"}800{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[18, 0, -9, 15, 6, 18, 9],\n [-4, 1, -6, 1, 12, -1, 9],\n [-15, 5, -10, 13, 13, 2, 8],\n [17, -11, 0, 10, 0, -14, 3],\n [16, -9, -4, -17, 3, 16, 0],\n [-7, 15, 1, -12, 5, -16, -13],\n [14, 15, 14, 10, 4, -15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}801{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -9, -12, 5, 1, 5, 4],\n [-9, 1, 2, 0, -4, 14, 2],\n [-12, 2, 4, 4, -2, -18, -5],\n [5, 0, 4, 1, 0, 4, 14],\n [1, -4, -2, 0, 7, -2, -12],\n [5, 14, -18, 4, -2, 10, -6],\n [4, 2, -5, 14, -12, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188", "dataset": "MATH"}802{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 3, -1, -1, 15, 17, 18],\n [0, 10, -7, -1, 12, -4, 11],\n [0, 0, -4, 14, -17, -11, 14],\n [0, 0, 0, 2, 9, 1, 1],\n [0, 0, 0, 0, 12, -12, -2],\n [0, 0, 0, 0, 0, -10, -7],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185", "dataset": "MATH"}803{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[16, -4, 0, 7, 16, 4, -9],\n [3, -8, 7, -18, 17, 2, -11],\n [1, -2, -4, 2, -18, -16, 12],\n [12, 2, 4, -2, 3, 3, 17],\n [-11, -11, -5, 5, 3, -4, 1],\n [8, 9, 3, 12, -10, 4, -14],\n [-2, -14, -12, -11, -12, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}804{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 7) rounded to the nearest integer?\n[[-15, 13, 10, 11, -16, -14, 0],\n [-11, 18, 12, 8, -6, -13, -18],\n [11, -8, 12, -3, -4, -14, -4],\n [-18, -4, 17, -11, 3, 8, 15],\n [11, -7, -17, 3, -2, 16, 4],\n [10, 10, 0, -2, -11, -12, -8],\n [-16, -17, 0, 9, 9, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}805{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, -7, -7, 6, 18, 12, -2],\n [-7, 11, -17, -3, -18, 15, -18],\n [17, -16, 15, -7, 8, 18, 6],\n [-7, 14, -10, -18, 4, 9, -16],\n [17, -14, 10, -6, -15, -13, -13],\n [-8, 8, 16, -15, 8, -3, -1],\n [-12, -8, -11, -13, -14, -13, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}806{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, 13, -10, -4, 2, 9, 8],\n [0, -2, 18, 5, 12, 16, -15],\n [0, 0, -9, 18, 2, 2, -3],\n [0, 0, 0, 14, 10, 12, 5],\n [0, 0, 0, 0, -5, -14, 17],\n [0, 0, 0, 0, 0, -12, -15],\n [0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5392", "dataset": "MATH"}807{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -9, -2, -16, -10, -1, 11],\n [0, 13, 8, 2, 5, -16, -3],\n [0, 0, -11, -15, 13, 16, 11],\n [0, 0, 0, 12, -2, -17, 18],\n [0, 0, 0, 0, 14, 0, -16],\n [0, 0, 0, 0, 0, -14, -7],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}808{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, 16, 13, -3, -13, -10, 3],\n [0, 13, 7, -1, 18, -7, 15],\n [0, 0, 5, -5, -2, 12, -15],\n [0, 0, 0, -7, 16, -17, 10],\n [0, 0, 0, 0, -5, 10, -4],\n [0, 0, 0, 0, 0, -7, 1],\n [0, 0, 0, 0, 0, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}809{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, 16, -17, -16, -5, -2, 16],\n [-15, 11, -5, 8, -6, 1, 5],\n [-9, -12, -2, 3, -8, 4, 3],\n [-1, 7, 11, -6, -15, 8, -9],\n [9, 2, -8, 1, 17, 0, -9],\n [-4, -1, -12, 11, -5, 18, 11],\n [8, 18, -2, 11, -1, -16, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-147", "dataset": "MATH"}810{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[18, 11, 2, 1, 3, 17, 17],\n [2, 5, 2, -12, -11, 3, 3],\n [11, 15, 10, -9, -14, 15, -9],\n [-10, 13, -14, 16, -8, -3, 8],\n [1, -18, 7, -8, -4, -1, 5],\n [9, 6, 4, -8, 14, -3, 17],\n [4, -13, 5, -13, -9, 3, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}811{"messages": [{"content": "Find the value at position (5, 4) of the inverse of matrix 1/252 * A where A =\n[[-14, 9, -10, 9, 6, 8, 5],\n [0, -17, -17, -14, 2, -9, -1],\n [0, 0, 17, 2, -17, 14, 4],\n [0, 0, 0, 18, -9, 13, 17],\n [0, 0, 0, 0, -6, 16, -17],\n [0, 0, 0, 0, 0, 7, 9],\n [0, 0, 0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}812{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 6, -10, -8, 18, 2, -17],\n [15, -6, -14, -8, 10, 9, 9],\n [-14, 1, 18, -9, 13, 10, -17],\n [-18, 1, -18, -15, -4, 11, -13],\n [-18, -12, -14, -12, 17, -16, -7],\n [-4, 1, 2, 13, -7, 18, -12],\n [12, -18, -8, 15, 0, -8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}813{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[14, 2, -6, 7, 13, 2, -1],\n [2, 18, -16, -12, -4, 2, 6],\n [-6, -16, -8, 8, 8, 2, 10],\n [7, -12, 8, -3, -6, -12, -4],\n [13, -4, 8, -6, 0, -6, -7],\n [2, 2, 2, -12, -6, -5, 12],\n [-1, 6, 10, -4, -7, 12, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "691", "dataset": "MATH"}814{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -15, -9, 16, -3, 8, 1],\n [0, 14, -12, 3, -2, -10, -9],\n [0, 0, 12, -14, -1, -13, 9],\n [0, 0, 0, -16, -1, -15, 13],\n [0, 0, 0, 0, -17, -8, 14],\n [0, 0, 0, 0, 0, 13, -12],\n [0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}815{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (6, 4) of the inverse. Round your answer to the nearest integer:\n[[13, -4, 2, -5, -3, -18, -1],\n [15, 7, 17, 2, -18, 8, -8],\n [-5, 9, 8, 3, 2, 5, 0],\n [5, 7, 6, 10, -9, -8, 5],\n [5, -7, -12, -2, 16, -13, -7],\n [-4, 13, 4, -12, 12, 10, 9],\n [-7, 8, -15, 2, -10, 15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}816{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 4, 5, -9, -13, 2, 18],\n [0, 2, 3, 16, -14, -4, 0],\n [0, 0, -15, 2, 5, 7, -17],\n [0, 0, 0, -5, 1, -17, -15],\n [0, 0, 0, 0, 1, -13, 9],\n [0, 0, 0, 0, 0, 4, 16],\n [0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475", "dataset": "MATH"}817{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -14, 8, -8, 11, 18, 15],\n [0, -3, 11, 5, -16, 10, -7],\n [0, 0, -17, 10, -10, 9, 18],\n [0, 0, 0, 13, 9, -4, 5],\n [0, 0, 0, 0, 17, 9, 13],\n [0, 0, 0, 0, 0, 16, 5],\n [0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-828", "dataset": "MATH"}818{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, 12, 8, -13, 2, 0, -9],\n [12, -17, 4, -13, 0, -2, -11],\n [8, 4, 12, 8, 10, 4, 2],\n [-13, -13, 8, 15, 2, 5, 8],\n [2, 0, 10, 2, -2, 8, 4],\n [0, -2, 4, 5, 8, 18, 0],\n [-9, -11, 2, 8, 4, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427", "dataset": "MATH"}819{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, 2, 7, -4, 16, -8, -10],\n [0, -15, 11, 9, 6, 3, 6],\n [0, 0, 13, 7, 9, 1, -17],\n [0, 0, 0, 3, -8, 11, 9],\n [0, 0, 0, 0, 17, 6, 5],\n [0, 0, 0, 0, 0, -11, -14],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "848", "dataset": "MATH"}820{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, -3, -4, 12, 2, 11, -5],\n [-3, -1, -5, 6, -8, -8, -2],\n [-4, -5, 4, 10, -2, 10, -10],\n [12, 6, 10, -7, 4, -11, 14],\n [2, -8, -2, 4, 2, 5, 6],\n [11, -8, 10, -11, 5, -9, -8],\n [-5, -2, -10, 14, 6, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}821{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-13, 5, 2, 4, -14, -12, -16],\n [-6, -7, -13, 15, -4, -1, -16],\n [3, 16, 9, -7, -18, 17, 11],\n [4, 18, 9, -14, 17, -9, -14],\n [-5, 5, 9, 2, -7, 1, 13],\n [2, -2, -18, 9, -17, -2, -5],\n [-5, -1, 15, -18, -1, 15, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-112", "dataset": "MATH"}822{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-3, -6, 6, -8, 12, 6, 1],\n [-6, -3, 3, 1, 0, 1, 1],\n [6, 3, 5, -1, -4, -8, 0],\n [-8, 1, -1, -12, 10, 8, -12],\n [12, 0, -4, 10, 13, 4, -6],\n [6, 1, -8, 8, 4, -12, 0],\n [1, 1, 0, -12, -6, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}823{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, -9, 13, -2, -9, 3, -13],\n [8, 1, -18, -2, -18, 18, -4],\n [-18, -2, -17, -1, -7, 10, 4],\n [-10, -11, -3, 4, 10, -9, -7],\n [-7, 11, -9, -5, -15, 1, -12],\n [11, 5, -9, 17, -2, 2, -16],\n [-18, -1, -17, -15, 13, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "375", "dataset": "MATH"}824{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -10, -12, 8, 2, 16, 5],\n [13, -7, 4, 17, 10, -16, -11],\n [15, -5, 17, 13, -12, -9, -7],\n [4, -8, -6, -7, -12, -9, -12],\n [8, -12, 5, 4, 6, 17, 14],\n [18, -12, 11, 12, 18, 2, 15],\n [2, 1, 15, -11, 13, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}825{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[-14, 11, -7, 8, -6, -9, 17],\n [0, -3, 17, 7, 1, 15, 18],\n [0, 0, 10, 12, -17, 6, -16],\n [0, 0, 0, -10, -10, -7, -15],\n [0, 0, 0, 0, -2, -7, -8],\n [0, 0, 0, 0, 0, 13, -8],\n [0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}826{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-10, -12, 8, -16, 3, -3, -11],\n [-14, 11, 9, 8, 3, 11, 18],\n [-12, 11, -6, 3, -8, -14, 3],\n [-4, 18, 12, 10, -2, -13, -2],\n [15, 4, 11, -6, 11, 1, -13],\n [12, 0, -13, 15, 9, -6, -9],\n [-12, -1, 3, -5, 17, -11, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}827{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[14, 5, -5, -14, 0, -16, -18],\n [0, 14, -2, -10, 12, 16, -16],\n [0, 0, -5, -13, 10, -10, 17],\n [0, 0, 0, 6, 18, 4, -8],\n [0, 0, 0, 0, -3, -6, 18],\n [0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3564", "dataset": "MATH"}828{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[11, -2, 15, -5, 8, 8, -8],\n [-2, 2, 5, 15, 8, 4, -3],\n [15, 5, 7, 6, -2, 11, -10],\n [-5, 15, 6, -9, 10, -1, -13],\n [8, 8, -2, 10, -18, 4, 7],\n [8, 4, 11, -1, 4, 13, 4],\n [-8, -3, -10, -13, 7, 4, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-81", "dataset": "MATH"}829{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[4, 4, 8, -10, 2, 2, -14],\n [4, -18, 4, 4, 1, -7, -12],\n [8, 4, -2, 8, -1, -10, 2],\n [-10, 4, 8, -15, -6, -8, 0],\n [2, 1, -1, -6, 2, 0, -10],\n [2, -7, -10, -8, 0, 17, -2],\n [-14, -12, 2, 0, -10, -2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}830{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -8, 9, 8, -1, 11, -6],\n [0, -17, 1, -7, 10, -11, 1],\n [0, 0, -3, 4, 15, 13, -2],\n [0, 0, 0, -11, 4, 2, 0],\n [0, 0, 0, 0, -6, -16, 15],\n [0, 0, 0, 0, 0, -17, 7],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}831{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -7, 17, -17, 1, -16, 15],\n [0, -9, 5, -1, 14, -12, 10],\n [0, 0, -2, 18, -16, 5, -1],\n [0, 0, 0, -2, 2, -15, 13],\n [0, 0, 0, 0, 7, 5, -9],\n [0, 0, 0, 0, 0, 4, 13],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-758848", "dataset": "MATH"}832{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[17, 4, -7, 4, 14, 9, 4],\n [-12, -17, -18, -15, -11, 10, -1],\n [18, 12, -13, 5, -4, -7, -5],\n [8, 18, -6, -16, -3, -7, -5],\n [15, 12, -14, -7, 7, -2, -8],\n [14, -15, 13, 12, -8, -2, 8],\n [-11, 2, 14, -14, 13, 6, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}833{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 2, -2, 1, -7, -8, -4],\n [2, -16, 12, -1, 13, -5, 15],\n [-2, 12, -7, 2, 0, 8, 9],\n [1, -1, 2, 10, -6, -6, 2],\n [-7, 13, 0, -6, 18, 4, 8],\n [-8, -5, 8, -6, 4, -11, 2],\n [-4, 15, 9, 2, 8, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}834{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[13, -8, -17, 13, -14, 12, -6],\n [3, 16, 0, 10, 4, 0, -3],\n [12, -3, 7, -16, 4, -10, 5],\n [14, -5, 9, 5, -12, 6, -17],\n [-18, 4, -1, -11, 15, -11, 10],\n [-6, -18, 10, 18, -18, -14, -17],\n [3, 11, -8, 10, -16, -6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394", "dataset": "MATH"}835{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-9, -16, -10, 8, -6, -12, 4],\n [-16, -1, 5, 6, 12, -4, -9],\n [-10, 5, -15, -10, 12, -4, 2],\n [8, 6, -10, -10, 12, 3, 8],\n [-6, 12, 12, 12, 7, -2, -2],\n [-12, -4, -4, 3, -2, -6, -6],\n [4, -9, 2, 8, -2, -6, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-387", "dataset": "MATH"}836{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[11, 4, -3, -8, 0, 0, -4],\n [4, 2, -10, 4, 7, 2, 4],\n [-3, -10, -5, 7, -6, 5, 8],\n [-8, 4, 7, 1, -9, -10, 3],\n [0, 7, -6, -9, -16, 0, -12],\n [0, 2, 5, -10, 0, -2, 4],\n [-4, 4, 8, 3, -12, 4, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}837{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[13, 12, -8, -3, 4, 0, -2],\n [12, 13, -12, 16, -14, -17, -1],\n [-8, -12, -17, -8, 2, -8, -6],\n [-3, 16, -8, 13, 8, 3, -12],\n [4, -14, 2, 8, -13, -14, -8],\n [0, -17, -8, 3, -14, -10, 6],\n [-2, -1, -6, -12, -8, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}838{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-7, 11, 8, -14, 1, 2, -16],\n [0, 5, -12, 5, -8, -17, -13],\n [0, 0, -10, 9, 0, -15, -15],\n [0, 0, 0, -17, -13, -7, 18],\n [0, 0, 0, 0, -15, 15, 3],\n [0, 0, 0, 0, 0, -1, 10],\n [0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}839{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, -9, 18, -7, 0, -17, -4],\n [-11, 16, 11, -10, 11, 0, 10],\n [-17, 9, -11, 6, -9, 3, 16],\n [5, 7, 12, 4, -17, 14, 5],\n [-7, 18, -10, -16, 4, 5, 14],\n [11, -17, 3, -8, -7, 0, 1],\n [-10, -1, -1, 17, 8, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-71", "dataset": "MATH"}840{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -10, -2, -2, -4, 5, -12],\n [-10, -11, 8, -6, 5, 2, -4],\n [-2, 8, 1, -12, -4, -2, -2],\n [-2, -6, -12, 14, 8, 14, 11],\n [-4, 5, -4, 8, 14, -3, 0],\n [5, 2, -2, 14, -3, -6, 0],\n [-12, -4, -2, 11, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1324", "dataset": "MATH"}841{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[8, -6, 12, 6, 4, -2, -6],\n [-6, -13, 11, 4, 2, -2, 1],\n [12, 11, -1, 3, 0, 3, 0],\n [6, 4, 3, 12, 2, -6, -8],\n [4, 2, 0, 2, 8, -12, 0],\n [-2, -2, 3, -6, -12, 0, 10],\n [-6, 1, 0, -8, 0, 10, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}842{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/252 * A where A =\n[[1, -1, 0, -14, 0, 6, 6],\n [-1, 8, 13, 10, 0, -2, -3],\n [0, 13, 13, -13, 4, -8, 10],\n [-14, 10, -13, 1, -4, -16, 0],\n [0, 0, 4, -4, 6, -8, 4],\n [6, -2, -8, -16, -8, 9, 9],\n [6, -3, 10, 0, 4, 9, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}843{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 14, -18, -14, 13, -18, 16],\n [0, 10, -2, 11, 16, -18, -15],\n [0, 0, -14, -5, 7, 4, 3],\n [0, 0, 0, -15, 13, -10, -17],\n [0, 0, 0, 0, 10, 18, -14],\n [0, 0, 0, 0, 0, -16, -18],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1131", "dataset": "MATH"}844{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, 4, 4, 9, -6, -8, 6],\n [4, -5, 4, 10, -2, -7, -9],\n [4, 4, 10, -9, 0, -7, 0],\n [9, 10, -9, -5, -8, 7, 15],\n [-6, -2, 0, -8, -6, 12, 0],\n [-8, -7, -7, 7, 12, -14, 3],\n [6, -9, 0, 15, 0, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479", "dataset": "MATH"}845{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, 4, 6, 0, 0, -4, -12],\n [4, -6, 6, -10, -8, 2, 6],\n [6, 6, 14, 11, 2, 5, -12],\n [0, -10, 11, 13, 0, 12, 9],\n [0, -8, 2, 0, -14, 2, 2],\n [-4, 2, 5, 12, 2, -14, 8],\n [-12, 6, -12, 9, 2, 8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}846{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[17, 14, -2, -14, 1, 4, -15],\n [0, 11, 10, 15, -9, 1, 5],\n [0, 0, -6, 4, -9, 3, -5],\n [0, 0, 0, 9, -11, -14, 2],\n [0, 0, 0, 0, -12, 6, 17],\n [0, 0, 0, 0, 0, -7, 1],\n [0, 0, 0, 0, 0, 0, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1046", "dataset": "MATH"}847{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -2, -4, -2, 10, 9, 0],\n [-2, -5, 0, 8, 4, -16, 8],\n [-4, 0, 6, -2, 14, -2, -4],\n [-2, 8, -2, 18, -5, 8, -14],\n [10, 4, 14, -5, -18, -2, -2],\n [9, -16, -2, 8, -2, -14, -1],\n [0, 8, -4, -14, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}848{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 10, 8, -1, -2, 1, -2],\n [10, 16, -6, 2, 0, 10, -9],\n [8, -6, 0, -6, 8, -2, -11],\n [-1, 2, -6, -3, 12, -8, -6],\n [-2, 0, 8, 12, -14, -6, 14],\n [1, 10, -2, -8, -6, 17, 4],\n [-2, -9, -11, -6, 14, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1766", "dataset": "MATH"}849{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (2, 6) of the inverse. Round your answer to the nearest integer:\n[[3, -15, -16, -9, 18, 0, -1],\n [0, 12, -2, 5, -18, -14, 13],\n [0, 0, 3, 15, -5, -3, -14],\n [0, 0, 0, 8, -13, -8, 2],\n [0, 0, 0, 0, 4, -18, -15],\n [0, 0, 0, 0, 0, -7, -8],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}850{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -18, -11, -3, -4, 0, 6],\n [0, -17, 6, 12, -15, -15, -7],\n [0, 0, 10, 3, 17, -3, -4],\n [0, 0, 0, 4, 15, 1, -17],\n [0, 0, 0, 0, 3, 9, 6],\n [0, 0, 0, 0, 0, 5, -2],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5770", "dataset": "MATH"}851{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-17, -9, -3, -3, 0, 14, 0],\n [-9, 5, 9, -14, 10, -2, 0],\n [-3, 9, 9, 2, 13, 8, -9],\n [-3, -14, 2, -9, -6, -4, -4],\n [0, 10, 13, -6, -9, -8, -10],\n [14, -2, 8, -4, -8, -3, 15],\n [0, 0, -9, -4, -10, 15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}852{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, -2, 12, 10, -6, 2, -2],\n [-2, 11, 3, -2, 2, 12, 12],\n [12, 3, -16, 0, 13, 12, 1],\n [10, -2, 0, -10, -6, -6, 0],\n [-6, 2, 13, -6, 7, -2, 2],\n [2, 12, 12, -6, -2, -12, -8],\n [-2, 12, 1, 0, 2, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-69", "dataset": "MATH"}853{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -5, 14, 6, 0, -10, 18],\n [0, 17, -4, -14, -2, 11, -12],\n [0, 0, -9, -13, -6, -5, -18],\n [0, 0, 0, 18, -7, -14, -13],\n [0, 0, 0, 0, -16, -3, -2],\n [0, 0, 0, 0, 0, -7, 8],\n [0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}854{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, 2, 0, 0, 8, 10, 11],\n [2, -1, -2, -10, 8, -1, 4],\n [0, -2, -5, 0, 8, -10, 5],\n [0, -10, 0, -2, 8, -6, 3],\n [8, 8, 8, 8, 16, 16, -7],\n [10, -1, -10, -6, 16, -1, 8],\n [11, 4, 5, 3, -7, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "711", "dataset": "MATH"}855{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-17, 8, 4, -4, -6, 3, -9],\n [8, -1, -6, -1, 1, 2, 2],\n [4, -6, -5, 0, -3, -6, -1],\n [-4, -1, 0, -6, -6, 4, 4],\n [-6, 1, -3, -6, 7, -1, -4],\n [3, 2, -6, 4, -1, 7, 9],\n [-9, 2, -1, 4, -4, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-103", "dataset": "MATH"}856{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, -14, -16, -2, -6, -16, 9],\n [0, -1, 16, -5, -3, -7, -8],\n [0, 0, -6, 11, 7, -1, -6],\n [0, 0, 0, -2, -13, -14, 14],\n [0, 0, 0, 0, 16, 8, -7],\n [0, 0, 0, 0, 0, -4, 14],\n [0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28719", "dataset": "MATH"}857{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (7, 6) rounded to the nearest integer?\n[[5, 11, -9, -8, 3, -16, 4],\n [0, -6, 17, -16, 3, 6, 1],\n [0, 0, 3, 18, -1, 1, -14],\n [0, 0, 0, -7, 7, 14, 14],\n [0, 0, 0, 0, -2, 5, 3],\n [0, 0, 0, 0, 0, 16, -14],\n [0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}858{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[1, -3, -2, -2, 15, -8, 16],\n [0, 17, -11, 0, 14, 4, -17],\n [0, 0, -12, 10, 12, 11, 16],\n [0, 0, 0, -9, -18, -1, 0],\n [0, 0, 0, 0, -18, 16, -2],\n [0, 0, 0, 0, 0, -7, -15],\n [0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "415", "dataset": "MATH"}859{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[-14, 9, -7, 17, -6, 2, 13],\n [0, 18, -10, 18, -17, -16, -9],\n [0, 0, 13, 2, 15, 6, 13],\n [0, 0, 0, -18, 17, 2, -3],\n [0, 0, 0, 0, -5, 4, 5],\n [0, 0, 0, 0, 0, 18, -4],\n [0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}860{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[2, 0, -15, 3, -4, -13, -8],\n [11, 5, 3, 11, -15, -13, 7],\n [0, -17, -15, -14, 16, 10, -3],\n [-7, 2, -10, -8, -11, 7, 13],\n [-15, 15, 9, 6, 16, 0, 16],\n [10, -5, 2, 17, -5, -4, 11],\n [-7, -14, 8, -4, 7, -10, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}861{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[-6, 14, 15, -15, -6, -9, -18],\n [-8, -10, 4, -6, -14, 6, -9],\n [-14, 3, 6, 18, 1, 9, 2],\n [-8, 10, -14, 18, -14, 14, 17],\n [-11, -13, -4, -4, -10, -14, 7],\n [4, -3, 16, -9, 8, -3, 2],\n [-7, -10, -3, -10, 10, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}862{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, 4, -8, 8, 16, 0, 6],\n [4, -2, 4, 8, 4, 4, 6],\n [-8, 4, 5, 0, 16, 4, -10],\n [8, 8, 0, -11, 6, 0, -4],\n [16, 4, 16, 6, -17, 7, 2],\n [0, 4, 4, 0, 7, 4, 9],\n [6, 6, -10, -4, 2, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}863{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, 8, 2, -18, 13, -5, -5],\n [14, 17, -7, 6, -4, 1, 15],\n [-5, 11, -6, -5, 10, 7, -16],\n [6, 8, -3, -8, 10, 5, 10],\n [15, -8, 1, 1, -10, 4, 17],\n [8, 5, 6, 6, 14, 12, -9],\n [-4, -18, -3, 2, -17, -16, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}864{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, 8, 17, 16, 5, -11, -12],\n [-15, 11, -9, 6, 13, 13, 13],\n [-9, -10, 6, 6, -3, -3, 11],\n [-14, -12, -6, -11, 14, -9, 1],\n [13, 10, -18, 8, 1, -5, -4],\n [-13, -17, 10, 13, -14, 3, 9],\n [13, 10, -16, 12, -6, -13, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}865{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, 2, -9, 0, 7, 3, 1],\n [2, 2, -2, -11, 1, -2, -4],\n [-9, -2, -14, -2, 8, -12, 3],\n [0, -11, -2, 0, -4, -4, 6],\n [7, 1, 8, -4, 15, -4, -10],\n [3, -2, -12, -4, -4, -13, -2],\n [1, -4, 3, 6, -10, -2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}866{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -4, 4, -3, -14, 7, 4],\n [-4, -6, 0, -4, -4, 3, -7],\n [4, 0, -18, -6, -6, 8, -6],\n [-3, -4, -6, -16, -11, 0, -4],\n [-14, -4, -6, -11, 4, -8, 6],\n [7, 3, 8, 0, -8, -13, 4],\n [4, -7, -6, -4, 6, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}867{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[8, -9, 12, -4, -2, 4, -2],\n [-9, -7, 3, 10, -1, 2, -4],\n [12, 3, 17, -1, 12, -6, 13],\n [-4, 10, -1, -15, 2, -4, -6],\n [-2, -1, 12, 2, -13, 7, 12],\n [4, 2, -6, -4, 7, -4, -4],\n [-2, -4, 13, -6, 12, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16886", "dataset": "MATH"}868{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, -17, -12, 2, 12, 4, 6],\n [16, 16, -12, -14, 13, -14, 6],\n [12, 1, 3, -6, -17, 3, -10],\n [-17, 13, -11, -3, 14, -8, 13],\n [-11, 13, 2, 6, 1, -18, 2],\n [-12, 6, -10, 3, -17, 0, -13],\n [-14, -9, -18, 7, 7, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}869{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -5, 13, 16, -2, -9, 16],\n [-3, -13, -15, -10, 10, -12, -3],\n [-13, -16, -5, -5, -10, 17, 4],\n [-4, -12, 1, 0, -13, -18, -12],\n [16, 6, 4, 6, -8, 15, 12],\n [-7, -10, -6, 1, 2, 3, -18],\n [-2, -15, -13, 0, 11, 4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}870{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[10, -2, 0, 8, 6, -6, -4],\n [-2, 6, 1, 0, 0, 4, 2],\n [0, 1, -14, 0, 2, -8, 16],\n [8, 0, 0, 11, 2, 0, -7],\n [6, 0, 2, 2, 12, 6, -4],\n [-6, 4, -8, 0, 6, -4, -3],\n [-4, 2, 16, -7, -4, -3, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}871{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[10, -4, 2, -4, 0, -13, -2],\n [-4, -4, 0, -14, 0, 6, -4],\n [2, 0, 17, 8, -9, -16, -6],\n [-4, -14, 8, 0, 0, -17, 2],\n [0, 0, -9, 0, 17, -4, -12],\n [-13, 6, -16, -17, -4, -15, 9],\n [-2, -4, -6, 2, -12, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265", "dataset": "MATH"}872{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, 4, 1, 10, 0, -4, -1],\n [4, -7, 2, 16, 14, 9, 14],\n [1, 2, 1, -6, -8, -6, -7],\n [10, 16, -6, 16, 2, 1, -6],\n [0, 14, -8, 2, 14, 0, 0],\n [-4, 9, -6, 1, 0, -7, -8],\n [-1, 14, -7, -6, 0, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "830", "dataset": "MATH"}873{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-3, 2, 14, -2, -10, 0, -12],\n [2, 17, 1, 2, -4, -7, 2],\n [14, 1, -5, -16, -9, 1, 4],\n [-2, 2, -16, -14, 9, -12, -10],\n [-10, -4, -9, 9, -14, -4, 2],\n [0, -7, 1, -12, -4, -1, 6],\n [-12, 2, 4, -10, 2, 6, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}874{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, 18, 17, 1, -3, -11, 3],\n [-14, -14, -8, 0, -2, 18, -1],\n [-10, -2, 14, 1, -1, 5, -6],\n [9, -16, 17, -8, 2, 18, -17],\n [-13, -14, 13, 18, -8, -2, -5],\n [-17, -1, 14, 11, -4, 10, 7],\n [-18, -2, -17, -4, 3, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}875{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 5, 15, 2, -17, -3, 2],\n [0, -11, -5, 3, -1, -14, 11],\n [0, 0, 12, 12, -10, 18, -13],\n [0, 0, 0, 14, 11, 5, 9],\n [0, 0, 0, 0, -10, -8, -13],\n [0, 0, 0, 0, 0, 6, 16],\n [0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}876{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 10, -1, 16, -6, -2, -7],\n [10, -7, -4, 3, -4, -6, 0],\n [-1, -4, 2, -4, 0, 2, 2],\n [16, 3, -4, 12, 5, -8, 0],\n [-6, -4, 0, 5, -15, 15, -11],\n [-2, -6, 2, -8, 15, 18, 0],\n [-7, 0, 2, 0, -11, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}877{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 12, 14, 2, 16, 2, -4],\n [0, -17, 11, 9, -2, 1, 10],\n [0, 0, -9, 0, -18, 15, -5],\n [0, 0, 0, -3, -9, 13, 1],\n [0, 0, 0, 0, 12, 11, 5],\n [0, 0, 0, 0, 0, 7, 14],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6392", "dataset": "MATH"}878{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, -1, -18, -4, -14, 8, -2],\n [0, 7, -17, 9, 4, 1, 17],\n [0, 0, 9, 3, -2, 12, -8],\n [0, 0, 0, 4, 10, 4, 17],\n [0, 0, 0, 0, 7, 13, 2],\n [0, 0, 0, 0, 0, 16, -5],\n [0, 0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4732", "dataset": "MATH"}879{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -12, 9, -17, -18, 18, 5],\n [0, -12, 10, -18, 11, 13, -9],\n [0, 0, 18, 8, -9, 3, 5],\n [0, 0, 0, -14, -13, 13, 1],\n [0, 0, 0, 0, -18, 16, 0],\n [0, 0, 0, 0, 0, -12, -14],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}880{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, -10, 9, -9, 16, -12, 6],\n [11, 7, -7, -6, -15, -18, -13],\n [-17, 8, -1, 10, 14, -16, 1],\n [-15, -1, -11, 3, 3, 0, 9],\n [-17, -10, 16, 3, 7, 15, -12],\n [11, 6, -10, 8, -18, 14, -11],\n [13, 0, 17, 3, 7, -16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}881{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[16, -12, -4, -15, 18, 9, -10],\n [16, 6, -10, 14, -2, -7, -10],\n [-14, 7, 0, 16, -17, -12, -10],\n [3, 14, -3, 5, -11, 11, 7],\n [16, -2, -9, -2, -12, -17, -8],\n [-16, 1, -6, 4, -2, 10, 13],\n [16, 16, 15, 2, -3, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3256", "dataset": "MATH"}882{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-5, -16, -12, -8, 14, 0, 4],\n [4, 10, -13, -14, 13, 7, -5],\n [-1, 2, 6, 1, 5, -16, 3],\n [-11, 10, -12, -13, -13, -7, 3],\n [7, 6, 0, 17, 16, -6, 6],\n [13, 11, 2, -11, -12, -16, 18],\n [-16, -1, -10, 5, -12, 14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}883{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 2, 0, 14, -2, -2, -6],\n [2, 1, -15, -1, 4, 10, 14],\n [0, -15, -16, -4, -10, -10, -7],\n [14, -1, -4, -11, 5, -4, -2],\n [-2, 4, -10, 5, -4, 2, -8],\n [-2, 10, -10, -4, 2, -17, -6],\n [-6, 14, -7, -2, -8, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}884{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[16, -7, -9, 18, -17, -16, -5],\n [1, -15, 7, -4, -10, -16, -17],\n [11, 18, -2, -16, -10, -11, -10],\n [-2, 5, -11, -5, -3, -1, 5],\n [8, 9, -12, 15, 8, 15, 0],\n [-13, 11, 9, -7, -4, -4, 17],\n [-16, -18, -12, -10, -18, -14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}885{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -17, 4, 10, 0, 1, -7],\n [0, 16, -12, 4, -2, -17, -14],\n [0, 0, -8, 5, 14, 8, 16],\n [0, 0, 0, 13, -8, -16, 2],\n [0, 0, 0, 0, 9, 17, 9],\n [0, 0, 0, 0, 0, -7, 5],\n [0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}886{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, 0, 0, 0, 0, -6, -6],\n [0, -17, -4, -11, -8, 2, -12],\n [0, -4, 0, 8, 2, -4, -10],\n [0, -11, 8, 10, 0, -6, 10],\n [0, -8, 2, 0, -7, 0, 0],\n [-6, 2, -4, -6, 0, 6, 0],\n [-6, -12, -10, 10, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}887{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-9, 8, -9, 8, -8, -4, 8],\n [8, -13, 12, -12, 4, -6, -15],\n [-9, 12, 5, 12, 3, 6, 12],\n [8, -12, 12, 18, 9, 6, 2],\n [-8, 4, 3, 9, 17, 2, -6],\n [-4, -6, 6, 6, 2, 1, -7],\n [8, -15, 12, 2, -6, -7, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}888{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-10, -17, 9, 15, -9, 0, 10],\n [0, -13, -12, 17, -11, 0, -9],\n [0, 0, 8, 10, 0, -1, 4],\n [0, 0, 0, -12, 7, -3, 13],\n [0, 0, 0, 0, 14, 6, -2],\n [0, 0, 0, 0, 0, 15, 6],\n [0, 0, 0, 0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}889{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -11, 0, -1, -2, -1, 0],\n [0, -8, -12, 8, 18, -14, -11],\n [0, 0, 7, -4, -3, 10, 9],\n [0, 0, 0, 14, -1, -7, -9],\n [0, 0, 0, 0, 7, -4, 2],\n [0, 0, 0, 0, 0, 7, 7],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}890{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-4, 5, 2, 4, 12, 15, 9],\n [0, 3, -16, -10, -13, -18, 3],\n [0, 0, 18, 0, -18, 5, -2],\n [0, 0, 0, 13, 14, 11, 15],\n [0, 0, 0, 0, -18, 3, 14],\n [0, 0, 0, 0, 0, -13, 1],\n [0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-150", "dataset": "MATH"}891{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -12, 4, -3, 6, 6, -10],\n [-12, -9, -4, 12, 8, -3, 6],\n [4, -4, 6, 4, -2, 10, 2],\n [-3, 12, 4, -3, 6, 10, -5],\n [6, 8, -2, 6, -15, 2, 18],\n [6, -3, 10, 10, 2, -16, -9],\n [-10, 6, 2, -5, 18, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}892{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[10, 16, -7, -11, 6, 8, -13],\n [0, -8, -13, -14, -12, 0, -13],\n [0, 0, 1, 6, -11, 18, -17],\n [0, 0, 0, -18, 14, 5, -14],\n [0, 0, 0, 0, -1, 6, 2],\n [0, 0, 0, 0, 0, -16, 1],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}893{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, -11, 11, 9, 7, 15, 13],\n [0, 1, -5, 4, -16, 0, -5],\n [0, 0, -18, 0, -4, 6, -18],\n [0, 0, 0, 1, -14, -4, -17],\n [0, 0, 0, 0, -10, 8, 9],\n [0, 0, 0, 0, 0, -13, 11],\n [0, 0, 0, 0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18044", "dataset": "MATH"}894{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-12, -4, 4, 17, 12, -11, 11],\n [15, 14, -18, -3, -8, 8, 3],\n [0, -13, 1, -16, -18, 4, -16],\n [15, -2, 8, 4, -8, -4, 7],\n [-8, -12, -11, -14, -2, 4, -17],\n [8, 2, -12, 7, 11, -7, -8],\n [-2, -9, -3, -4, -4, 1, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "673", "dataset": "MATH"}895{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[13, 3, 16, -5, 11, 12, -9],\n [-13, 8, -8, 17, -9, -3, 5],\n [2, 17, 4, 2, 13, -2, -2],\n [2, -15, 4, 6, 13, -13, -5],\n [-3, 13, -3, 0, 18, 2, -4],\n [7, 11, -4, -6, 8, 4, 15],\n [15, 4, 1, -10, 1, -5, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}896{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, 15, 10, 13, -14, -15, 4],\n [0, 14, 5, -3, 13, 0, 7],\n [0, 0, -1, -12, 13, 5, -3],\n [0, 0, 0, 15, 0, -5, -6],\n [0, 0, 0, 0, -7, -5, 17],\n [0, 0, 0, 0, 0, 9, 4],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3060", "dataset": "MATH"}897{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[-16, -8, -9, -7, -8, -18, 13],\n [-8, -3, -8, 7, 6, 6, -14],\n [-9, -8, -11, -1, -1, 6, 0],\n [-7, 7, -1, 18, -12, 2, 4],\n [-8, 6, -1, -12, -2, 0, 0],\n [-18, 6, 6, 2, 0, 15, 0],\n [13, -14, 0, 4, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36", "dataset": "MATH"}898{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[16, -10, -10, -2, -4, -14, 1],\n [-10, 0, 2, -12, -3, -2, 3],\n [-10, 2, 13, -4, 2, -12, 1],\n [-2, -12, -4, -15, -2, -7, -8],\n [-4, -3, 2, -2, 3, 2, -1],\n [-14, -2, -12, -7, 2, -5, -2],\n [1, 3, 1, -8, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}899{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (6, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -16, 17, -6, -18, -8, 5],\n [0, -17, -2, -2, 1, -4, -15],\n [0, 0, -18, -15, -17, 8, 15],\n [0, 0, 0, -14, 10, 6, -5],\n [0, 0, 0, 0, -13, 3, -16],\n [0, 0, 0, 0, 0, -6, 15],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42", "dataset": "MATH"}900{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 18, 18, -12, 14, 3, 8],\n [0, -3, 2, -8, 2, -10, 8],\n [0, 0, 4, 10, -3, -16, -3],\n [0, 0, 0, 16, -12, -11, 16],\n [0, 0, 0, 0, -18, 6, -7],\n [0, 0, 0, 0, 0, 5, -6],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4825", "dataset": "MATH"}901{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -5, -6, 5, -4, -4, 10],\n [-5, -15, -3, -8, 1, 0, 0],\n [-6, -3, 10, 8, -1, 4, 0],\n [5, -8, 8, 15, 6, 2, 12],\n [-4, 1, -1, 6, 12, 2, 2],\n [-4, 0, 4, 2, 2, 8, 2],\n [10, 0, 0, 12, 2, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "467", "dataset": "MATH"}902{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[13, 2, -8, -8, -9, 0, -5],\n [2, -11, 3, -4, 0, 0, 3],\n [-8, 3, 6, -7, 12, 16, -4],\n [-8, -4, -7, 15, -6, -9, -13],\n [-9, 0, 12, -6, 2, 6, -4],\n [0, 0, 16, -9, 6, -12, 0],\n [-5, 3, -4, -13, -4, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}903{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-13, 11, -2, 0, -2, -9, -9],\n [11, -17, 10, -2, 6, -12, 8],\n [-2, 10, 13, 12, -6, 2, -16],\n [0, -2, 12, -3, -6, -1, -4],\n [-2, 6, -6, -6, -12, 8, 2],\n [-9, -12, 2, -1, 8, 6, 4],\n [-9, 8, -16, -4, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-394", "dataset": "MATH"}904{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -9, -3, 16, -4, 4, 18],\n [-11, 7, 3, -14, 15, 8, 0],\n [16, 1, -6, -1, -1, -18, 13],\n [6, 2, 8, -8, -18, 0, 13],\n [-11, 0, -3, 16, -17, -7, 10],\n [-9, 3, 15, 2, 18, -14, -13],\n [13, -16, -9, -14, 5, 1, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273", "dataset": "MATH"}905{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 4) rounded to the nearest integer?\n[[12, -2, 5, -1, 7, -12, -5],\n [0, 11, -2, 1, -9, 5, -7],\n [0, 0, -10, -1, -12, 9, 17],\n [0, 0, 0, -15, 16, -10, -7],\n [0, 0, 0, 0, 14, -18, 9],\n [0, 0, 0, 0, 0, -11, -3],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}906{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, 18, -10, -1, -10, 2, -18],\n [0, -14, 0, 16, 14, -1, -5],\n [0, 0, -3, 12, 16, 1, -18],\n [0, 0, 0, -12, 1, 18, 17],\n [0, 0, 0, 0, -16, 17, -10],\n [0, 0, 0, 0, 0, 11, 2],\n [0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "283", "dataset": "MATH"}907{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 2, 1, 18, -2, 9, 12],\n [0, 13, 13, 4, 2, 6, 14],\n [0, 0, 9, -17, 13, 7, -14],\n [0, 0, 0, -1, -5, 9, 11],\n [0, 0, 0, 0, -7, 6, -15],\n [0, 0, 0, 0, 0, 16, 2],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4366", "dataset": "MATH"}908{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 11, 10, -9, 13, -10, 6],\n [-3, -4, -1, 4, -16, -12, -8],\n [5, 16, 6, 9, -7, 4, -2],\n [18, -1, -10, 16, 17, -1, 1],\n [2, 1, -13, -10, 10, 10, -6],\n [17, 8, -13, 13, 9, -18, 12],\n [11, -1, 10, 4, 3, -17, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79", "dataset": "MATH"}909{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 13, -13, -5, 5, 2, -5],\n [-7, -15, 2, -2, 10, -3, -1],\n [-8, 13, 9, -3, 15, 11, 3],\n [-14, -10, -6, 4, 8, 13, 12],\n [14, 7, -1, -7, -16, -14, -5],\n [-7, -15, -3, -8, 17, -17, -6],\n [-11, 2, 7, 16, -4, 11, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-75", "dataset": "MATH"}910{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-3, -12, -8, 1, 0, 6, -12],\n [-12, -15, 6, 0, -8, 11, -2],\n [-8, 6, -4, 8, 6, 3, 2],\n [1, 0, 8, 13, -12, -10, -2],\n [0, -8, 6, -12, 10, -10, 7],\n [6, 11, 3, -10, -10, -14, 1],\n [-12, -2, 2, -2, 7, 1, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}911{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, 9, -9, -3, -9, 7, 15],\n [15, -5, -1, -18, -2, 3, 18],\n [-3, -12, -4, 2, -17, 6, -10],\n [1, -9, 2, -15, 11, 15, 11],\n [-5, 3, -18, -11, -8, -18, -14],\n [-9, -6, 2, 17, 14, 9, -10],\n [-8, 10, -12, 8, 3, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}912{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 5) of the inverse. Round your answer to the nearest integer:\n[[9, 1, -4, -4, -7, -2, 4],\n [0, -3, 8, 4, -18, -12, -1],\n [0, 0, -17, 7, 13, 4, -1],\n [0, 0, 0, -17, 11, 12, -3],\n [0, 0, 0, 0, -17, 11, 11],\n [0, 0, 0, 0, 0, 7, 16],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}913{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (7, 3) of the inverse. Round your answer to the nearest integer:\n[[18, 9, 0, 9, -5, -2, -9],\n [9, 2, -3, -4, -12, -6, 1],\n [0, -3, -18, -2, -2, 2, -12],\n [9, -4, -2, -10, -1, -4, -12],\n [-5, -12, -2, -1, 3, 1, -12],\n [-2, -6, 2, -4, 1, 6, 8],\n [-9, 1, -12, -12, -12, 8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}914{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 18, -1, -4, 1, -17, 6],\n [0, 8, -6, 9, -4, 10, 2],\n [0, 0, 18, -16, 16, -5, -17],\n [0, 0, 0, 8, 15, -14, 6],\n [0, 0, 0, 0, 7, 8, 7],\n [0, 0, 0, 0, 0, -6, -10],\n [0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1799", "dataset": "MATH"}915{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 2, -6, -4, 12, -14, -3],\n [2, -3, 6, 6, 11, -3, 4],\n [-6, 6, 14, -6, 4, 2, -6],\n [-4, 6, -6, 7, -6, 0, 6],\n [12, 11, 4, -6, 5, -10, -2],\n [-14, -3, 2, 0, -10, -14, 9],\n [-3, 4, -6, 6, -2, 9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}916{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-15, -4, 13, 3, 4, -3, 4],\n [-4, 5, 8, 5, -4, 8, -5],\n [13, 8, 12, 15, -12, -6, 0],\n [3, 5, 15, 5, -4, 2, -8],\n [4, -4, -12, -4, 15, 1, 2],\n [-3, 8, -6, 2, 1, -17, 1],\n [4, -5, 0, -8, 2, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-160", "dataset": "MATH"}917{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 0, -2, -6, 8, 1, -8],\n [0, -13, 3, -8, 14, -1, 2],\n [-2, 3, -17, -18, -4, -10, -2],\n [-6, -8, -18, -17, 1, 0, 1],\n [8, 14, -4, 1, 13, -1, -4],\n [1, -1, -10, 0, -1, 2, 0],\n [-8, 2, -2, 1, -4, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51", "dataset": "MATH"}918{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -7, 0, -6, -2, 2, -5],\n [-7, 1, 4, 5, 0, 3, -12],\n [0, 4, 4, 8, -6, -5, -4],\n [-6, 5, 8, -10, 3, -2, 4],\n [-2, 0, -6, 3, 1, -4, 14],\n [2, 3, -5, -2, -4, 14, -6],\n [-5, -12, -4, 4, 14, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14783", "dataset": "MATH"}919{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[1, 0, 14, 4, -10, -1, -17],\n [-2, -3, 5, 12, -18, 9, 14],\n [18, -15, -18, 14, -9, -16, 18],\n [2, -10, 5, -11, 5, 5, -9],\n [16, -15, -10, -8, -6, 8, 11],\n [-7, 0, -15, 15, 4, 7, -12],\n [-1, -15, -11, 3, 7, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}920{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -4, -1, 8, -13, 15, -14],\n [-7, 10, 18, -7, 6, 15, -8],\n [4, 5, -1, -9, -14, 12, 6],\n [-2, 9, -18, -17, -17, 8, -11],\n [8, 18, -2, -15, 12, -14, 6],\n [9, 0, 18, 4, 17, -6, -2],\n [11, 4, -16, -6, 13, 16, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}921{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-16, 10, -9, 1, 15, -4, -18],\n [7, 13, -17, 13, 10, 1, 4],\n [-7, -9, 0, -9, 0, 7, 5],\n [-10, 10, 10, 18, 9, -16, 4],\n [-15, -5, -6, 9, 1, 9, 13],\n [-5, -6, -8, -4, -10, -16, -14],\n [9, -4, -16, 16, -12, 11, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}922{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 12, -1, 9, 2, -10, 15],\n [0, 5, -3, 9, 16, -13, -8],\n [0, 0, -6, -4, -11, 5, -8],\n [0, 0, 0, -12, -14, 13, 9],\n [0, 0, 0, 0, 1, 11, 3],\n [0, 0, 0, 0, 0, -9, 16],\n [0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}923{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[6, 13, -2, -8, 3, -7, -6],\n [13, 18, -11, 14, 0, -1, -4],\n [-2, -11, 17, 4, -2, 12, 2],\n [-8, 14, 4, -1, 0, -2, -4],\n [3, 0, -2, 0, -18, 4, -4],\n [-7, -1, 12, -2, 4, 1, -11],\n [-6, -4, 2, -4, -4, -11, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}924{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, -4, -10, -5, -9, 3, 12],\n [0, -2, -18, -5, 16, -18, 8],\n [0, 0, -10, 17, 13, 1, 8],\n [0, 0, 0, 10, -14, 14, -11],\n [0, 0, 0, 0, -14, -16, -3],\n [0, 0, 0, 0, 0, 6, -11],\n [0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-137", "dataset": "MATH"}925{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[9, -4, 10, -15, 15, 18, 5],\n [2, -17, -12, -8, -7, -15, 16],\n [7, -1, 18, -3, -7, 18, 0],\n [-4, 3, 1, -6, 4, 12, 7],\n [13, 2, -2, 10, 10, 3, 0],\n [-5, 4, -17, 13, 14, -12, 15],\n [-15, 4, 1, 3, 10, 18, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}926{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 1, 10, 8, 2, 4, 8],\n [1, 4, 2, -12, 9, 7, 3],\n [10, 2, 4, 1, -8, 0, -2],\n [8, -12, 1, 16, -4, 2, -14],\n [2, 9, -8, -4, 5, 0, 2],\n [4, 7, 0, 2, 0, 9, 2],\n [8, 3, -2, -14, 2, 2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427", "dataset": "MATH"}927{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[3, -17, 14, 8, 0, -15, 0],\n [6, -13, -6, 3, -15, -17, -16],\n [11, -15, 10, 14, -6, 13, 9],\n [18, 9, 8, 6, 11, -13, 11],\n [-10, -13, 10, 4, -13, 3, -17],\n [12, -13, -14, 1, -7, -11, 14],\n [12, -16, 0, -11, 11, 12, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685", "dataset": "MATH"}928{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-13, -17, 4, 11, -10, -12, -4],\n [-4, 2, -5, -8, -8, 1, -6],\n [11, 1, -11, 18, 14, 7, -11],\n [-1, -5, -1, 2, 4, -15, -9],\n [-8, 1, 0, -18, 12, -17, -14],\n [15, -15, 8, -16, 7, -18, -3],\n [16, 0, -3, 14, 12, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-342", "dataset": "MATH"}929{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[-13, 16, -16, 13, -6, -5, -11],\n [0, -5, -8, 16, 17, -16, 6],\n [-6, -3, 9, 8, -9, -1, -11],\n [-12, 3, -10, 10, 18, 10, 9],\n [2, 14, 7, -4, -17, -7, 14],\n [-4, -18, 14, -15, 9, -5, -7],\n [-13, 1, 2, -3, -7, 1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}930{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-17, -2, 10, 4, 12, -14, -3],\n [-2, -9, 8, -12, 14, -9, -4],\n [10, 8, 14, -2, -9, 0, 12],\n [4, -12, -2, 12, -7, 2, -8],\n [12, 14, -9, -7, -1, -12, -8],\n [-14, -9, 0, 2, -12, -4, -8],\n [-3, -4, 12, -8, -8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-67", "dataset": "MATH"}931{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-16, -8, -16, 11, -13, -13, 12],\n [0, 2, -13, 10, -8, 3, -13],\n [0, 0, 17, -18, 3, -10, -11],\n [0, 0, 0, -11, -7, 12, 14],\n [0, 0, 0, 0, -15, -7, 4],\n [0, 0, 0, 0, 0, -10, -13],\n [0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}932{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[-12, 16, 11, 10, -18, -18, -12],\n [0, 17, 12, 6, 5, -18, 12],\n [0, 0, -16, -7, 1, 11, -9],\n [0, 0, 0, 13, 0, 11, 14],\n [0, 0, 0, 0, -7, 17, -15],\n [0, 0, 0, 0, 0, -9, 10],\n [0, 0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}933{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-3, -10, 4, -1, 0, 2, 15],\n [-10, -5, 9, -17, -8, 5, -5],\n [4, 9, 17, -7, -8, 2, -2],\n [-1, -17, -7, 10, 10, -3, 9],\n [0, -8, -8, 10, -16, 11, -8],\n [2, 5, 2, -3, 11, -10, -5],\n [15, -5, -2, 9, -8, -5, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-162", "dataset": "MATH"}934{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[15, 9, -11, 2, 5, 5, -6],\n [0, 6, 9, -11, 12, -12, -2],\n [0, 0, -12, -9, 9, 10, 16],\n [0, 0, 0, -11, 11, 11, 12],\n [0, 0, 0, 0, -2, -8, 3],\n [0, 0, 0, 0, 0, -5, 3],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}935{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[9, 17, -9, 18, 6, -2, -15],\n [0, 6, 13, -11, -7, 2, 8],\n [0, 0, 2, -18, -10, -16, 0],\n [0, 0, 0, 17, -15, -1, 13],\n [0, 0, 0, 0, -17, 18, 18],\n [0, 0, 0, 0, 0, -12, -17],\n [0, 0, 0, 0, 0, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2218", "dataset": "MATH"}936{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[12, -2, -3, -9, 16, 14, 16],\n [8, -12, 8, -7, 14, -6, -17],\n [-16, -8, -14, -17, 9, -6, 16],\n [-6, -7, -1, -1, -2, 3, -6],\n [0, 5, 0, 2, 5, 11, 9],\n [16, -2, 15, -10, -6, -5, 7],\n [2, 1, -8, 16, 12, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}937{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-14, -2, 2, -5, -16, 12, 6],\n [-2, 7, -2, 0, 8, -12, 7],\n [-14, -17, -3, -8, 4, 16, -13],\n [18, -18, 14, -1, -16, 0, -9],\n [1, -8, 13, 1, 13, 18, 3],\n [-15, -6, -13, 10, -17, 6, 13],\n [7, 7, 3, -9, 4, -15, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-69", "dataset": "MATH"}938{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[14, -2, 6, 14, -11, -9, 10],\n [-2, -18, -1, -2, 8, -10, -4],\n [6, -1, -11, 0, 12, -4, 0],\n [14, -2, 0, -5, -8, 10, 2],\n [-11, 8, 12, -8, 9, 12, 8],\n [-9, -10, -4, 10, 12, -4, -12],\n [10, -4, 0, 2, 8, -12, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-108", "dataset": "MATH"}939{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[-5, -18, -8, 11, 5, -15, 3],\n [0, -3, 14, 14, -9, -17, -15],\n [0, 0, 14, 14, 1, -6, -8],\n [0, 0, 0, -6, 9, 3, 0],\n [0, 0, 0, 0, -10, 0, 4],\n [0, 0, 0, 0, 0, 18, 16],\n [0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}940{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -4, -6, -1, 4, 10, -12],\n [-4, -8, 0, 2, 9, 8, -2],\n [-6, 0, -7, 2, 2, -8, 6],\n [-1, 2, 2, 12, -2, -2, -10],\n [4, 9, 2, -2, -9, 0, -12],\n [10, 8, -8, -2, 0, -17, 2],\n [-12, -2, 6, -10, -12, 2, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}941{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, -5, -14, 12, 13, 15, -9],\n [12, 8, -1, -14, -2, -8, -14],\n [18, 2, 5, 11, -3, 3, -17],\n [0, 18, -17, -8, 14, -10, 6],\n [-13, -8, 8, -11, 12, 8, -14],\n [-4, -17, -4, 12, 1, -16, -9],\n [7, -9, -6, 2, 15, 13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}942{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, -18, -7, 16, 5, -9, 5],\n [-1, -11, -6, -3, -5, -10, -10],\n [-14, -8, 0, -9, -3, 10, -14],\n [-1, 16, 17, 3, 5, -7, -7],\n [16, 0, 18, -5, 4, 3, -8],\n [-17, -9, -14, 11, 2, 14, 6],\n [-12, 9, -3, 18, -16, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2011", "dataset": "MATH"}943{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[0, 4, -5, -16, -4, 7, 0],\n [4, -4, -4, 2, 6, -5, 2],\n [-5, -4, 0, 2, -12, -2, 6],\n [-16, 2, 2, -5, 12, 0, -2],\n [-4, 6, -12, 12, -9, 16, -3],\n [7, -5, -2, 0, 16, -3, 1],\n [0, 2, 6, -2, -3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}944{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/252 * A where A =\n[[-1, 16, 5, 4, 14, 10, -9],\n [-4, -9, 7, 10, 15, -1, -17],\n [6, 2, 12, 3, -10, 8, 6],\n [6, 8, -9, 11, -15, 2, 11],\n [14, 7, -17, 4, 12, -15, 1],\n [6, -18, -17, -13, -12, -15, -1],\n [-14, 6, -18, 15, -16, -2, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1529", "dataset": "MATH"}945{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -17, -18, 15, -11, -10, 9],\n [0, 1, -12, 16, 0, -2, -1],\n [-12, 8, 11, 4, 1, 4, 7],\n [-5, 12, 8, -10, 4, -9, 4],\n [-9, -17, 18, -18, -1, 16, -12],\n [3, 6, 4, -10, 8, -8, 8],\n [9, -1, 17, 15, -6, 11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}946{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[3, 5, 11, 1, -13, 14, -4],\n [0, 13, -5, -11, 17, 3, 1],\n [0, 0, 9, 4, 5, 4, -15],\n [0, 0, 0, 12, 14, 0, -9],\n [0, 0, 0, 0, 11, 4, 17],\n [0, 0, 0, 0, 0, 3, -1],\n [0, 0, 0, 0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}947{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 16, -10, -4, 0, 18, -13],\n [17, -14, -16, -9, -6, -15, 14],\n [15, 17, 14, 2, -14, -6, -2],\n [-9, -9, -17, 2, -18, 11, -1],\n [16, 3, -16, -13, 17, -3, -16],\n [17, -8, -2, 0, -11, -5, 7],\n [6, -9, 13, -4, -15, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}948{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-6, -7, -4, 10, 4, -6, 16],\n [-7, 11, -14, -17, 11, 16, -9],\n [-10, -2, 11, 16, -12, -7, 15],\n [-16, 14, -6, -8, 1, 12, 14],\n [15, -10, -12, -10, 7, -17, -14],\n [-17, -9, 12, 14, -13, -5, -5],\n [-4, 14, 12, -2, -4, 1, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}949{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[10, -10, 10, 15, -10, 11, -2],\n [0, 13, 13, -12, 13, -14, -16],\n [0, 0, -3, -8, -6, -1, -5],\n [0, 0, 0, 2, 7, -17, -3],\n [0, 0, 0, 0, -12, 8, 3],\n [0, 0, 0, 0, 0, -17, -3],\n [0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3989", "dataset": "MATH"}950{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -18, 13, -13, 3, -8, 4],\n [0, -5, 1, -12, 0, 7, 3],\n [0, 0, -9, 0, 12, -9, 18],\n [0, 0, 0, 2, 1, -12, -4],\n [0, 0, 0, 0, 13, -4, -12],\n [0, 0, 0, 0, 0, 3, 6],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2018", "dataset": "MATH"}951{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -10, -13, 12, 15, -6, 17],\n [13, 3, 10, -8, -13, -14, -18],\n [-9, -9, 5, -12, 3, 2, 3],\n [14, 6, 12, -3, -4, 10, 0],\n [-2, 7, 17, 17, 16, 4, -10],\n [15, -1, -3, 13, 9, 13, -1],\n [15, 10, 2, -18, -3, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}952{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, 8, 1, 12, -3, -5, 13],\n [13, -17, 3, 18, -2, 13, -2],\n [15, -12, 10, -2, 5, -11, 4],\n [14, 10, 0, -14, 18, 4, 7],\n [5, 2, 14, 7, -9, 10, 16],\n [9, -7, -12, -3, 1, 10, 16],\n [9, -12, 3, -5, 17, -9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2249", "dataset": "MATH"}953{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, -3, 16, -8, 14, 15, 14],\n [0, 1, -9, 0, -7, -9, -12],\n [0, 0, 14, -2, 6, 12, -18],\n [0, 0, 0, -18, -14, -7, -5],\n [0, 0, 0, 0, -5, -10, 8],\n [0, 0, 0, 0, 0, 9, -6],\n [0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "438", "dataset": "MATH"}954{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -3, 6, -18, 2, 1, -14],\n [-2, -18, -6, -1, -15, -5, -14],\n [14, 7, -15, 11, -2, 9, -13],\n [8, 17, -12, -18, -9, -6, 13],\n [-5, 14, 11, -10, -13, -9, -8],\n [1, 6, -7, 3, -7, -5, 17],\n [-5, -17, -17, -13, 6, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}955{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-10, 4, 12, -2, 10, -12, -4],\n [4, -3, 11, 0, -8, -6, 1],\n [12, 11, 14, 14, 12, 0, -6],\n [-2, 0, 14, 14, -8, 2, -2],\n [10, -8, 12, -8, -2, 0, 0],\n [-12, -6, 0, 2, 0, 11, 3],\n [-4, 1, -6, -2, 0, 3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7531", "dataset": "MATH"}956{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -16, -14, 15, -10, 5, -14],\n [8, 1, -17, 4, 15, 10, 16],\n [11, -16, -9, 15, -18, -13, -13],\n [-3, -18, -14, 6, 8, 7, -3],\n [7, 18, 9, 9, 11, -6, 6],\n [0, -6, -8, 4, -5, -9, 15],\n [4, 2, 1, 13, -5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1069", "dataset": "MATH"}957{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[11, 9, -5, 2, 15, -14, 12],\n [-16, 4, 11, 11, 17, -12, -14],\n [-13, -5, -8, 18, -17, 12, 8],\n [-3, -17, 7, -3, -10, -10, -14],\n [17, -12, 13, 10, 18, -16, 11],\n [12, 8, -13, 10, -10, 1, -8],\n [0, -9, -14, 4, -13, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49", "dataset": "MATH"}958{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[2, 2, 4, -6, 1, -2, 12],\n [2, 9, -10, 6, 5, 17, -10],\n [4, -10, 17, -2, 7, -2, -5],\n [-6, 6, -2, -1, -14, -16, -10],\n [1, 5, 7, -14, 16, -6, -4],\n [-2, 17, -2, -16, -6, 9, -16],\n [12, -10, -5, -10, -4, -16, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}959{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 7, 14, 2, 4, 18, 18],\n [-7, 18, 2, -6, 14, -13, -7],\n [11, 18, -1, -3, -12, -18, 9],\n [-16, -9, -5, -4, -13, -3, -1],\n [16, 6, 14, 14, 0, -8, -16],\n [-18, 6, 13, 17, -15, 4, -3],\n [-8, 3, 14, -6, 2, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49", "dataset": "MATH"}960{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-18, 3, 8, 13, -11, 15, -1],\n [0, -18, -3, 11, 4, 12, 9],\n [0, 0, -10, -17, -17, 13, -3],\n [0, 0, 0, 14, 2, 0, -6],\n [0, 0, 0, 0, -16, 2, 4],\n [0, 0, 0, 0, 0, 17, -11],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}961{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -12, -3, 3, 9, 13, -12],\n [0, -17, -11, -12, 2, 3, 16],\n [0, 0, -17, -2, 1, -13, -8],\n [0, 0, 0, 14, 17, 15, -2],\n [0, 0, 0, 0, -11, -2, -18],\n [0, 0, 0, 0, 0, -16, 15],\n [0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}962{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 10, 0, 4, 0, -8, -8],\n [10, -16, -7, -12, 2, 2, 12],\n [0, -7, 8, -4, 4, -10, 6],\n [4, -12, -4, -13, 11, 16, -12],\n [0, 2, 4, 11, 10, -9, -16],\n [-8, 2, -10, 16, -9, 16, 2],\n [-8, 12, 6, -12, -16, 2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "137", "dataset": "MATH"}963{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, -2, 13, 11, -4, 9, -16],\n [0, -14, -17, -3, -2, -7, 7],\n [0, 0, -3, -1, -11, 8, 7],\n [0, 0, 0, 4, 3, 14, -1],\n [0, 0, 0, 0, -15, 7, 0],\n [0, 0, 0, 0, 0, -12, 5],\n [0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1657", "dataset": "MATH"}964{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 17, 3, -8, -15, 13, 5],\n [0, -16, -17, 4, 1, -11, 16],\n [0, 0, 12, 12, -18, -7, -1],\n [0, 0, 0, 6, 4, -16, 11],\n [0, 0, 0, 0, 15, -10, 7],\n [0, 0, 0, 0, 0, 3, 3],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187", "dataset": "MATH"}965{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, 8, 10, -5, -15, -11, -14],\n [8, 5, 15, 9, 5, -14, -6],\n [-1, -2, 11, 0, 3, -1, 7],\n [-4, 9, 11, 9, 1, -15, -15],\n [18, -4, 15, -8, 4, 16, 16],\n [-8, -17, -4, 9, 12, 13, 15],\n [3, 10, -11, 3, -7, 4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}966{"messages": [{"content": "Find the value at position (6, 4) of the inverse of matrix 1/252 * A where A =\n[[-7, 2, -7, 12, -10, -4, 13],\n [-10, 5, -11, 9, -1, 18, 17],\n [18, 13, 2, 10, -1, 4, 14],\n [-10, -15, -3, -16, -11, -3, -17],\n [0, 5, -3, -17, 13, -18, -1],\n [13, -10, -16, 5, -8, 9, -3],\n [10, -7, -15, 7, -15, -8, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}967{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 0, 7, 13, -2, -3, 14],\n [0, -16, -4, 2, -2, 2, 6],\n [7, -4, -11, 10, -8, 4, -4],\n [13, 2, 10, -13, -6, -12, -12],\n [-2, -2, -8, -6, -11, 8, 2],\n [-3, 2, 4, -12, 8, 17, -5],\n [14, 6, -4, -12, 2, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}968{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, 6, 7, 14, -11, -6, 7],\n [-2, 5, 5, -7, 12, -3, -3],\n [11, 9, -16, 14, 5, 11, 9],\n [-17, -6, 18, -9, -6, 0, -13],\n [-1, -10, -2, -15, -13, -8, 7],\n [-8, -11, -16, -17, -1, -17, 7],\n [-7, 18, 7, 17, -3, -5, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}969{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/252 * A where A =\n[[2, -12, -8, 10, 18, 9, -15],\n [-15, 8, -13, 15, -1, 11, 14],\n [1, 17, -14, 16, 0, -7, 7],\n [0, -8, 1, -10, 1, 8, -14],\n [-9, -10, 6, -6, 13, -11, 8],\n [3, 9, -1, 4, 12, 15, -12],\n [-14, 2, -13, 16, 4, -16, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}970{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[9, 7, 14, 13, 6, 5, 8],\n [0, 1, 14, -14, 10, -14, -2],\n [0, 0, 3, 12, -18, -4, 0],\n [0, 0, 0, 7, -13, -17, 10],\n [0, 0, 0, 0, -14, -9, -13],\n [0, 0, 0, 0, 0, 6, 16],\n [0, 0, 0, 0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8878", "dataset": "MATH"}971{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 9, -12, 15, -17, -10, -4],\n [12, 17, -4, 14, 12, 8, -17],\n [-10, -18, 0, -10, -17, 18, -18],\n [-7, 7, -9, -18, -18, 12, -8],\n [-14, 16, -8, -15, 2, 17, 9],\n [-11, 1, 2, 16, 13, 17, -14],\n [-15, -12, 15, 1, -12, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}972{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[-10, 0, 1, 9, 13, 15, -3],\n [0, -8, -15, -1, -13, 13, -14],\n [0, 0, -2, 18, -4, 16, -11],\n [0, 0, 0, -5, 4, 1, -13],\n [0, 0, 0, 0, -17, 8, 13],\n [0, 0, 0, 0, 0, -2, -9],\n [0, 0, 0, 0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6039", "dataset": "MATH"}973{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, -16, 10, 16, -9, -18, -18],\n [0, 3, 0, 16, -13, 15, -4],\n [0, 0, 3, 10, -5, 11, -4],\n [0, 0, 0, 3, 14, 4, -12],\n [0, 0, 0, 0, -4, -6, -16],\n [0, 0, 0, 0, 0, 1, 9],\n [0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-165360", "dataset": "MATH"}974{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, -6, 3, -4, 1, -8, -5],\n [-6, -14, 5, -6, -6, -13, -11],\n [3, 5, 17, 9, -2, -8, -7],\n [-4, -6, 9, -8, 10, 2, -2],\n [1, -6, -2, 10, 15, -6, -6],\n [-8, -13, -8, 2, -6, -17, 4],\n [-5, -11, -7, -2, -6, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}975{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, -6, -14, -5, -12, -13, -7],\n [-3, 13, -8, -15, 10, 15, -10],\n [-9, -11, 17, 13, -13, -13, 8],\n [-17, -10, -14, 15, -5, -9, -12],\n [1, -8, -6, -2, 18, 17, 14],\n [-9, 15, -6, 6, 14, -9, 5],\n [-14, -9, 8, 17, 14, 9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}976{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[12, 10, 2, 13, 9, 2, 16],\n [0, -2, 10, -17, 14, -15, 6],\n [0, 0, 10, 18, -11, 1, -13],\n [0, 0, 0, 1, -15, 3, 14],\n [0, 0, 0, 0, -8, 18, 3],\n [0, 0, 0, 0, 0, -4, 7],\n [0, 0, 0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2690", "dataset": "MATH"}977{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, 14, 4, 0, 14, 4, -1],\n [14, -16, -8, 10, 10, -4, -8],\n [4, -8, -3, -7, -14, 4, -14],\n [0, 10, -7, 6, -4, -11, 10],\n [14, 10, -14, -4, -17, -4, 6],\n [4, -4, 4, -11, -4, 14, 10],\n [-1, -8, -14, 10, 6, 10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2461", "dataset": "MATH"}978{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/252 * A where A =\n[[7, 17, -1, 10, 12, -6, 11],\n [0, -13, -17, -11, -9, 3, -9],\n [0, 0, -15, 0, 1, -15, 7],\n [0, 0, 0, -13, 8, -3, -3],\n [0, 0, 0, 0, 1, -10, 2],\n [0, 0, 0, 0, 0, -12, 3],\n [0, 0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-328", "dataset": "MATH"}979{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, 14, -13, 3, 0, 3, 12],\n [0, 11, -15, 7, -12, -7, -18],\n [0, 0, -11, 14, -15, -13, -16],\n [0, 0, 0, 18, 8, -14, -2],\n [0, 0, 0, 0, -17, -9, 0],\n [0, 0, 0, 0, 0, -1, -17],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2884", "dataset": "MATH"}980{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[16, 15, -16, -17, 8, -17, -14],\n [2, -12, 6, -18, -10, -17, -16],\n [18, -15, 2, 7, 18, -5, -9],\n [7, -9, 18, -1, 8, -2, -9],\n [-8, 5, 0, -3, 4, -7, 0],\n [6, -16, -6, 2, 3, 10, 6],\n [4, -7, 4, -14, 10, -14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}981{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -2, 11, -17, -4, 4, 7],\n [-8, 5, -10, -5, 5, -12, -9],\n [14, 14, 8, -11, -5, -12, -1],\n [7, -4, 14, -8, 0, -1, 3],\n [17, -1, -1, 3, 6, 12, -10],\n [0, 6, -4, -14, -8, -6, 15],\n [-11, 6, 8, -8, -1, -9, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}982{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[17, -2, -14, 4, -16, 18, -9],\n [8, -12, 10, -13, -10, -11, -5],\n [-10, -8, -8, 16, -8, 17, -16],\n [0, -11, 9, -18, 11, -8, 10],\n [12, -9, 16, 10, 18, -17, -18],\n [13, 5, -17, -16, -10, 5, -7],\n [15, 15, 4, 0, 13, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}983{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, 12, -8, -15, -1, 10, 12],\n [0, 8, 11, -8, -5, -15, 17],\n [0, 0, 14, 2, 5, -6, 15],\n [0, 0, 0, 1, 10, -8, -11],\n [0, 0, 0, 0, -10, -9, 6],\n [0, 0, 0, 0, 0, 8, -15],\n [0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303", "dataset": "MATH"}984{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, 4, -12, -5, -3, -14, 8],\n [4, -13, -4, -6, -16, 4, 6],\n [-12, -4, 7, 0, -5, 11, -2],\n [-5, -6, 0, -18, -2, 8, 7],\n [-3, -16, -5, -2, -9, 14, 0],\n [-14, 4, 11, 8, 14, -14, -2],\n [8, 6, -2, 7, 0, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}985{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (5, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, 5, -9, 6, 9, -1, -5],\n [0, 1, 6, -7, -10, -10, 6],\n [0, 0, -17, 6, -1, 5, -1],\n [0, 0, 0, -13, -3, 4, 9],\n [0, 0, 0, 0, 12, 8, 8],\n [0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}986{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-8, 10, 2, 11, -6, 10, -4],\n [10, -12, 1, 10, -12, -14, 8],\n [2, 1, -18, 6, 4, -5, 2],\n [11, 10, 6, 6, -9, 1, -6],\n [-6, -12, 4, -9, -13, 6, 3],\n [10, -14, -5, 1, 6, -15, -6],\n [-4, 8, 2, -6, 3, -6, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}987{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (2, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 6, -18, -16, 2, 9, -16],\n [13, 13, 11, -6, 15, -15, -1],\n [13, -5, 13, -13, -2, -11, 16],\n [5, -16, -2, 17, -2, 11, 6],\n [3, 18, -8, -7, 2, -4, -7],\n [3, 16, -3, 14, -5, -1, -3],\n [-16, 7, -4, 17, 8, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}988{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-17, 8, 5, 16, -15, 7, 17],\n [0, 15, -6, -18, -18, -10, -8],\n [0, 0, 17, -4, -17, -9, -8],\n [0, 0, 0, 17, 10, 13, 14],\n [0, 0, 0, 0, 18, -5, 3],\n [0, 0, 0, 0, 0, -17, 18],\n [0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}989{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/252 * A where A =\n[[-9, -16, -7, -6, 15, -18, 6],\n [0, 6, -13, -15, 7, 7, 7],\n [0, 0, 9, -17, 2, -5, 18],\n [0, 0, 0, -18, 3, 6, 11],\n [0, 0, 0, 0, -16, -11, 6],\n [0, 0, 0, 0, 0, -9, 8],\n [0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}990{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 1, -2, 3, 14, 7, 8],\n [0, 4, -3, -5, -5, 7, 8],\n [0, 0, 8, -4, 6, -1, 11],\n [0, 0, 0, -2, 6, -4, 6],\n [0, 0, 0, 0, -7, -8, 14],\n [0, 0, 0, 0, 0, -4, -4],\n [0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2035", "dataset": "MATH"}991{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[18, -14, -1, -8, -11, 1, -8],\n [8, 10, 6, 0, -17, -17, -12],\n [12, 14, -8, -6, -9, 1, 2],\n [-5, 5, -12, -14, -13, 16, -10],\n [-18, 1, -13, 13, -6, 2, 18],\n [-7, -13, -4, 2, 2, 9, 17],\n [-2, -12, 4, 3, -9, -1, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "713", "dataset": "MATH"}992{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -5, 4, 5, -3, 2, -2],\n [-5, -10, 14, 6, -8, -10, 10],\n [4, 14, 15, -5, 16, -6, 14],\n [5, 6, -5, -10, -2, -14, 11],\n [-3, -8, 16, -2, -18, 8, 6],\n [2, -10, -6, -14, 8, 9, -12],\n [-2, 10, 14, 11, 6, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-126", "dataset": "MATH"}993{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -7, -5, -11, -17, 15, 5],\n [0, -9, -12, -18, -9, -14, 2],\n [0, 0, 12, 8, -13, 12, 17],\n [0, 0, 0, 3, -6, 0, 14],\n [0, 0, 0, 0, 6, 3, 4],\n [0, 0, 0, 0, 0, 5, -14],\n [0, 0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}994{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 3, -5, 9, -15, -3, 4],\n [-6, 1, -14, 0, 2, -14, -5],\n [17, -13, -14, 5, 10, 10, -17],\n [-13, 15, -7, 3, -15, -13, -16],\n [-6, 4, 16, 7, -10, 4, -15],\n [15, 18, -11, 15, 18, -13, -12],\n [17, -14, -16, -2, 0, -18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}995{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -15, -9, 13, -18, 4, -2],\n [0, 8, -4, -12, 14, -14, 15],\n [0, 0, -17, -3, -2, -7, -14],\n [0, 0, 0, 1, -10, -3, 16],\n [0, 0, 0, 0, 4, 17, 3],\n [0, 0, 0, 0, 0, 10, -1],\n [0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2297", "dataset": "MATH"}996{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/252 * A where A =\n[[5, 4, 1, 14, 8, 10, -12],\n [4, 6, 2, -2, -4, -8, 1],\n [1, 2, 3, 6, 10, 0, 0],\n [14, -2, 6, -11, 10, 4, -8],\n [8, -4, 10, 10, 12, -2, 2],\n [10, -8, 0, 4, -2, 11, -1],\n [-12, 1, 0, -8, 2, -1, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}997{"messages": [{"content": "Calculate the inverse matrix of 1/252 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 0, 5, 9, -6, -10, -10],\n [2, 5, 12, 10, -9, -15, -16],\n [-6, 2, -11, -10, -18, -5, -7],\n [17, 3, 17, -3, -8, -16, 15],\n [6, 7, -16, 1, 12, -18, 7],\n [6, -8, -3, 1, -17, 10, -12],\n [6, -15, 15, 6, -11, 13, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-237", "dataset": "MATH"}998{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, 18, 17, -9, -13, -3, 6],\n [0, 12, -11, -2, -5, 11, -1],\n [0, 0, 12, 14, 4, -14, -4],\n [0, 0, 0, 9, -13, -14, 6],\n [0, 0, 0, 0, 12, -4, 0],\n [0, 0, 0, 0, 0, -11, -15],\n [0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}999{"messages": [{"content": "For the inverse of 1/252 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[0, 4, 6, -12, -11, -16, 4],\n [14, 9, 3, 16, 15, 11, 17],\n [-5, -10, 3, 9, -5, -4, 18],\n [5, 15, -16, 4, 1, -4, -3],\n [-12, 14, 0, -1, -1, -16, -16],\n [17, -3, 4, 4, -4, -10, -1],\n [-13, 18, -13, 2, 11, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}1000{"messages": [{"content": "Find the inverse of 1/252 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[0, 0, -14, 0, 10, -2, 4],\n [0, -12, 2, -9, 6, -6, -14],\n [-14, 2, 5, -2, 3, 8, -13],\n [0, -9, -2, 12, 2, -10, 10],\n [10, 6, 3, 2, 12, -13, -16],\n [-2, -6, 8, -10, -13, 12, -2],\n [4, -14, -13, 10, -16, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}1001