{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 4, 13, -1, -5, -8],\n [0, 5, -9, 10, 3, 7],\n [0, 0, 8, 5, -12, -8],\n [0, 0, 0, 5, -14, 8],\n [0, 0, 0, 0, 12, 5],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-798", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 1, 11, 11, 15, -6],\n [0, 12, 0, -1, 14, 14],\n [0, 0, 3, -4, 7, 4],\n [0, 0, 0, 3, -9, 5],\n [0, 0, 0, 0, 9, 12],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 12, -1, 12, -9],\n [-4, 13, -8, -1, -13, -2],\n [1, -12, 2, -8, -12, -14],\n [14, -10, 6, -6, -12, 6],\n [13, 15, 2, 10, -4, -14],\n [-6, 14, -12, -2, 15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[-1, -8, -2, 7, 12, 9],\n [0, -8, 5, 0, -3, 2],\n [0, 0, 8, 10, 9, 12],\n [0, 0, 0, -7, 13, -1],\n [0, 0, 0, 0, -7, 8],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1340", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 1, -8, -13, -13, -15],\n [11, -11, -6, -9, 10, -7],\n [12, -9, -7, -8, -4, -14],\n [-15, 0, 7, 7, 14, 8],\n [-11, -13, -4, -8, 6, 11],\n [-13, -15, -13, -11, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -15, -11, 10, 7, 15],\n [-2, -9, 11, -7, -1, -1],\n [10, -6, 12, -3, 3, 15],\n [-9, 1, 4, 13, -12, 14],\n [-11, 7, -9, -3, -1, -5],\n [13, -12, -3, -9, 11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, 12, -14, -6, -3, 14],\n [0, 5, -10, 12, 12, -4],\n [0, 0, 14, 14, -5, 10],\n [0, 0, 0, -9, 14, -15],\n [0, 0, 0, 0, 9, 4],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1907", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[11, -7, 14, -11, -15, 3],\n [-6, -4, 8, -1, 11, 6],\n [8, -7, 4, 1, 14, 1],\n [10, 4, -4, 14, -9, -14],\n [-13, 1, -11, 1, 8, 1],\n [11, 1, -14, -14, 12, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-289", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, -11, -15, -15, 3, 14],\n [-14, 5, -4, 10, -10, 7],\n [-12, 7, -5, 8, 11, 1],\n [15, -10, 8, -11, 4, -14],\n [-10, 6, -5, 15, 0, 0],\n [-15, -7, 12, 11, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -5, -2, 7, 10, -12],\n [-5, 10, -4, 4, 2, -2],\n [-2, -4, -7, -15, 0, 2],\n [7, 4, -15, -5, 14, 4],\n [10, 2, 0, 14, 14, 2],\n [-12, -2, 2, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 4, 12, 1, -14, -15],\n [0, 14, -4, -11, -11, 11],\n [7, -7, -7, -13, 3, 0],\n [0, -13, 4, 8, 6, 8],\n [-15, 8, 4, -5, 1, -8],\n [-12, -10, -8, 4, 14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 14, 9, -13, 9, 13],\n [2, -2, 2, -14, 6, -13],\n [0, 13, -7, -12, -15, -12],\n [-15, -2, 5, 0, 4, 8],\n [-8, -9, -13, 1, -15, 0],\n [-4, 11, 3, 6, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-2, 10, 2, 1, -1, 0],\n [10, -8, -2, 12, -6, 5],\n [2, -2, 12, 0, -10, -10],\n [1, 12, 0, 3, 0, -13],\n [-1, -6, -10, 0, 14, 12],\n [0, 5, -10, -13, 12, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 8, 13, 1, -2, 5],\n [15, -13, 12, -15, 4, 15],\n [13, 5, 7, -15, -13, 2],\n [9, -6, 15, 6, 10, -13],\n [-8, -2, 8, 2, -1, 6],\n [7, -14, 15, 11, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-167", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[10, 4, 1, -2, -2, -4],\n [4, 0, -11, 12, -10, 5],\n [1, -11, 2, 0, 0, 2],\n [-2, 12, 0, 9, -7, -2],\n [-2, -10, 0, -7, 0, 5],\n [-4, 5, 2, -2, 5, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-161", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (3, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 7, 15, 6, 3, 9],\n [0, 15, 14, 13, 6, 10],\n [0, 0, 1, 4, -6, -10],\n [0, 0, 0, 12, -11, -15],\n [0, 0, 0, 0, -4, -11],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-105", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -13, 7, -8, 4, 0],\n [0, 2, 12, -6, 14, 3],\n [0, 0, 15, 3, 12, 10],\n [0, 0, 0, 10, 5, 14],\n [0, 0, 0, 0, 5, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3323", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[4, 8, -4, 2, -13, 12],\n [0, -15, 13, 3, -5, -11],\n [0, 0, -15, -15, -8, -6],\n [0, 0, 0, -3, -4, 15],\n [0, 0, 0, 0, 2, -13],\n [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": "1746", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 10, 14, -14, 3, -7],\n [-9, -12, 10, 5, 2, -3],\n [-5, 13, 8, -12, 9, 5],\n [13, 9, -12, -6, -11, -7],\n [8, -13, 1, -13, 0, -12],\n [2, 1, -9, 8, 7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3235", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 2, 8, 9, -5, 2],\n [2, -13, -2, 8, 2, 8],\n [8, -2, 0, 5, 1, 0],\n [9, 8, 5, -12, -6, 8],\n [-5, 2, 1, -6, -9, 11],\n [2, 8, 0, 8, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-55", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 13, -10, -9, -2, -3],\n [0, -6, -7, 2, 11, 10],\n [0, 0, 13, -11, -10, 3],\n [0, 0, 0, -15, 6, 4],\n [0, 0, 0, 0, -3, -12],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 4, -4, 2, -10, 11],\n [4, -9, 13, 0, -3, -1],\n [-4, 13, 14, 12, 8, 10],\n [2, 0, 12, -7, 2, -4],\n [-10, -3, 8, 2, 9, 0],\n [11, -1, 10, -4, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-139", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -10, 10, -4, -3, -3],\n [0, -1, 5, 0, 6, 5],\n [0, 0, -11, -12, -13, 3],\n [0, 0, 0, -1, -7, 1],\n [0, 0, 0, 0, 5, 6],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-340", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -6, 0, -8, -10, -4],\n [0, 12, 5, -8, 10, 12],\n [0, 0, -8, 10, 12, 2],\n [0, 0, 0, -7, -12, 11],\n [0, 0, 0, 0, -15, 5],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "796", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-2, -13, 13, -10, 2, 3],\n [-11, -1, 9, -14, -6, 8],\n [14, 2, 11, -3, -11, 7],\n [8, -15, 6, -15, 2, -1],\n [1, -5, 5, 10, 15, 9],\n [6, 11, 11, 1, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 6) of the inverse of matrix 1/180 * A where A =\n[[-14, -4, 1, 2, -7, 4],\n [-4, 7, -10, 8, 3, -7],\n [1, -10, -10, -12, 2, 2],\n [2, 8, -12, -6, -6, -4],\n [-7, 3, 2, -6, -2, 0],\n [4, -7, 2, -4, 0, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -8, -14, 12, 15, -8],\n [-9, 10, 10, -14, 6, 6],\n [-13, 11, 2, -4, -15, 6],\n [-4, -11, 14, 14, 11, 9],\n [1, 0, 15, -1, 7, -1],\n [-11, 5, -2, -14, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-9, -12, 14, -3, -4, 5],\n [-12, 2, 0, -1, 6, 2],\n [14, 0, 4, 10, -10, -10],\n [-3, -1, 10, 14, 10, -2],\n [-4, 6, -10, 10, -12, 3],\n [5, 2, -10, -2, 3, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-96", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[8, -11, -14, -10, 5, -14],\n [-3, 14, -5, -5, 0, -5],\n [3, -1, 9, 7, 7, 0],\n [15, -5, 6, 0, -8, -12],\n [-8, -12, 8, 9, -13, -13],\n [11, 13, 2, 13, 10, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, 5, -11, 2, 12, -6],\n [13, 6, 5, -10, -15, -11],\n [-7, -4, 10, -2, -14, 1],\n [-2, 10, -3, 11, -7, 10],\n [9, -1, 9, 6, -1, 8],\n [14, -5, 15, 0, 13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -12, -15, -8, 1, -13],\n [0, 4, -1, -1, 15, 8],\n [0, 0, 10, 12, 7, -2],\n [0, 0, 0, 10, -2, 11],\n [0, 0, 0, 0, -1, 7],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3787", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, -6, 6, -4, -2],\n [-2, -11, 2, -2, -11, 4],\n [-6, 2, 6, 4, 4, 1],\n [6, -2, 4, 4, 3, -13],\n [-4, -11, 4, 3, 2, -1],\n [-2, 4, 1, -13, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-8, 1, -4, 3, -6, -7],\n [0, -10, 4, 10, -14, 11],\n [0, 0, -3, -10, -11, 9],\n [0, 0, 0, 5, -10, -10],\n [0, 0, 0, 0, -5, 14],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[7, -13, 3, 15, -8, -11],\n [0, 8, 15, -10, -14, 4],\n [0, 0, -12, -1, -10, 6],\n [0, 0, 0, -10, 3, 14],\n [0, 0, 0, 0, -8, 10],\n [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": "-176", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, -12, 3, 4, -15, 4],\n [1, -4, -1, -15, 10, -2],\n [-10, -11, 14, -5, 15, -12],\n [-3, -5, -13, -15, -10, 2],\n [8, -6, -11, 7, -6, -4],\n [-14, -3, -8, -14, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -11, -7, 1, -7, -5],\n [-1, 8, -10, 7, -13, 14],\n [15, 1, -11, 14, 12, -4],\n [2, -2, 5, 8, -5, -7],\n [-14, -4, -13, -13, -15, -8],\n [6, 12, 13, -8, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, -2, 12, 14, -13, 5],\n [-11, -11, 3, 11, -2, 10],\n [14, -12, 9, -3, -6, 9],\n [2, -8, -8, -9, -8, -2],\n [3, 13, -10, -15, 7, 15],\n [-1, -15, 9, 1, -15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "307", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[7, -14, -2, 5, -8, -8],\n [0, -9, 3, -10, -10, -13],\n [0, 0, -8, -6, 4, -1],\n [0, 0, 0, 4, 14, -9],\n [0, 0, 0, 0, 9, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "219", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 5) of the inverse of matrix 1/180 * A where A =\n[[-12, 0, -8, -4, -12, 7],\n [0, -15, -3, 2, -4, 9],\n [-8, -3, -3, 0, 0, -2],\n [-4, 2, 0, -11, 0, -6],\n [-12, -4, 0, 0, 11, 12],\n [7, 9, -2, -6, 12, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[11, -11, 4, -5, 14, -6],\n [0, -10, -10, -8, 7, -1],\n [0, 0, -5, -4, 10, -3],\n [0, 0, 0, 9, -15, -1],\n [0, 0, 0, 0, -4, -12],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the inverse of matrix 1/180 * A where A =\n[[15, -6, 1, 12, 15, 10],\n [0, 6, 3, 13, -2, -8],\n [0, 0, -5, 7, -15, -2],\n [0, 0, 0, -2, -12, 6],\n [0, 0, 0, 0, 6, 7],\n [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": "-440", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, -7, -6, 4, 9, 5],\n [10, -7, -13, 15, 4, 9],\n [10, -5, -10, -14, -9, 2],\n [11, -14, 11, 1, -5, 11],\n [-4, 11, 3, 6, 8, 9],\n [-9, 4, -10, 5, 8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-119", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 13, 15, -5, 6, 10],\n [12, 2, 5, 1, -9, 1],\n [4, -7, 1, 4, 6, 6],\n [12, 15, 13, -8, 1, -9],\n [-15, -3, 14, 7, 3, 11],\n [8, 3, 14, 14, 13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 13, 14, 0, -8, 3],\n [0, -15, -2, 3, -1, 2],\n [0, 0, 12, 1, 2, 14],\n [0, 0, 0, -12, -15, -8],\n [0, 0, 0, 0, -6, -6],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-76", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[7, 12, 2, -9, 13, -8],\n [0, 9, 7, -13, 8, 7],\n [0, 0, 13, -8, 6, 9],\n [0, 0, 0, 3, -15, 12],\n [0, 0, 0, 0, 8, -2],\n [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": "183", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-11, 6, 5, -2, 15, 7],\n [0, 2, -9, -6, -9, -15],\n [0, 0, 3, 0, 13, 3],\n [0, 0, 0, 2, -14, -15],\n [0, 0, 0, 0, -6, 15],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -3, -7, 12, -3, -2],\n [-3, -4, -2, 1, 4, -2],\n [-7, -2, 1, 0, 4, 0],\n [12, 1, 0, 1, -3, 4],\n [-3, 4, 4, -3, -14, 2],\n [-2, -2, 0, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -12, 10, 10, 13, -3],\n [0, 7, -11, -5, -10, 2],\n [0, 0, -12, -7, -10, -14],\n [0, 0, 0, -10, 10, -4],\n [0, 0, 0, 0, 5, 11],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, -3, 9, 5, -9, -6],\n [-3, 1, 10, 5, 12, 14],\n [10, -2, -14, 12, 6, -5],\n [-15, 3, 5, -12, 3, 10],\n [13, 5, -5, -8, -5, -12],\n [1, 11, -9, -8, -13, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 2, 11, 8, 4],\n [-2, 8, -6, 10, -13, -8],\n [2, -6, -13, 0, 0, 5],\n [11, 10, 0, -5, -10, 3],\n [8, -13, 0, -10, -7, -6],\n [4, -8, 5, 3, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[-6, 9, -9, -13, -13, 2],\n [-11, -4, -4, 3, 14, -10],\n [-14, -4, 3, -11, -4, 11],\n [11, 1, 13, 1, -6, 9],\n [7, 1, -1, -4, 14, 0],\n [8, 3, -8, 15, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[7, -11, 6, 0, -10, -8],\n [9, 2, 9, -4, -1, 11],\n [10, -7, -3, 10, -1, -6],\n [0, -9, 1, 7, 10, 5],\n [6, 10, -9, -2, -1, 5],\n [-9, -7, 3, 0, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[11, 7, 13, 2, 15, 14],\n [0, -9, -13, 2, 11, -6],\n [0, 0, -2, 15, 8, -13],\n [0, 0, 0, -14, -13, -11],\n [0, 0, 0, 0, 7, -4],\n [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": "1399", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[6, 9, -3, 2, -15, 0],\n [0, -6, -4, 14, -14, 7],\n [0, 0, -14, 14, 11, 7],\n [0, 0, 0, -13, 11, -9],\n [0, 0, 0, 0, 1, 13],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, -1, 9, -6, 14, 9],\n [0, -9, 4, -11, -15, 14],\n [0, 0, -3, -2, 8, 14],\n [0, 0, 0, 14, -11, 9],\n [0, 0, 0, 0, -1, -7],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-337", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, 10, -11, 13, -11, -5],\n [0, -10, -9, 8, 15, -2],\n [0, 0, 14, -3, -14, 9],\n [0, 0, 0, 11, -8, 4],\n [0, 0, 0, 0, 3, -3],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 1, 10, -13, 8, -10],\n [0, -11, 6, -1, 7, 1],\n [0, 0, 4, 10, 1, 13],\n [0, 0, 0, 2, 2, 14],\n [0, 0, 0, 0, -10, -3],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-507", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -11, -14, -5, -7, 8],\n [-13, 11, 12, 13, -7, -13],\n [9, -14, -4, -6, -7, -1],\n [-8, 9, -11, -5, 11, -14],\n [8, 12, -1, -10, -8, 11],\n [-11, 0, 10, 2, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, 2, -2, 4],\n [0, 2, 1, 4, 8, 12],\n [0, 1, -13, 2, -4, -7],\n [2, 4, 2, -3, -12, -8],\n [-2, 8, -4, -12, 12, -9],\n [4, 12, -7, -8, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 5, -6, -12, 15],\n [0, -10, 12, -9, -11, -5],\n [0, 0, 9, 3, 15, 7],\n [0, 0, 0, 5, 14, -9],\n [0, 0, 0, 0, -2, -3],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3817", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 1, -7, 1, -8, 15],\n [-14, 12, 8, -3, -13, 0],\n [-10, 3, 14, -9, -6, -7],\n [-14, 15, 12, 12, -1, 14],\n [-11, 13, 6, -12, 4, -12],\n [2, -12, 11, 1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[1, -6, 6, -15, 6, 10],\n [8, 11, 2, 2, -2, -1],\n [13, -4, -12, 11, -13, 4],\n [13, -4, -9, 13, -5, -15],\n [-10, -1, -1, 3, -5, 10],\n [7, 10, -14, -2, -14, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-792", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-12, 1, -13, -3, -7, -9],\n [-1, 7, 13, 13, -5, 4],\n [-14, -1, -2, 4, 6, -5],\n [11, -13, 1, 14, -4, 8],\n [12, 13, 5, -1, 0, -11],\n [11, 4, -10, 3, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[-13, 11, -15, 10, 12, -10],\n [-1, -14, 13, -13, 1, 9],\n [8, -4, 2, -1, -4, 0],\n [11, -8, 12, -2, 9, 1],\n [13, 5, -8, -1, 11, -2],\n [2, 4, -9, -13, 13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, 8, 12, 10, -13, 4],\n [-2, -1, 9, 14, -2, -9],\n [1, 14, -4, 4, -12, -7],\n [-10, 0, 9, 12, 15, 6],\n [6, 5, 5, -14, 8, -8],\n [-5, -3, 1, -8, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[14, 2, -2, -1, 15, -10],\n [-5, -3, 9, -15, 12, -10],\n [-7, -8, -5, 6, 3, 8],\n [-7, 1, -4, 9, -2, -1],\n [0, 6, 6, 12, 4, -15],\n [-6, -8, 2, 12, -15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-15, -15, -7, -3, 14, -15],\n [0, 4, 10, 6, -9, -14],\n [0, 0, 10, -2, 10, 2],\n [0, 0, 0, 7, -4, 1],\n [0, 0, 0, 0, 11, -10],\n [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": "-195", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 5, -8, 1, -2, 9],\n [5, 4, 4, 2, 12, 6],\n [-8, 4, 4, 5, -9, -2],\n [1, 2, 5, 15, -8, 6],\n [-2, 12, -9, -8, -5, 0],\n [9, 6, -2, 6, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, 3, 10, 3, 7, -2],\n [0, -3, -8, 13, 7, 5],\n [0, 0, -4, 2, -10, 2],\n [0, 0, 0, 8, -7, 11],\n [0, 0, 0, 0, -13, 13],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-346", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-4, 1, 14, 5, 15, 10],\n [13, 8, 4, -11, -12, 12],\n [-4, 14, 4, 12, 8, 2],\n [1, 3, -7, -12, 10, 5],\n [-14, -12, -14, -1, -14, -12],\n [-10, -9, -6, 3, 3, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 13, -4, -13, -3, 2],\n [-8, 5, -1, -15, -13, 10],\n [-8, -12, 0, 14, 7, -6],\n [-4, -2, -2, -14, 7, -11],\n [-11, -10, -3, -7, 14, 6],\n [12, 13, -1, -2, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "387", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[9, 4, -14, -9, -10, 1],\n [11, 9, 9, 12, -14, -13],\n [-11, -11, 15, -15, -8, -4],\n [8, -12, -3, 7, -1, 15],\n [-5, -6, -13, 6, -2, 0],\n [-6, 13, -6, -4, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, -11, 4, -8, -5, -4],\n [-15, 9, 6, 4, 12, 9],\n [-5, -11, -1, -11, -4, -11],\n [1, 1, 8, -4, 8, 12],\n [-1, -1, -10, -4, 11, 13],\n [4, 2, -2, -14, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 4, 10, 13, -15, 7],\n [-13, -10, -11, 5, 11, -11],\n [-15, 1, 3, -2, -4, -6],\n [4, 5, 2, 8, 11, -5],\n [14, -14, 9, 2, 13, 9],\n [-9, 15, 8, -1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[7, -4, -10, 4, 7, 14],\n [0, 4, 0, 2, -6, 12],\n [0, 0, 2, 5, -15, 7],\n [0, 0, 0, -11, -1, 6],\n [0, 0, 0, 0, 7, 10],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7666", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[10, -8, -1, -8, 1, -4],\n [0, -8, 9, -2, -12, -15],\n [0, 0, 15, 0, -2, 5],\n [0, 0, 0, 10, 14, 12],\n [0, 0, 0, 0, -7, -15],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-3, 15, -7, -5, -12, -14],\n [13, -10, -2, -12, -10, 3],\n [-10, -14, 2, -3, -7, 7],\n [3, -3, -5, -15, 8, 14],\n [6, -9, 9, 5, -1, -15],\n [-4, 10, -9, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, 0, 0, -11, -6, 5],\n [0, -4, -6, -2, -8, -8],\n [0, -6, -2, 0, -1, -6],\n [-11, -2, 0, 10, -2, -7],\n [-6, -8, -1, -2, 13, 5],\n [5, -8, -6, -7, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1121", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, -4, -12, -1, -5, 0],\n [7, -10, -2, 2, -4, 11],\n [-5, -3, 5, 7, -5, 7],\n [0, -1, 5, 12, -1, 9],\n [-12, -5, 3, -1, -12, 5],\n [-3, 6, 3, -14, -2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1969", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-12, 0, 5, 4, -2, 11],\n [13, -1, 12, -13, -8, 0],\n [-6, -12, 14, 2, -14, 1],\n [-3, -12, 10, 9, 14, -5],\n [-9, 15, -4, -6, -9, -3],\n [15, -9, 15, 8, 1, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[13, 0, 2, -3, 7, -2],\n [0, -9, 0, -4, -6, 10],\n [2, 0, -1, 8, -2, 0],\n [-3, -4, 8, 6, 3, -8],\n [7, -6, -2, 3, 8, 9],\n [-2, 10, 0, -8, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 6) rounded to the nearest integer?\n[[1, 10, 11, -11, -12, 2],\n [0, 3, -12, 12, -9, -6],\n [0, 0, 3, -12, -6, -15],\n [0, 0, 0, -1, 1, -13],\n [0, 0, 0, 0, 5, 1],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-9, -5, -6, -7, -2, -3],\n [13, 9, 14, 9, -14, -13],\n [-9, 5, 2, -13, -6, 6],\n [13, -9, -7, 1, -5, -9],\n [8, 12, -2, 3, -12, 10],\n [-10, -6, -9, -3, -2, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "659", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, -11, -15, -12, -13, -7],\n [-8, -15, 11, -10, -7, -9],\n [-12, -3, 1, 12, -14, 12],\n [-11, -4, 11, 5, -8, -10],\n [-8, 2, -13, 6, -4, 13],\n [10, -13, 6, -10, -14, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, -3, 7, 12, 3, -8],\n [0, -11, 4, -8, 8, -4],\n [0, 0, 14, 5, 4, -10],\n [0, 0, 0, -9, -15, 5],\n [0, 0, 0, 0, -14, 13],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-84", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -7, 5, -14, 11, 9],\n [-7, -15, -5, -13, 4, 14],\n [7, 10, -12, 2, 7, -10],\n [-13, 6, -5, -1, 6, 12],\n [-11, 4, -6, -4, -1, 1],\n [-6, -10, 2, -3, -13, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[8, -6, 14, -2, -10, -13],\n [0, -9, 4, -2, -7, -1],\n [5, -13, -14, 11, -14, -13],\n [2, -2, 4, 2, -6, 9],\n [-14, 9, 13, 6, -15, -12],\n [15, -2, -15, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 13, 4, -13, -13, -7],\n [0, 9, -3, 5, -14, -8],\n [0, 0, -12, 9, -1, -12],\n [0, 0, 0, 12, -3, 15],\n [0, 0, 0, 0, 12, 15],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -6, 8, 5, 0, 2],\n [-6, -6, 11, -6, 14, 4],\n [8, 11, 15, 0, -2, -11],\n [5, -6, 0, -13, 4, -10],\n [0, 14, -2, 4, -9, -6],\n [2, 4, -11, -10, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-621", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 5) of the inverse. Round your answer to the nearest integer:\n[[-8, 1, -11, -9, 12, 4],\n [0, 4, -12, 12, -10, -9],\n [0, 0, -11, 4, 15, 14],\n [0, 0, 0, 11, 12, 6],\n [0, 0, 0, 0, 6, -11],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/180 * A where A =\n[[6, 0, 2, 4, -2, 7],\n [0, 8, 0, -11, -2, 1],\n [2, 0, 2, -3, 0, 8],\n [4, -11, -3, -12, 8, 0],\n [-2, -2, 0, 8, 5, -4],\n [7, 1, 8, 0, -4, -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"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[4, -4, 8, 5, -4, 0],\n [-4, 13, -1, 3, 2, -7],\n [8, -1, -3, -3, -11, 3],\n [5, 3, -3, -15, -10, 12],\n [-4, 2, -11, -10, 2, 2],\n [0, -7, 3, 12, 2, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "761", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-14, -8, 11, 6, -8, 1],\n [-1, 1, 12, 7, 8, -3],\n [3, -11, -4, -15, 7, -11],\n [-8, -3, -8, 9, 7, -5],\n [-15, -3, 3, 8, -13, 8],\n [1, -11, 4, 5, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, -2, -12, -5, 4, -1],\n [3, -9, 3, 12, 3, -5],\n [10, -11, -11, 14, 6, -8],\n [-6, -10, -1, 0, 12, 1],\n [15, -8, -8, 9, -7, -14],\n [-1, 2, -13, 1, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, 2, -10, -5, 2, 8],\n [2, 14, 6, 4, -6, -1],\n [-10, 6, 11, 4, -8, 8],\n [-5, 4, 4, 0, 6, -11],\n [2, -6, -8, 6, -8, 6],\n [8, -1, 8, -11, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-578", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[12, 12, 5, 4, 4, -2],\n [12, 4, 6, -6, 4, -2],\n [5, 6, 5, -6, 4, 3],\n [4, -6, -6, -4, 4, -2],\n [4, 4, 4, 4, 5, 2],\n [-2, -2, 3, -2, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, -5, 6, 6, -5, 9],\n [0, 12, 13, -3, 2, -14],\n [0, 0, -1, 4, 11, 2],\n [0, 0, 0, 7, 8, -4],\n [0, 0, 0, 0, 13, -15],\n [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": "3474", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, 14, -9, -4, -1, 9],\n [-11, -1, -8, -6, 10, 0],\n [-8, -15, -4, -11, -13, -15],\n [-12, -8, -13, -6, -14, -5],\n [9, -6, 5, -2, -9, 11],\n [11, -14, -7, 0, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[4, -12, 6, -6, 10, 10],\n [6, -4, 1, -2, -2, 9],\n [-14, 5, 9, 4, -5, 0],\n [3, 15, 7, -10, 8, 3],\n [-11, 10, -12, -1, 13, -12],\n [4, -6, 8, 6, -13, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-11, -10, 5, 6, -8, -9],\n [5, -6, -10, -2, -12, 12],\n [9, -3, 4, 1, 7, -9],\n [-12, 13, -2, -13, 8, -11],\n [0, 10, 7, 4, -12, 8],\n [14, 8, -14, 14, 2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 6) of the inverse of matrix 1/180 * A where A =\n[[15, 12, 12, 3, 1, 15],\n [0, 3, 6, 8, -3, -4],\n [0, 0, -10, 5, 15, -12],\n [0, 0, 0, -12, 14, 7],\n [0, 0, 0, 0, 15, 4],\n [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": "89", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 11, -3, 3, 5],\n [0, -6, -13, -2, 10, 3],\n [0, 0, -11, 4, 1, 5],\n [0, 0, 0, -10, 10, -12],\n [0, 0, 0, 0, -13, -15],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-163", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 8, 2, 2, 2, 12],\n [8, 8, 2, -12, 2, 6],\n [2, 2, -6, 10, 3, 1],\n [2, -12, 10, 12, 2, 2],\n [2, 2, 3, 2, 15, -6],\n [12, 6, 1, 2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/180 * A where A =\n[[-12, 8, -5, 4, 2, 10],\n [0, 9, 5, -12, 2, -15],\n [0, 0, -10, 15, -1, 2],\n [0, 0, 0, 8, -1, 0],\n [0, 0, 0, 0, -4, 8],\n [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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-11, -13, 7, 10, -11, 8],\n [0, 3, 3, 9, 5, -4],\n [0, 0, -7, -15, 2, 5],\n [0, 0, 0, 9, -9, 6],\n [0, 0, 0, 0, 13, 13],\n [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": "730", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, 1, 1, -14, -10, -2],\n [-10, -14, -15, -6, 5, -11],\n [-14, 6, 0, 9, -14, -6],\n [-14, 0, 0, 3, 13, -9],\n [6, -4, 8, -1, -8, -10],\n [12, 11, -6, -13, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-41", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, -10, -2, 1, 11, 12],\n [-10, -2, 4, 8, 4, 11],\n [-2, 4, -1, 10, 2, 0],\n [1, 8, 10, -7, 4, 1],\n [11, 4, 2, 4, -14, 2],\n [12, 11, 0, 1, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-6, 4, -13, -10, -9, 4],\n [0, 9, 11, 2, -5, 3],\n [0, 0, -5, 8, -4, -6],\n [0, 0, 0, 12, -7, -12],\n [0, 0, 0, 0, -7, -1],\n [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": "107", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[12, 4, -10, -4, -14, -9],\n [0, -13, -3, -13, 11, 2],\n [-5, -8, -10, -15, 12, -15],\n [7, -8, -11, 12, 0, -5],\n [-11, -12, 14, -10, -2, 6],\n [3, -7, -4, -5, -2, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, 7, 5],\n [5, 14, -3, -14, -12, 12],\n [-10, 10, 15, 11, 7, 11],\n [-11, 9, -13, -15, -12, 9],\n [4, -14, 10, 14, 14, -11],\n [-13, 13, 12, 13, -7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 2, -10, 3, 12, -4],\n [0, -5, -14, -1, -4, -4],\n [0, 0, 8, -14, 6, -13],\n [0, 0, 0, 10, 0, 5],\n [0, 0, 0, 0, -15, 5],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "426", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[2, 10, -5, 9, 7, 0],\n [0, 1, -11, -4, -5, 14],\n [0, 0, -13, -15, 4, 13],\n [0, 0, 0, -13, -8, 8],\n [0, 0, 0, 0, -7, 4],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -12, 10, 9, -1, -10],\n [-1, 15, 5, -13, 9, 5],\n [5, -2, 4, -2, -12, -4],\n [1, -9, -7, -13, 12, -3],\n [-1, 2, 3, -15, -10, 11],\n [11, 7, 11, 11, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 2) rounded to the nearest integer?\n[[-2, 2, 4, -7, 7, -2],\n [2, -13, 4, 12, 9, -4],\n [4, 4, 1, 0, -5, 10],\n [-7, 12, 0, 7, 4, 2],\n [7, 9, -5, 4, -13, -4],\n [-2, -4, 10, 2, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-2, 15, -7, 11, 12, 7],\n [9, 12, 3, -1, 4, -2],\n [8, -10, 5, 13, -12, -8],\n [1, 14, -7, -15, 8, 4],\n [9, -2, -5, 5, -13, -7],\n [11, -2, 14, -7, -12, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-12, 5, 0, 0, -1, 1],\n [5, 6, -4, 2, 15, 1],\n [0, -4, 13, 0, 3, -2],\n [0, 2, 0, -5, -6, -6],\n [-1, 15, 3, -6, 0, 4],\n [1, 1, -2, -6, 4, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-68", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 13, -7, -12, -13, 1],\n [-14, 8, -15, -8, -3, 7],\n [-1, -8, -4, 6, -4, -2],\n [-1, -1, -7, 3, 10, 4],\n [13, 6, -8, 5, 3, -10],\n [4, 9, 13, 3, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1035", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-9, 4, -1, -2, 4, -6],\n [4, -13, 8, -7, 0, 6],\n [-1, 8, 7, -8, -10, 2],\n [-2, -7, -8, 6, 0, -2],\n [4, 0, -10, 0, 10, -2],\n [-6, 6, 2, -2, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, 1, -13, -8, -2],\n [-13, 0, -3, 4, 8, 1],\n [-3, 13, -10, 1, -2, 1],\n [14, -8, -5, 4, 12, -15],\n [10, -9, 5, 5, 1, 14],\n [-6, -5, 6, 14, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "305", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, -5, -2, 6],\n [-3, 3, 4, 3, 5, -5],\n [-4, 4, -5, -2, 0, -4],\n [-5, 3, -2, -3, -12, 2],\n [-2, 5, 0, -12, -8, 6],\n [6, -5, -4, 2, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, 10, -9, 12, 10, -11],\n [0, 9, 11, -2, 7, 14],\n [0, 0, 7, 1, -1, 4],\n [0, 0, 0, -12, 14, -15],\n [0, 0, 0, 0, 3, -1],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[10, 3, -1, -7, -9, -14],\n [0, 13, -7, -6, -14, 3],\n [0, 0, -6, -2, 2, 3],\n [0, 0, 0, -9, 12, -13],\n [0, 0, 0, 0, -14, 13],\n [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": "275", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, -7, 14, -4, -13, -5],\n [-15, 7, -3, -1, 10, -11],\n [5, 14, 1, 15, 15, 9],\n [7, 8, 9, -10, 12, 5],\n [6, -5, 2, -12, -13, -3],\n [7, -7, 5, -10, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[12, -4, -14, -13, -13, 12],\n [-4, -1, -7, 15, 7, -8],\n [-5, 0, 10, 11, 9, 6],\n [-12, 12, -15, 8, -9, -14],\n [8, 12, -11, -9, -12, -11],\n [8, -15, -15, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[13, -6, 12, 2, 12, -13],\n [-5, -1, 15, 11, 14, -5],\n [1, 1, -10, -11, -8, -14],\n [0, 4, 8, -4, -10, -15],\n [15, -12, 1, -3, 2, -11],\n [14, 8, 8, 11, -13, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -8, 10, 0, -6, 9],\n [-8, 11, 4, 6, -6, -8],\n [10, 4, -1, 9, 10, -2],\n [0, 6, 9, -11, -8, 12],\n [-6, -6, 10, -8, -12, 0],\n [9, -8, -2, 12, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "253", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, 14, 4, 1, -3, 0],\n [6, -12, -11, -11, -7, 1],\n [-3, -14, -3, 6, 5, 11],\n [7, 3, -13, -6, -14, -3],\n [3, 10, 1, 5, -2, 15],\n [-4, 5, -4, -5, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9000", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, -14, 8, 4, -2, 7],\n [-14, -3, 6, -4, -7, -12],\n [8, 6, 1, -2, 8, -5],\n [4, -4, -2, 8, 1, 4],\n [-2, -7, 8, 1, 12, -4],\n [7, -12, -5, 4, -4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, 2, -12, -6, 4, 0],\n [2, -4, 9, 2, 4, -8],\n [-12, 9, -11, 6, 9, 10],\n [-6, 2, 6, -4, -5, 4],\n [4, 4, 9, -5, -4, 3],\n [0, -8, 10, 4, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-649", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-10, -5, -15, 14, 8, 7],\n [0, 11, -5, 9, 3, 2],\n [0, 0, 5, -2, 11, 2],\n [0, 0, 0, 15, -1, -12],\n [0, 0, 0, 0, 15, -7],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-15, 2, 9, 10, 2, -2],\n [2, -11, 2, -3, 2, 0],\n [9, 2, 0, -6, 3, 10],\n [10, -3, -6, 6, -5, 4],\n [2, 2, 3, -5, -14, 1],\n [-2, 0, 10, 4, 1, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1332", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, -13, 3, 2, -8, 10],\n [1, -8, -9, 14, -9, -13],\n [-15, -12, 9, -11, -15, -1],\n [-11, -3, -8, -8, -11, 12],\n [-7, 15, -15, -12, -13, -14],\n [15, -8, 7, -7, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -12, 6, 2, -12, -10],\n [-12, -8, -14, -1, 3, -8],\n [6, -14, -3, 0, 8, 10],\n [2, -1, 0, -8, 0, 2],\n [-12, 3, 8, 0, -10, 10],\n [-10, -8, 10, 2, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[15, 12, -14, -9, -13, -8],\n [0, -2, 8, 14, 7, 11],\n [0, 0, -9, 5, -9, -15],\n [0, 0, 0, 5, -3, 5],\n [0, 0, 0, 0, 9, 6],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-225", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, -5, -2, -3, 0, 6],\n [-5, -2, 5, 4, 2, -5],\n [-2, 5, -1, 8, 14, 15],\n [-3, 4, 8, 7, -5, -2],\n [0, 2, 14, -5, -14, -2],\n [6, -5, 15, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (5, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -1, 9, 15, 1, 10],\n [13, 10, 2, 6, -10, 1],\n [7, 8, 2, -8, -7, -10],\n [-11, -4, 9, 13, 12, -5],\n [9, -15, -5, 3, -7, 11],\n [-14, -4, -12, -12, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 2, 5, 5, -2, 4],\n [2, -4, 6, -2, 3, 3],\n [5, 6, 13, -4, 4, 3],\n [5, -2, -4, -6, -2, 4],\n [-2, 3, 4, -2, -11, -14],\n [4, 3, 3, 4, -14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-7, -7, -10, -5, 6, 8],\n [0, -15, -12, -3, 7, -3],\n [0, 0, -7, 8, -8, -9],\n [0, 0, 0, 12, -10, -4],\n [0, 0, 0, 0, 6, 6],\n [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": "-32", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-3, 9, 1, 6, 6, -6],\n [0, -4, -1, 5, -6, -2],\n [0, 0, -10, 8, -14, 6],\n [0, 0, 0, -6, -13, 9],\n [0, 0, 0, 0, -4, 6],\n [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": "805", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, 12, 10, -10, -15, 4],\n [0, 12, 0, -1, 1, -8],\n [0, 0, -4, 11, 6, 5],\n [0, 0, 0, 14, -7, -14],\n [0, 0, 0, 0, 9, -15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-4, -2, -2, -6, -4, 0],\n [-2, -9, -10, -2, 8, -5],\n [-2, -10, -15, 6, 1, 4],\n [-6, -2, 6, 11, 0, 2],\n [-4, 8, 1, 0, -14, -4],\n [0, -5, 4, 2, -4, -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"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -12, 10, -8, -7, 7],\n [0, 8, 4, 2, -5, -1],\n [0, 0, -7, 1, 11, 10],\n [0, 0, 0, 9, 10, 9],\n [0, 0, 0, 0, -5, -3],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "426", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[12, 0, -3, -7, -2, 5],\n [0, -10, 12, 4, 10, -2],\n [-3, 12, -7, -6, 4, 4],\n [-7, 4, -6, 4, -6, 3],\n [-2, 10, 4, -6, 2, 0],\n [5, -2, 4, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[-12, -13, 12, 0, 8, 11],\n [0, 14, 9, -4, -5, -11],\n [0, 0, 3, 7, 7, -10],\n [0, 0, 0, -10, -12, -4],\n [0, 0, 0, 0, -14, 1],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -1, 4, -10, 4],\n [-10, -1, 12, -4, -8, -2],\n [-1, 12, 4, 2, 7, 7],\n [4, -4, 2, -7, 0, -6],\n [-10, -8, 7, 0, -6, 14],\n [4, -2, 7, -6, 14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the inverse of matrix 1/180 * A where A =\n[[-14, -2, -6, 4, 10, 5],\n [-2, 11, 3, 10, 0, 0],\n [-6, 3, -6, 0, -8, 10],\n [4, 10, 0, -14, 2, -14],\n [10, 0, -8, 2, -13, -4],\n [5, 0, 10, -14, -4, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-152", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-9, 4, 6, 4, 6, -6],\n [4, 4, 0, 0, 0, 6],\n [6, 0, -15, 3, -11, 8],\n [4, 0, 3, 4, 0, -10],\n [6, 0, -11, 0, -11, 9],\n [-6, 6, 8, -10, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[3, 0, -9, -2, 12, -2],\n [0, 11, -12, 10, -1, -13],\n [0, 0, -13, -1, 8, 11],\n [0, 0, 0, -12, -14, 13],\n [0, 0, 0, 0, -13, -14],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "828", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -3, -11, 15, 14, 5],\n [0, -7, 9, 13, 9, 12],\n [0, 0, -11, 9, -6, -8],\n [0, 0, 0, 5, 13, 4],\n [0, 0, 0, 0, -12, 12],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4790", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 6) of the inverse of matrix 1/180 * A where A =\n[[-7, 2, 0, 3, 8, 1],\n [2, 14, -6, 8, 2, 11],\n [0, -6, 9, 1, 3, 9],\n [3, 8, 1, -9, 2, 12],\n [8, 2, 3, 2, -8, -2],\n [1, 11, 9, 12, -2, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[11, -14, 15, 14, -7, 1],\n [-5, -6, 6, 9, 1, -12],\n [0, 4, -1, 9, 11, 5],\n [-11, -10, 1, -15, 15, 9],\n [3, -12, 1, -7, 15, 8],\n [-14, -8, -1, -9, 11, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10679", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -1, 7, 10, -9, 13],\n [14, 9, 1, -14, 11, -7],\n [13, -7, -3, -10, -10, 4],\n [4, 5, -13, 1, 15, 1],\n [-4, 0, -1, -3, 7, -15],\n [1, -13, 10, -1, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 3, -5, 4, -13],\n [-8, -2, 10, -15, -2, -14],\n [13, 7, -12, 8, 11, 13],\n [3, -10, 9, -15, 1, -8],\n [3, 5, -15, -11, 11, 0],\n [-10, -8, -3, 0, 14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 4) rounded to the nearest integer?\n[[3, 2, -7, 2, -2, -1],\n [2, 4, 12, -10, -2, 4],\n [-7, 12, 6, 0, 8, -10],\n [2, -10, 0, 8, 5, 0],\n [-2, -2, 8, 5, 3, -6],\n [-1, 4, -10, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[-9, -1, 7, -2, 7, 3],\n [0, 13, 8, 4, 13, 8],\n [0, 0, -6, -7, 9, -8],\n [0, 0, 0, -6, 1, -14],\n [0, 0, 0, 0, 14, -7],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-302", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, 4, -7, 0, -8],\n [-2, -14, 8, -3, 2, -6],\n [4, 8, -6, -10, 8, 7],\n [-7, -3, -10, 11, 3, -7],\n [0, 2, 8, 3, 6, 2],\n [-8, -6, 7, -7, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[14, 5, -14, 6, -13, -10],\n [-1, 11, -6, -7, -15, 0],\n [-10, -7, 11, -12, 11, 12],\n [-14, 13, -12, -15, 3, 10],\n [9, -6, 5, -1, 11, 6],\n [3, 0, 5, 11, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -14, 4, 1, -6, 7],\n [-14, 1, -8, -8, -4, -6],\n [4, -8, 3, -8, -6, -4],\n [1, -8, -8, -6, -4, 6],\n [-6, -4, -6, -4, 11, 6],\n [7, -6, -4, 6, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1683", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-14, -8, -5, 13, 2, -13],\n [0, 10, -15, -5, 0, 2],\n [0, 0, 7, -6, 2, -10],\n [0, 0, 0, 11, 15, -3],\n [0, 0, 0, 0, -10, -15],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -6, 1, -7, 13, -10],\n [-5, 9, -9, 1, 12, 12],\n [-15, 6, -11, -7, 2, 8],\n [11, 5, -14, 13, 10, -5],\n [11, 12, -10, 10, -8, -12],\n [2, 12, -5, -11, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/180 * A where A =\n[[2, -2, 5, -4, 2, 12],\n [-2, -3, -3, 6, -12, 1],\n [5, -3, 8, -12, 1, 0],\n [-4, 6, -12, -2, -10, -2],\n [2, -12, 1, -10, 5, 6],\n [12, 1, 0, -2, 6, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 5) rounded to the nearest integer?\n[[2, -3, -8, 3, 4, -4],\n [-3, -13, 0, -3, -3, -12],\n [-8, 0, 11, 10, -4, 2],\n [3, -3, 10, 15, 8, -1],\n [4, -3, -4, 8, -2, 4],\n [-4, -12, 2, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, 0, -15, 1, 5],\n [0, -7, -10, 3, -3, -13],\n [0, 0, -7, 6, -11, -6],\n [0, 0, 0, 7, 0, -13],\n [0, 0, 0, 0, -7, 13],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, 0, 7, -3, 1, 7],\n [0, 5, -14, -11, -10, -4],\n [0, 0, 6, 6, -15, 14],\n [0, 0, 0, -6, 3, -2],\n [0, 0, 0, 0, 3, -12],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4320", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-9, 6, -3, -4, 4, 0],\n [6, -1, 14, 8, -4, -1],\n [-3, 14, -7, -7, -1, 0],\n [-4, 8, -7, -6, -3, -8],\n [4, -4, -1, -3, -14, 8],\n [0, -1, 0, -8, 8, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, 0, 1, 5, 13],\n [0, -9, 8, 10, 1, -9],\n [0, 0, 10, 1, -13, -9],\n [0, 0, 0, 5, -15, 1],\n [0, 0, 0, 0, 11, 13],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 4, 4, 0, -1, -1],\n [4, 8, -11, 2, 1, 2],\n [4, -11, 3, -3, 0, 10],\n [0, 2, -3, 13, 1, 6],\n [-1, 1, 0, 1, -13, -6],\n [-1, 2, 10, 6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -14, -8, 6, -10],\n [0, -1, 9, -8, -12, -1],\n [0, 0, 9, 1, -3, 2],\n [0, 0, 0, 6, -1, 4],\n [0, 0, 0, 0, -13, 3],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[14, -1, -2, 12, 6, -8],\n [-1, 15, 4, -2, 1, -2],\n [-2, 4, 1, 3, 2, 6],\n [12, -2, 3, 8, -4, 7],\n [6, 1, 2, -4, 10, 0],\n [-8, -2, 6, 7, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -13, -11, 3, -4],\n [0, 11, -9, 12, -7, 15],\n [0, 0, 13, 10, 1, 0],\n [0, 0, 0, 5, 10, -12],\n [0, 0, 0, 0, 14, -6],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, -8, -8, 11, 9, -8],\n [-3, 11, -14, 14, 14, -4],\n [-6, -4, -5, -1, 0, 1],\n [10, -14, 2, -4, 3, 10],\n [7, 2, 14, 1, 14, -10],\n [9, -1, -13, -10, -13, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -15, 14, -3, 12, 5],\n [0, -2, -3, 11, -12, -9],\n [0, 0, -9, 5, -1, -1],\n [0, 0, 0, -10, 8, 4],\n [0, 0, 0, 0, -15, 12],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 5, -13, -1, -11, 12],\n [8, -2, 2, 0, -10, 9],\n [8, -2, 11, 8, -8, 15],\n [13, -9, -8, -3, -10, 2],\n [-14, -8, -5, -15, 6, 13],\n [-10, 0, 11, 4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[13, 6, 12, 12, 4, -12],\n [6, 11, -8, 10, 6, 8],\n [12, -8, 1, -5, 2, -4],\n [12, 10, -5, 6, 0, 11],\n [4, 6, 2, 0, -13, 4],\n [-12, 8, -4, 11, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, 7, -1, -5, 10, -13],\n [-13, 0, -11, 5, 13, -6],\n [3, 9, -12, 13, 13, 15],\n [3, -5, -14, -6, 13, -5],\n [9, 4, 0, 3, 7, 8],\n [-5, -2, -14, 7, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[15, 11, -11, 3, 5, -4],\n [0, -12, 6, 1, -6, 4],\n [0, 0, -2, -5, -5, 13],\n [0, 0, 0, 6, 2, 8],\n [0, 0, 0, 0, -11, 7],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-6, -4, 2, -6, 1, -4],\n [-4, -1, -4, 0, 0, 10],\n [2, -4, 1, 8, -2, -6],\n [-6, 0, 8, 0, -10, -3],\n [1, 0, -2, -10, -8, 9],\n [-4, 10, -6, -3, 9, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-308", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, 8, -4, 0, -6, 2],\n [8, -10, -11, -10, 5, 2],\n [-4, -11, -4, 2, 0, -2],\n [0, -10, 2, -8, 8, 7],\n [-6, 5, 0, 8, 0, -2],\n [2, 2, -2, 7, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "424", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 2) rounded to the nearest integer?\n[[-1, 8, 0, 11, 5, 7],\n [0, 15, -7, -13, 3, 4],\n [0, 0, 1, -1, 15, 7],\n [0, 0, 0, 15, 5, 14],\n [0, 0, 0, 0, 5, 7],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -2, -5, -14, 2, -9],\n [-4, 10, -14, 11, 4, 2],\n [-10, 8, -6, 4, -1, -11],\n [4, -13, -11, 14, 9, -8],\n [-8, -8, -4, 8, 7, -8],\n [-5, -2, -8, 13, 14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, 4, -10, 14, 4, -11],\n [4, -3, 2, -2, 2, 0],\n [-10, 2, 2, -2, 14, 0],\n [14, -2, -2, 6, -8, 6],\n [4, 2, 14, -8, 14, -2],\n [-11, 0, 0, 6, -2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-4, -8, 10, 10, 2, 0],\n [-8, 7, 4, 6, -7, 12],\n [10, 4, 5, 8, -6, 0],\n [10, 6, 8, 0, 0, -3],\n [2, -7, -6, 0, -6, -2],\n [0, 12, 0, -3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -3, 0, -2, 0, 1],\n [-3, -3, -5, -4, 13, -2],\n [0, -5, 3, 7, 0, 5],\n [-2, -4, 7, 0, 10, -10],\n [0, 13, 0, 10, -8, -6],\n [1, -2, 5, -10, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[-3, 8, 4, 11, -2, 2],\n [8, -12, 12, -2, -1, 0],\n [4, 12, -10, 14, -12, 8],\n [11, -2, 14, -13, 6, -10],\n [-2, -1, -12, 6, 6, 14],\n [2, 0, 8, -10, 14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, -13, -6, -13, 11],\n [-4, 1, 11, 15, 13, 15],\n [-11, 14, 4, 9, 15, -7],\n [15, 14, 5, 10, 4, -9],\n [15, 6, -12, -3, -3, 15],\n [-6, 2, 1, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-62", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 0, -2, -13, 3],\n [2, 1, 2, 10, -4, -6],\n [0, 2, 7, -2, 2, -1],\n [-2, 10, -2, 11, 3, -4],\n [-13, -4, 2, 3, 13, 8],\n [3, -6, -1, -4, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "491", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[14, 2, 1, 3, 14, 4],\n [2, 2, -2, -3, 5, 9],\n [1, -2, 7, -3, 0, -2],\n [3, -3, -3, 4, -1, 1],\n [14, 5, 0, -1, 14, -8],\n [4, 9, -2, 1, -8, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-4, -13, -5, -14, 0, -7],\n [-1, -4, -15, -3, -2, 9],\n [9, -8, -8, 11, 14, -4],\n [-15, -5, -8, -6, 14, 3],\n [-5, -9, -5, 15, 1, -15],\n [10, 13, 5, 5, -8, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[8, -6, -4, 2, 1, -10],\n [-6, 3, 4, -11, 2, 6],\n [-4, 4, -5, 12, 1, -4],\n [2, -11, 12, -8, -4, -10],\n [1, 2, 1, -4, 3, 8],\n [-10, 6, -4, -10, 8, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-194", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, 0, -6, 4, 9, 0],\n [0, -12, 2, 4, 8, 1],\n [-6, 2, -12, 10, 12, -8],\n [4, 4, 10, -13, -8, 4],\n [9, 8, 12, -8, -6, -1],\n [0, 1, -8, 4, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, 6, 8, 2, -2, -5],\n [6, -7, 4, -7, 1, 0],\n [8, 4, 7, -8, -5, -2],\n [2, -7, -8, 10, 9, 11],\n [-2, 1, -5, 9, 4, -10],\n [-5, 0, -2, 11, -10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -7, 4, -8, -2],\n [4, -7, 6, -8, 8, 2],\n [-7, 6, 15, 4, 6, 2],\n [4, -8, 4, 0, -4, 2],\n [-8, 8, 6, -4, 14, -6],\n [-2, 2, 2, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 5, 14, 13, -15, 4],\n [0, 13, -1, 10, 10, -2],\n [0, 0, -2, 9, 5, 8],\n [0, 0, 0, -10, 1, -5],\n [0, 0, 0, 0, -12, 11],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -13, -8, 2, -6, 9],\n [4, 1, -8, 7, -5, 13],\n [-11, 10, -3, 5, 7, -11],\n [8, 11, -3, -10, 13, -11],\n [-7, 11, 0, -14, -15, -8],\n [12, 3, 14, -5, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "493", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, 10, -3, 11, -8],\n [0, 13, 13, 6, 12, 10],\n [0, 0, -9, 15, 10, 5],\n [0, 0, 0, 7, 15, 4],\n [0, 0, 0, 0, 6, -8],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1327", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 6, -6, 5, -1, 1],\n [6, -10, -13, -3, 0, -8],\n [14, -1, 1, 1, 6, 10],\n [-3, 1, -10, 1, 0, -2],\n [-3, -10, -13, -2, -2, -1],\n [-8, 13, -1, 6, 13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-103", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 1, 15, 5, 8, -13],\n [0, -10, -11, 6, 10, 1],\n [0, 0, -14, 10, -1, -11],\n [0, 0, 0, -10, 11, 2],\n [0, 0, 0, 0, -2, -2],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2557", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[15, -5, -1, -4, -13, 1],\n [0, 3, 4, -12, -13, 10],\n [0, 0, -8, 8, 13, 13],\n [0, 0, 0, 2, -15, -13],\n [0, 0, 0, 0, -2, -11],\n [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": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[11, 0, 12, 0, 14, -12],\n [-3, 10, 12, -3, -14, 15],\n [-13, 6, -8, 8, -1, -5],\n [15, -7, -9, -3, -14, -8],\n [-9, 8, -4, 3, -9, -6],\n [13, 9, 0, -13, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, 2, 2, -11, 5, 13],\n [-9, 12, -14, -5, 14, -3],\n [7, -11, 14, -10, 8, 10],\n [13, -2, -4, -12, 13, 7],\n [-10, -6, 2, -1, -8, 10],\n [-7, -11, -6, 4, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[8, 11, 15, -13, -6, -5],\n [0, 1, -12, 15, -12, 1],\n [0, 0, -11, 6, 8, -10],\n [0, 0, 0, 4, 6, 0],\n [0, 0, 0, 0, -6, -13],\n [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": "258", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 1, 11, -7, -7, 7],\n [0, 3, 13, -1, -11, -1],\n [0, 0, 14, 9, 12, -14],\n [0, 0, 0, -1, 9, -6],\n [0, 0, 0, 0, 10, 14],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1595", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 0, -14, -6, -13, -5],\n [0, 5, 5, 6, -3, -9],\n [0, 0, 14, -14, -4, 9],\n [0, 0, 0, 11, -5, 0],\n [0, 0, 0, 0, 5, 11],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1569", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -1, 0, -6, -4, 12],\n [0, -12, -9, 6, -14, 10],\n [0, 0, 11, -1, 15, -8],\n [0, 0, 0, 7, -2, 15],\n [0, 0, 0, 0, 14, -5],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "976", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, 4, 13, 4, 9, -10],\n [0, -12, -14, 6, 0, 2],\n [0, 0, -12, 14, -3, 3],\n [0, 0, 0, -5, 14, 6],\n [0, 0, 0, 0, 4, -1],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, 4, -1, -1, 9, 4],\n [0, -12, 2, 2, -11, 4],\n [0, 0, -5, -11, 6, 10],\n [0, 0, 0, -14, -3, -6],\n [0, 0, 0, 0, -12, 3],\n [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": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[12, -15, -1, 12, 5, -6],\n [0, -14, -6, 8, -12, -4],\n [0, 0, -5, -8, 2, -5],\n [0, 0, 0, -4, -13, -6],\n [0, 0, 0, 0, 1, 0],\n [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": "1008", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 3) of the inverse. Round your answer to the nearest integer:\n[[12, 9, 13, -6, 12, -6],\n [-8, -15, -3, 8, -7, 6],\n [-6, -1, -11, 6, 0, -3],\n [6, 9, 4, 2, -5, 11],\n [-7, 0, -14, 10, 9, -14],\n [-4, -8, -7, -4, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-192", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 10, -3, -1, 8, -8],\n [10, -14, -4, -6, 8, -7],\n [-3, -4, 11, 0, 14, 4],\n [-1, -6, 0, -1, -6, -11],\n [8, 8, 14, -6, 8, 4],\n [-8, -7, 4, -11, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -12, 12, -10, -4, -2],\n [-12, -12, -2, -8, 6, -7],\n [12, -2, 13, -12, 2, 7],\n [-10, -8, -12, 4, 6, -9],\n [-4, 6, 2, 6, 0, 7],\n [-2, -7, 7, -9, 7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 15, -2, -10, -4, 0],\n [0, -3, 7, -2, 13, -9],\n [0, 0, -4, 1, -7, 6],\n [0, 0, 0, -11, -3, 11],\n [0, 0, 0, 0, -2, -1],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2119", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[12, 3, -2, 6, 14, 7],\n [-8, -3, 11, 4, -13, -11],\n [-7, 13, -10, 15, 9, 15],\n [6, -14, -3, -11, 12, 11],\n [9, -8, 7, -15, 4, -4],\n [7, -5, -9, -1, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-5, 8, 6, 7, -8, -8],\n [8, -2, -7, -12, 1, 3],\n [6, -7, -15, -4, -1, 8],\n [7, -12, -4, 13, -6, 0],\n [-8, 1, -1, -6, -11, 8],\n [-8, 3, 8, 0, 8, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 2, -2, -2],\n [0, -3, 0, 2, -4, 4],\n [6, 0, 12, 0, 4, 1],\n [2, 2, 0, 3, -4, 8],\n [-2, -4, 4, -4, 3, 2],\n [-2, 4, 1, 8, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 1, -3, -3, -2, 4],\n [1, 15, 9, -6, 4, 7],\n [-3, 9, -5, -6, -14, 0],\n [-3, -6, -6, 4, -12, 0],\n [-2, 4, -14, -12, -8, 0],\n [4, 7, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 6) rounded to the nearest integer?\n[[-5, 0, 9, -2, 9, -6],\n [0, -10, -6, -4, 0, 0],\n [9, -6, -2, 7, 7, 5],\n [-2, -4, 7, 13, -3, 0],\n [9, 0, 7, -3, -5, 6],\n [-6, 0, 5, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, 1, 5, -3, 0, 5],\n [1, -1, 6, 12, 12, 7],\n [5, 6, -15, 0, 1, 4],\n [-3, 12, 0, 1, 0, 2],\n [0, 12, 1, 0, -3, -6],\n [5, 7, 4, 2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, -6, 3, 8, 8, 11],\n [-6, 7, 6, -8, -2, -4],\n [3, 6, 1, -4, -10, -9],\n [8, -8, -4, 13, -6, -4],\n [8, -2, -10, -6, -4, -4],\n [11, -4, -9, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2748", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[6, 10, -12, -15, -9, 14],\n [2, -7, 13, -13, -8, 13],\n [8, 3, -12, 2, 4, 11],\n [-5, 11, -2, 9, 2, 12],\n [12, 13, 0, -13, -1, 11],\n [11, 15, -12, -11, 1, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-485", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[0, -7, 3, 2, 0, -8],\n [-7, 14, 5, 10, 2, -9],\n [3, 5, 14, -10, 4, 1],\n [2, 10, -10, 13, -2, 12],\n [0, 2, 4, -2, -3, -2],\n [-8, -9, 1, 12, -2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, 15, 14, -11, 14],\n [0, -6, -15, -6, -11, -4],\n [0, 0, 11, -9, -7, 6],\n [0, 0, 0, 13, -15, -5],\n [0, 0, 0, 0, 4, -9],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, 2, -4, -10, -11, 10],\n [-15, -4, 11, 15, 10, -5],\n [-12, 11, 2, -12, 1, -14],\n [13, 8, 6, -14, -4, 15],\n [-10, -6, 9, 7, 9, 5],\n [7, 11, 0, 15, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[12, 11, -2, 8, -6, -10],\n [11, -3, 6, -6, 5, -10],\n [-2, 6, 11, -8, 2, -6],\n [8, -6, -8, 13, 12, -1],\n [-6, 5, 2, 12, 13, -6],\n [-10, -10, -6, -1, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 3, -13, -8, -8, 7],\n [0, 4, -1, -12, 3, 5],\n [0, 0, -8, 7, 0, -3],\n [0, 0, 0, 12, -2, -3],\n [0, 0, 0, 0, -9, -10],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, -15, -6, -5, 0, -2],\n [-8, 8, 1, 9, 2, -4],\n [9, 1, 12, 10, -2, 0],\n [-2, -7, -12, 9, 7, -5],\n [-10, -1, -11, -5, 9, 2],\n [14, -3, -5, -2, 12, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, 15, 9, 12, 3],\n [8, 11, -1, -7, -8, 4],\n [12, -15, -12, -2, 9, -14],\n [0, -13, 10, -8, -10, 0],\n [8, 0, -9, 14, -3, -3],\n [-11, 9, 4, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 4) of the inverse of matrix 1/180 * A where A =\n[[2, -8, -4, -1, -3, -2],\n [-8, 15, 2, 2, -4, 4],\n [-4, 2, 7, 2, 6, -4],\n [-1, 2, 2, -2, -4, 6],\n [-3, -4, 6, -4, -15, 6],\n [-2, 4, -4, 6, 6, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[3, 7, 0, -3, 1, 9],\n [7, 11, -1, -6, 4, 6],\n [0, -1, 14, 8, 2, 11],\n [-3, -6, 8, -13, 0, 0],\n [1, 4, 2, 0, 12, -4],\n [9, 6, 11, 0, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-192", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-3, 2, -8, -4, 4, -1],\n [2, 5, -2, -6, 6, 8],\n [-8, -2, -10, 7, 1, 9],\n [-4, -6, 7, 14, -9, -4],\n [4, 6, 1, -9, 5, 2],\n [-1, 8, 9, -4, 2, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-297", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -1, -8, 3, -6],\n [-9, 2, 0, 4, 11, -10],\n [11, -7, 5, -3, 9, 15],\n [5, 10, -8, 0, -3, -3],\n [1, 7, 4, -11, 6, 5],\n [12, 1, 12, -7, -14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 8, -10, -12, 4, -2],\n [8, -10, -9, 2, 2, 4],\n [-10, -9, -13, 5, 1, -8],\n [-12, 2, 5, 2, -6, 2],\n [4, 2, 1, -6, 14, -2],\n [-2, 4, -8, 2, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-117", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -14, 9, 0, -14, 13],\n [3, 7, 3, 9, 0, 6],\n [3, -7, -15, -6, 3, -15],\n [-14, 0, -4, -8, 7, 2],\n [-14, 9, 13, -3, -10, 5],\n [10, -10, -7, 0, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16308", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/180 * A where A =\n[[15, -2, 4, 6, 4, -4],\n [-2, 12, 4, -2, 0, -2],\n [4, 4, -12, 12, 0, -4],\n [6, -2, 12, -12, 2, 1],\n [4, 0, 0, 2, -11, 3],\n [-4, -2, -4, 1, 3, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[13, -3, -12, -6, -3, -6],\n [13, 15, -7, -8, -13, 0],\n [15, -2, -7, 14, 5, -5],\n [-13, -11, 13, -6, -3, -12],\n [8, -3, -4, -11, -6, 12],\n [8, -7, 4, -9, -14, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "729", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, 7, -9, -8, -9],\n [5, 7, 13, -2, 10, 3],\n [-11, 7, 15, 9, 15, 2],\n [4, -4, 7, 1, -3, -14],\n [9, -3, 10, -9, 12, -6],\n [7, -10, -13, 10, -13, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 8, 2, -8, 3, 4],\n [8, 12, 6, 10, -6, 12],\n [2, 6, -7, -12, -6, 4],\n [-8, 10, -12, 7, -6, 0],\n [3, -6, -6, -6, 14, 4],\n [4, 12, 4, 0, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -2, -4, 1, 7, 0],\n [-2, -6, 6, 12, 3, 4],\n [-4, 6, -6, -6, -2, 12],\n [1, 12, -6, 7, -4, 8],\n [7, 3, -2, -4, -2, 11],\n [0, 4, 12, 8, 11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -13, -5, -10, 13, -2],\n [0, 10, 0, 5, 6, 8],\n [0, 0, 11, -8, 3, 4],\n [0, 0, 0, -9, -7, -3],\n [0, 0, 0, 0, 8, 6],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -9, 11, -15, 11, 0],\n [0, -9, -4, 7, -7, 11],\n [0, 0, 5, -15, 2, 15],\n [0, 0, 0, 11, 15, 1],\n [0, 0, 0, 0, -13, 4],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-96", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[0, 13, 13, 15, 15, 1],\n [12, 8, 4, 7, 2, 2],\n [6, -2, 2, -1, -1, -10],\n [11, -1, 2, -12, 7, -8],\n [-1, -13, 14, -1, -3, -7],\n [-14, 8, -8, 13, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, -2, 0, 6],\n [-4, -2, 0, 2, -6, 8],\n [-4, 0, 13, 2, 2, 8],\n [-2, 2, 2, -8, 4, 6],\n [0, -6, 2, 4, 9, 10],\n [6, 8, 8, 6, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, -13, -11, 0, 2, 10],\n [1, -5, 1, 0, 10, 7],\n [-14, -12, 5, -9, -14, 14],\n [-10, 1, -9, 9, -11, -11],\n [4, 0, 3, -7, -11, -8],\n [-7, -11, -6, 9, -14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, -12, 6, 6, 6, -14],\n [7, 13, -10, 11, -2, -15],\n [2, -9, -15, 15, -15, -15],\n [8, -12, -12, 13, 2, 11],\n [-5, 11, -15, 12, -6, -7],\n [7, -12, 12, -10, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-48", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 4, 2, -2, 11, 0],\n [4, -3, -2, 0, 8, 2],\n [2, -2, -5, -4, 0, -2],\n [-2, 0, -4, 7, 8, -2],\n [11, 8, 0, 8, -12, -11],\n [0, 2, -2, -2, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, 6, 10, -15, -12, -2],\n [1, 4, 2, -5, 13, 5],\n [10, -2, -7, 11, -1, -4],\n [-6, 3, 8, 3, -10, 4],\n [8, 11, -10, -8, -15, 6],\n [1, 1, 8, -1, -9, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 15, 9, 7, 12, -13],\n [14, 14, 13, 6, -5, 4],\n [14, 13, 3, -7, -6, -14],\n [-15, 15, 14, 0, 2, 7],\n [10, 1, -10, -2, 7, 9],\n [-1, -2, 8, 6, -13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 3, 9, -4, -14, -13],\n [0, 13, -15, 4, 5, 13],\n [0, 0, -15, 3, -15, 11],\n [0, 0, 0, -4, 11, 13],\n [0, 0, 0, 0, 12, -15],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -9, -4, 5, -9, -4],\n [0, -14, -2, -3, -12, -2],\n [0, 0, -9, 3, -14, -6],\n [0, 0, 0, -11, -4, -10],\n [0, 0, 0, 0, 6, -1],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, -12, 3, -2, 5, 5],\n [-12, -1, -8, 12, 8, -2],\n [3, -8, -3, -4, 0, -2],\n [-2, 12, -4, 7, 8, -8],\n [5, 8, 0, 8, 0, -8],\n [5, -2, -2, -8, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 1) of the inverse. Round your answer to the nearest integer:\n[[13, -12, -12, -8, 4, -4],\n [-12, -13, 2, 3, -5, -6],\n [-12, 2, -15, 4, 2, 4],\n [-8, 3, 4, -9, 12, 0],\n [4, -5, 2, 12, 12, 0],\n [-4, -6, 4, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -4, 8, 0, -7, -1],\n [14, 11, 12, 1, -2, 11],\n [2, 10, -14, 15, -12, 2],\n [-9, -3, -1, 9, 7, 12],\n [6, 15, 10, -15, -5, -6],\n [9, -11, 0, -5, 5, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 8, -8, -2, 8],\n [0, 1, 8, -11, 9, -14],\n [0, 0, 14, 8, -7, -12],\n [0, 0, 0, 2, 0, 14],\n [0, 0, 0, 0, 5, 2],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7111", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -6, 0, 4, -11, -3],\n [2, 1, -7, -2, 1, 13],\n [15, -12, 2, 11, 4, 8],\n [8, -1, -5, -4, -7, -3],\n [-1, 11, -1, 12, -11, 7],\n [3, 10, 4, 10, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1400", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[10, -2, 12, 1, 2, 5],\n [-13, -14, -15, -6, 3, 1],\n [-4, -15, -4, 1, 8, 15],\n [-13, -5, 1, 7, 10, -13],\n [-8, 4, -12, 5, 6, -9],\n [-2, -2, -12, 0, 8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[6, 10, -12, -4, 4, -1],\n [10, 0, 6, 2, -8, 14],\n [-12, 6, -10, -1, -6, -6],\n [-4, 2, -1, -5, 10, 7],\n [4, -8, -6, 10, 9, -8],\n [-1, 14, -6, 7, -8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[10, -5, -14, -2, -4, 14],\n [1, -4, 10, -4, -15, -3],\n [-2, 8, 14, -14, -4, 10],\n [5, 12, 0, -12, -8, -14],\n [-6, -7, 7, -1, -3, 7],\n [1, 14, 0, 12, -14, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 11, -2, -13, 7, -4],\n [0, -14, -12, -2, 0, 3],\n [0, 0, 13, -2, -10, -3],\n [0, 0, 0, -4, 4, 11],\n [0, 0, 0, 0, -8, -9],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-5, -11, 0, -9, 11, -11],\n [0, -1, -13, 10, -11, 7],\n [0, 0, -7, -1, -13, 13],\n [0, 0, 0, 5, -8, 5],\n [0, 0, 0, 0, -6, 8],\n [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": "10903", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 2) rounded to the nearest integer?\n[[-6, -4, -10, -4, 7, -2],\n [0, -7, -6, 10, 1, 1],\n [0, 0, 15, 3, -15, -4],\n [0, 0, 0, -3, -14, -6],\n [0, 0, 0, 0, 2, -11],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-10, -8, 13, 3, -5, 15],\n [9, 15, -4, -7, -14, -8],\n [10, -5, 12, 5, -12, -6],\n [5, 4, 0, -8, -12, 13],\n [-6, -4, 13, -2, 0, 6],\n [2, 5, 6, 5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -8, 8, 11, -2, -2],\n [-8, -15, 3, 0, -1, 7],\n [8, 3, 6, -7, -2, -2],\n [11, 0, -7, 1, -2, 4],\n [-2, -1, -2, -2, 8, 0],\n [-2, 7, -2, 4, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-9, 8, -15, 11, 2, 8],\n [12, 9, 4, -4, 0, -6],\n [11, -6, -2, 9, 4, -6],\n [-6, 10, 9, -5, 7, -14],\n [9, 4, -8, 14, 7, 13],\n [15, -9, -8, -15, 5, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[2, -1, -15, -11, -14, 4],\n [0, 3, 2, 13, 6, 2],\n [0, 0, 8, -8, 13, 14],\n [0, 0, 0, 7, 4, 1],\n [0, 0, 0, 0, -12, -15],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 4, -2, 12, 0, 10],\n [4, 11, -4, 0, -6, 3],\n [-2, -4, 5, -1, 2, 6],\n [12, 0, -1, 10, 0, 10],\n [0, -6, 2, 0, 10, -6],\n [10, 3, 6, 10, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 4) rounded to the nearest integer?\n[[-5, 1, 11, -3, -3, -9],\n [1, -4, -2, 14, -11, -2],\n [11, -2, 8, 4, -2, 2],\n [-3, 14, 4, -7, -4, -4],\n [-3, -11, -2, -4, 4, -2],\n [-9, -2, 2, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 4) of the inverse of matrix 1/180 * A where A =\n[[8, 15, -9, -8, 12, -13],\n [15, -1, 0, -12, 5, -10],\n [-15, -12, -5, -4, 10, 13],\n [-11, 7, 13, 5, 0, -3],\n [-3, 1, 11, -9, -8, -3],\n [7, 11, 0, 14, 13, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, -8, 0, 15, 5, -6],\n [0, -4, -4, 10, -11, 0],\n [0, 0, -7, -4, -11, 6],\n [0, 0, 0, 8, -13, -11],\n [0, 0, 0, 0, -9, -6],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-113", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -12, 5, -15, -9, 8],\n [-7, -8, -11, 3, -6, -5],\n [9, -1, -10, -1, -11, 13],\n [3, 6, 3, -6, -4, 6],\n [-12, 15, 2, 0, -8, -12],\n [9, 7, -4, -14, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "831", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, -7, 13, 5, 2, -5],\n [0, 14, 15, 9, 7, -14],\n [0, 0, -12, 13, -7, 15],\n [0, 0, 0, 12, -6, 0],\n [0, 0, 0, 0, -6, -15],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -13, -2, -6, 6, -9],\n [10, 1, 14, -10, 7, 6],\n [-12, 1, 11, -7, -12, -9],\n [7, -14, 1, 8, -8, 7],\n [14, 15, -1, 15, -1, -8],\n [0, 3, -5, -14, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 4, 3, 3, 5, 7],\n [4, -1, 12, -5, -2, 5],\n [3, 12, -12, -2, 6, 8],\n [3, -5, -2, 2, 6, 11],\n [5, -2, 6, 6, 8, -2],\n [7, 5, 8, 11, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 4, -1, 7, 12, 0],\n [0, 5, -1, 1, 2, -11],\n [0, 0, 14, -3, 2, -2],\n [0, 0, 0, 4, 4, 3],\n [0, 0, 0, 0, -4, 5],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-55", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 2, -2, -6, -8, 2],\n [2, -6, 0, -6, 6, 8],\n [-2, 0, -8, -5, 0, 7],\n [-6, -6, -5, 14, 8, -4],\n [-8, 6, 0, 8, 9, 2],\n [2, 8, 7, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-92", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 0, -6, -4, -5, 2],\n [0, 8, -14, 12, 12, 0],\n [-6, -14, 10, -10, 4, 10],\n [-4, 12, -10, -9, 5, 0],\n [-5, 12, 4, 5, 8, 2],\n [2, 0, 10, 0, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, -11, 8, 5, 2, -1],\n [-10, 9, 13, 3, -15, -15],\n [-3, -13, -6, 5, -13, -7],\n [-8, -13, 9, 15, -3, -10],\n [-3, 7, 4, 4, -4, -3],\n [-14, 5, 8, 7, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-10, 3, 5, -3, 1, 7],\n [0, 1, 13, -14, 3, 3],\n [0, 0, 6, 15, -6, -6],\n [0, 0, 0, 1, 11, -1],\n [0, 0, 0, 0, 3, 1],\n [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": "-31650", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 1, -9, -12, -8, -3],\n [0, -10, 9, -11, 14, -4],\n [0, 0, 13, -7, -12, 3],\n [0, 0, 0, 2, -6, 9],\n [0, 0, 0, 0, 14, 8],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2300", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[12, 3, -2, -2, 0, 12],\n [3, -13, 5, 2, 8, 4],\n [-2, 5, -15, 2, 4, 0],\n [-2, 2, 2, 11, 6, 12],\n [0, 8, 4, 6, 0, -6],\n [12, 4, 0, 12, -6, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[13, 8, -7, -5, -2, 10],\n [8, -14, 1, -10, 0, 10],\n [-7, 1, 15, 4, 12, 2],\n [-5, -10, 4, 3, 0, -1],\n [-2, 0, 12, 0, -12, -12],\n [10, 10, 2, -1, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-69", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 6) rounded to the nearest integer?\n[[-2, 10, 12, 0, 6, 2],\n [10, -10, -4, -12, -2, 11],\n [12, -4, -9, 2, 3, -4],\n [0, -12, 2, 2, -2, 0],\n [6, -2, 3, -2, -14, -2],\n [2, 11, -4, 0, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, -2, 0, -4, 3],\n [12, 7, -10, 2, -6, -4],\n [-2, -10, -3, 4, -5, 0],\n [0, 2, 4, -2, -12, 8],\n [-4, -6, -5, -12, 6, 1],\n [3, -4, 0, 8, 1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, -4, 9, -8, -3, -12],\n [0, -2, -3, 11, -10, 1],\n [0, 0, 1, -13, 1, -7],\n [0, 0, 0, 4, -14, 4],\n [0, 0, 0, 0, 6, -1],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 8, -11, 4, -9, -9],\n [0, -7, 9, 5, -3, -4],\n [0, 0, -6, -15, 9, -8],\n [0, 0, 0, -13, -13, 8],\n [0, 0, 0, 0, -9, 5],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 15, -5, -3, -9, -3],\n [-14, -10, -7, 15, 4, 9],\n [-14, 2, 0, 9, -4, -9],\n [-9, 1, -3, -5, -10, 13],\n [7, 11, -2, -10, -10, -14],\n [6, 4, 9, -1, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, -1, -10, 8, 0, -12],\n [-1, 2, 2, -8, -4, -6],\n [-10, 2, 5, -6, 10, -6],\n [8, -8, -6, -6, -2, 6],\n [0, -4, 10, -2, 0, -4],\n [-12, -6, -6, 6, -4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -7, 0, 11, -11, 7],\n [12, 5, -9, -3, 4, 8],\n [13, 11, 14, 10, -3, 11],\n [10, -9, -6, -1, 5, 11],\n [-10, -11, 7, 12, -14, 5],\n [-1, 10, 0, 15, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[13, 6, 13, 10, 3, -9],\n [0, 14, -13, 8, 13, 4],\n [0, 0, -10, 10, -5, 11],\n [0, 0, 0, 15, -10, -2],\n [0, 0, 0, 0, -1, 2],\n [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": "862", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -9, -15, 9, -5, -10],\n [0, -13, 15, 3, -14, 2],\n [0, 0, 13, -6, -11, -7],\n [0, 0, 0, -10, 13, 15],\n [0, 0, 0, 0, 6, 5],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -11, -2, 10, 13, 5],\n [-3, 10, -10, 15, -4, 10],\n [-8, -11, 14, -1, 11, 0],\n [-15, 0, -11, -13, 4, -1],\n [15, -3, 8, 0, 7, -5],\n [5, -14, 6, 11, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, -2, 6, 4],\n [4, -8, -2, -4, 4, 2],\n [0, -2, -8, 4, 8, 12],\n [-2, -4, 4, -8, 12, -4],\n [6, 4, 8, 12, 0, 3],\n [4, 2, 12, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[0, -3, 2, -2, 10, -4],\n [-3, -9, -2, -1, 2, 7],\n [2, -2, 12, -8, -1, 5],\n [-2, -1, -8, 9, -5, 10],\n [10, 2, -1, -5, 10, 12],\n [-4, 7, 5, 10, 12, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, 0, -1, -6, -11, -10],\n [0, -7, 2, 2, -6, -2],\n [-1, 2, 5, 8, -1, 8],\n [-6, 2, 8, 9, 8, 8],\n [-11, -6, -1, 8, -10, 6],\n [-10, -2, 8, 8, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-4, 6, -11, 4, -9, 8],\n [0, 4, -15, -15, 1, 11],\n [-15, 5, 4, -3, 14, -7],\n [-1, -13, -2, 7, -5, 8],\n [6, -4, -3, 10, -3, -15],\n [8, 15, -6, -13, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, -11, -6, 3, 2],\n [2, 6, -3, -2, 0, 8],\n [-11, -3, -15, -6, -2, -3],\n [-6, -2, -6, -13, -6, 2],\n [3, 0, -2, -6, -7, -8],\n [2, 8, -3, 2, -8, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "457", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, -9, 1, 10, -15, -11],\n [0, -1, -14, -7, 15, -9],\n [-12, 4, 2, 5, -12, 12],\n [-3, -15, 12, 8, -13, 0],\n [14, 6, -12, 9, 7, 9],\n [0, 10, 3, -15, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the inverse of matrix 1/180 * A where A =\n[[6, 6, 0, 2, 2, -5],\n [6, -12, -5, -13, -10, 2],\n [0, -5, 2, 2, 3, 7],\n [2, -13, 2, -12, 1, 3],\n [2, -10, 3, 1, 10, 4],\n [-5, 2, 7, 3, 4, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, -2, 1, -11, -14, 4],\n [0, -2, -2, 11, -15, -13],\n [0, 0, 10, -1, 3, 4],\n [0, 0, 0, 3, 11, -11],\n [0, 0, 0, 0, 13, -9],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, -6, -6, -5, 1, -11],\n [-3, -6, -7, 1, -15, -12],\n [-12, 2, -7, 14, 9, 13],\n [13, 2, -2, 9, -1, -10],\n [8, -6, 13, -1, 13, -12],\n [2, 2, 9, 1, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[0, 4, 4, -2, -6, -6],\n [4, -6, 2, -6, 3, -1],\n [4, 2, 4, 4, 2, -1],\n [-2, -6, 4, -12, -2, 2],\n [-6, 3, 2, -2, -8, -8],\n [-6, -1, -1, 2, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 4, 2, 0, 6, -10],\n [4, 2, 4, 0, -11, -2],\n [2, 4, 14, -4, 3, 0],\n [0, 0, -4, -12, -2, 4],\n [6, -11, 3, -2, 7, 0],\n [-10, -2, 0, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -4, -1, -14, 2, -3],\n [0, -11, 10, -6, -4, -6],\n [0, 0, 15, 9, -14, -11],\n [0, 0, 0, -10, 6, 7],\n [0, 0, 0, 0, 9, 14],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -6, -4, 1, -12, -14],\n [-5, -9, -14, 10, 2, 5],\n [-12, -8, 4, -2, -4, 6],\n [5, 11, 14, 2, -5, 15],\n [13, 12, 14, -8, -14, 9],\n [-1, -7, 3, 4, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, -2, -1, -4, -4, -2],\n [-2, 11, -3, -2, 6, 2],\n [-1, -3, -6, 8, -1, 3],\n [-4, -2, 8, -11, -3, -2],\n [-4, 6, -1, -3, 10, 0],\n [-2, 2, 3, -2, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 11, -4, 2, 0, 0],\n [11, -15, -2, -1, -12, -8],\n [-4, -2, 5, 0, -2, -3],\n [2, -1, 0, 10, 0, -4],\n [0, -12, -2, 0, -10, 0],\n [0, -8, -3, -4, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-7, -8, 12, -6, 1, 7],\n [14, 13, 10, -10, -2, 6],\n [6, -10, 10, -9, -4, -13],\n [-2, 6, 3, 7, 0, -9],\n [-8, 2, 9, -3, 5, -7],\n [-6, 5, 7, 11, -7, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -14, 9, -3, -14, 3],\n [10, -14, -13, -10, -13, 15],\n [-6, 8, 11, -10, 7, 0],\n [1, 3, -13, 2, -9, -7],\n [4, -4, -11, -13, -5, 9],\n [14, -12, -11, -15, 11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-116", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -10, 15, 3, -8, 10],\n [0, -13, 10, -2, 9, 0],\n [0, 0, -13, 6, 10, 2],\n [0, 0, 0, 5, 9, -15],\n [0, 0, 0, 0, -10, 7],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, -8, 10, 4, -13, -4],\n [0, -4, -14, 8, -2, 6],\n [0, 0, -11, -7, 5, -5],\n [0, 0, 0, 1, -14, 8],\n [0, 0, 0, 0, -2, -11],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32735", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -14, -8, -7, 11, -13],\n [0, -9, -11, 5, 10, -11],\n [0, 0, 5, 13, 4, 15],\n [0, 0, 0, 2, 9, -14],\n [0, 0, 0, 0, 9, -13],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3554", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-4, -2, 3, 7, 4, 0],\n [-2, 14, -1, -5, -4, -4],\n [3, -1, -1, 10, -10, 7],\n [7, -5, 10, -11, 8, -2],\n [4, -4, -10, 8, 2, 0],\n [0, -4, 7, -2, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 0, -13, 10, 2],\n [0, 7, 5, -2, -1, 1],\n [0, 0, 5, 1, 7, 9],\n [0, 0, 0, -2, 13, 4],\n [0, 0, 0, 0, 8, -3],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-8, 2, -9, -10, 12, 3],\n [2, 3, -2, -1, 0, 0],\n [-9, -2, 4, 7, 0, -3],\n [-10, -1, 7, -5, 12, -6],\n [12, 0, 0, 12, 15, 6],\n [3, 0, -3, -6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, 14, -4, -13, 1, 5],\n [0, -5, -12, 0, 1, -7],\n [0, 0, 11, 4, 9, -14],\n [0, 0, 0, 13, -10, -13],\n [0, 0, 0, 0, 7, -15],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1529", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, 9, -2, 10, 6],\n [-9, -2, 15, 10, 15, 8],\n [11, 15, 13, -6, 1, -2],\n [-8, -12, 10, 0, 8, -3],\n [15, 6, 11, 9, 11, 4],\n [2, -2, 2, -11, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -13, -8, 4, 6, -6],\n [0, 3, 14, 5, 12, -13],\n [0, 0, -5, 15, 1, 0],\n [0, 0, 0, 7, 3, -4],\n [0, 0, 0, 0, -11, -1],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-233", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, -1, 4, -12, 6, 2],\n [-10, 7, 11, 10, 3, -5],\n [12, 8, -14, 11, -8, 13],\n [-5, -11, 2, 7, 14, 2],\n [-2, 6, -6, -13, -7, -13],\n [-5, 15, -4, -4, -13, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-9, -2, 8, 12, -5, -9],\n [9, 5, -6, -5, -1, 3],\n [0, 6, 5, 12, 4, -4],\n [2, 7, -3, -11, -12, 12],\n [-2, -8, -7, 9, 3, -13],\n [-11, 5, 10, 2, -15, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, 1, 1, -5, 15, -14],\n [-10, 6, -2, -13, -4, -12],\n [-4, -3, -14, -14, -1, 7],\n [13, 1, -9, 14, 12, -2],\n [-4, 14, 1, -2, -10, 3],\n [8, -10, 11, 2, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[8, 4, -4, -11, -6, -4],\n [4, -5, 1, 9, 7, -2],\n [-4, 1, -4, 0, -6, 12],\n [-11, 9, 0, 7, -4, -6],\n [-6, 7, -6, -4, 4, 6],\n [-4, -2, 12, -6, 6, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 6, -12, 4, -2, -6],\n [6, -8, -6, 5, 2, 0],\n [-12, -6, -14, 12, -8, 3],\n [4, 5, 12, 9, 0, -8],\n [-2, 2, -8, 0, -9, 10],\n [-6, 0, 3, -8, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, -7, 0, -3, -6],\n [0, 4, -2, -4, 9, 3],\n [0, 0, -1, 0, 11, -8],\n [0, 0, 0, 3, 3, 15],\n [0, 0, 0, 0, -2, -15],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2754", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -7, 2, -5, 0, -14],\n [-4, 6, -10, -5, 11, -8],\n [-4, 13, 11, 14, -14, -7],\n [-1, -14, 13, -15, -6, -14],\n [-4, 7, -8, -11, 6, 12],\n [-15, -1, -10, -4, 15, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 3, 11, -15, -5, 4],\n [0, 14, -8, -11, 1, 14],\n [0, 0, -6, -14, -7, 8],\n [0, 0, 0, -9, -1, 5],\n [0, 0, 0, 0, -13, 12],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[6, -9, -6, -6, -2, 4],\n [-9, 1, 4, 2, -1, 4],\n [-6, 4, 12, -4, -7, 6],\n [-6, 2, -4, -15, 6, -2],\n [-2, -1, -7, 6, -7, -5],\n [4, 4, 6, -2, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, -11, -6, -10, 8, 3],\n [0, -3, -15, 4, 9, -1],\n [0, 0, -6, -7, 1, -7],\n [0, 0, 0, -6, 9, 1],\n [0, 0, 0, 0, 6, -12],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-8, 0, 12, 3, -14, 2],\n [0, -4, -1, -11, 4, 8],\n [12, -1, -5, 6, 0, 6],\n [3, -11, 6, 13, 3, 0],\n [-14, 4, 0, 3, -9, -5],\n [2, 8, 6, 0, -5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[0, 4, 0, 3, 4, -9],\n [4, -3, 2, 4, -10, -1],\n [0, 2, 1, -1, -2, 4],\n [3, 4, -1, 12, -2, 3],\n [4, -10, -2, -2, 4, -7],\n [-9, -1, 4, 3, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[-2, 4, 8, 0, -3, 4],\n [4, 15, -11, -6, 12, 0],\n [8, -11, -3, 6, -4, 12],\n [0, -6, 6, -9, -9, -9],\n [-3, 12, -4, -9, -11, 4],\n [4, 0, 12, -9, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, -15, -2, 1, -6, -4],\n [0, -2, 14, 11, 0, -8],\n [0, 0, -6, 13, 1, 11],\n [0, 0, 0, 4, 0, 1],\n [0, 0, 0, 0, -8, -10],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -2, 10, -4, 8, 0],\n [-2, -7, -9, -6, 3, -6],\n [10, -9, 2, 2, 0, 10],\n [-4, -6, 2, -13, 0, 2],\n [8, 3, 0, 0, -11, 6],\n [0, -6, 10, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 6, -8, -3, 6, -2],\n [6, 5, 10, -2, 7, 0],\n [-8, 10, -7, 4, 4, 10],\n [-3, -2, 4, 6, -8, 2],\n [6, 7, 4, -8, -11, -6],\n [-2, 0, 10, 2, -6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/180 * A where A =\n[[11, 8, 2, -2, -1, -2],\n [8, 1, -2, 2, 10, 0],\n [2, -2, 6, 6, 7, -8],\n [-2, 2, 6, -14, 6, -4],\n [-1, 10, 7, 6, -6, -1],\n [-2, 0, -8, -4, -1, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, 11, 1, -12, 15, 7],\n [0, -5, -10, -10, 11, -7],\n [0, 0, -14, -12, -11, 1],\n [0, 0, 0, -4, 5, -8],\n [0, 0, 0, 0, 3, 3],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[4, 0, -5, -9, 1, 1],\n [0, -3, -6, -9, -2, 7],\n [0, 0, -12, 5, -11, 4],\n [0, 0, 0, -9, 15, -6],\n [0, 0, 0, 0, -15, -9],\n [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": "-102", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 6) of the inverse. Round your answer to the nearest integer:\n[[15, -12, -12, 12, 9, -3],\n [7, 3, -6, -11, -9, 8],\n [0, -15, -4, -14, -9, -5],\n [15, 13, 14, -3, 15, -14],\n [-9, -1, 9, -5, -14, -9],\n [-12, -5, 13, -14, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-9, -3, -11, 1, 5, -4],\n [0, 3, -9, -10, -8, -3],\n [0, 0, -7, 14, -5, 8],\n [0, 0, 0, -9, 9, -9],\n [0, 0, 0, 0, -5, -9],\n [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": "-4077", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[9, -11, 13, 12, 14, -9],\n [-7, 9, -15, 15, -15, 3],\n [-10, 2, -6, 12, -5, -15],\n [-15, -3, -11, 4, -15, 4],\n [-13, 2, -7, -2, 15, 11],\n [1, 7, -2, 13, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 5, 1, 6, 13, 9],\n [0, 7, 6, -11, -12, -12],\n [0, 0, 5, -3, 6, -11],\n [0, 0, 0, 7, -9, 4],\n [0, 0, 0, 0, 1, 5],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "330", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 12, -8, 8, -13, 9],\n [0, -15, -14, -1, 6, 12],\n [0, 0, 6, -2, 1, 11],\n [0, 0, 0, 10, -3, 11],\n [0, 0, 0, 0, -1, 3],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-260", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -2, 8, -5, 4, 2],\n [-2, -8, -2, 0, 2, 2],\n [8, -2, 9, 10, -4, -8],\n [-5, 0, 10, -10, -2, -1],\n [4, 2, -4, -2, 11, -2],\n [2, 2, -8, -1, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-396", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 6, -7, 8, 9, 13],\n [0, 10, -8, 3, 8, 0],\n [0, 0, -10, 6, -13, -6],\n [0, 0, 0, -12, 10, -4],\n [0, 0, 0, 0, 2, -9],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-3, 2, -7, 10, 8, 8],\n [-7, 15, 7, 13, -7, -6],\n [12, -14, -10, -1, -13, -5],\n [15, -10, -13, 8, 15, -5],\n [-1, -3, 4, 12, -6, -10],\n [-1, 9, 2, 2, -9, -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"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, 4, -7, 8, -14],\n [0, 4, -14, -5, 10, -9],\n [0, 0, -6, -11, -5, -15],\n [0, 0, 0, 3, -14, 5],\n [0, 0, 0, 0, 8, -12],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1364", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[14, 14, -15, 8, -2, -12],\n [-11, -5, 8, 12, 15, 7],\n [-3, 0, 8, -3, 8, 6],\n [10, -14, 0, -10, -2, -15],\n [1, -5, 3, -13, -5, 13],\n [-11, 1, 10, 6, -9, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 2) of the inverse of matrix 1/180 * A where A =\n[[12, 13, -5, -13, 4, -6],\n [0, -6, -2, -4, -1, -6],\n [0, 0, 10, 3, -15, 8],\n [0, 0, 0, -14, 1, 14],\n [0, 0, 0, 0, 11, -7],\n [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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[4, 1, 0, -4, 0, -2],\n [1, -12, -6, -4, 3, 4],\n [0, -6, -5, 2, -11, -10],\n [-4, -4, 2, -1, -3, 6],\n [0, 3, -11, -3, -11, -4],\n [-2, 4, -10, 6, -4, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 14, -8, 13, 13, -15],\n [-14, 14, -1, 4, 12, 2],\n [-5, 9, -6, 8, 8, -12],\n [-11, -12, -3, 9, -3, 2],\n [13, 11, 8, -14, 0, -15],\n [10, 3, -7, 12, -13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 13, -6, -15, -6, 5],\n [-7, 12, -1, -1, -13, 9],\n [-11, -7, 10, 6, -7, 7],\n [-9, 8, 7, -4, 9, 11],\n [-7, -10, 7, -14, 15, -7],\n [12, 13, 1, -15, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "455", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 1, 1, -14, -3, -2],\n [0, 12, -6, -13, 13, 11],\n [0, 0, -1, -7, -6, -8],\n [0, 0, 0, 2, -11, -10],\n [0, 0, 0, 0, 4, 0],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-81", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[6, 8, 12, -14, -8, 1],\n [8, -4, 0, -10, -2, -7],\n [12, 0, -10, 1, -6, 4],\n [-14, -10, 1, -4, -9, 2],\n [-8, -2, -6, -9, -1, -3],\n [1, -7, 4, 2, -3, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[3, -1, -10, 11, -5, 5],\n [0, 4, 4, 5, 2, 9],\n [0, 0, -14, 10, 14, -7],\n [0, 0, 0, -6, 7, -12],\n [0, 0, 0, 0, -12, 10],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 0, 0, 12, 5, 4],\n [0, 14, 8, -7, 2, -6],\n [0, 8, 6, 1, -6, 1],\n [12, -7, 1, -12, -4, -4],\n [5, 2, -6, -4, 0, -5],\n [4, -6, 1, -4, -5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 6, -14, -8, 11, -7],\n [0, -14, -10, 6, -8, 10],\n [0, 0, -7, -15, -7, -6],\n [0, 0, 0, 14, -6, -1],\n [0, 0, 0, 0, -3, 1],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-75", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, 13, 2, 4, -1, -2],\n [0, 1, 6, 15, 10, -8],\n [0, 0, 2, 14, 9, 15],\n [0, 0, 0, 12, -8, 15],\n [0, 0, 0, 0, 6, 1],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5247", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[14, 5, -4, -11, -5, 4],\n [-13, 5, -1, -2, -5, 4],\n [-8, -12, 11, -4, -8, -10],\n [-1, 14, -4, 0, 0, 11],\n [5, 4, 4, 12, -12, -5],\n [-3, 13, -7, -12, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-3, 14, 11, -1, 0, 0],\n [0, 1, -5, -8, 4, -13],\n [0, 0, 4, 0, -2, 0],\n [0, 0, 0, 15, 14, -5],\n [0, 0, 0, 0, 14, 11],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4022", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, -2, 14, -15, -3, 14],\n [0, -9, -1, 4, -6, -2],\n [0, 0, 8, 9, 6, -4],\n [0, 0, 0, 14, 9, 4],\n [0, 0, 0, 0, -14, 6],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 9, 7, -11, 7, 13],\n [9, -8, 0, 6, 0, -3],\n [4, 13, -1, -15, 6, -13],\n [-10, 6, -2, -12, 2, -1],\n [-7, 2, -13, -6, 1, -9],\n [-1, -15, 11, 9, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, -11, -9, 3, 9, 8],\n [13, -1, -13, -1, -11, 7],\n [-4, 14, 4, -11, -13, -7],\n [10, -7, -9, 10, -14, 7],\n [7, 11, 5, 0, -7, -3],\n [12, 11, 3, 4, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-97", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -15, 2, 15, 3, -7],\n [-3, -8, 7, -3, -1, -5],\n [-4, -2, -12, -15, 8, -12],\n [3, -7, -6, -12, 4, 14],\n [-7, -3, -4, -5, -4, 14],\n [2, 14, -4, 0, -11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-210", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[4, 9, -4, 5, 9, -5],\n [0, 14, 2, 14, 15, 9],\n [0, 0, 1, -2, -15, 1],\n [0, 0, 0, -11, -11, -7],\n [0, 0, 0, 0, 6, 14],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8995", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, 10, 9, -2, 0, 7],\n [10, -1, -2, -7, -5, 9],\n [9, -2, 7, 5, 8, -7],\n [-2, -7, 5, -6, -3, 10],\n [0, -5, 8, -3, -12, -8],\n [7, 9, -7, 10, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -15, 1, 10, 1, -9],\n [0, 4, -1, -3, 12, -14],\n [0, 0, 8, -3, 8, -5],\n [0, 0, 0, -6, -7, 11],\n [0, 0, 0, 0, -15, 1],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[13, 2, -1, -10, -9, 1],\n [0, -8, -4, 5, -2, -4],\n [0, 0, 6, 4, -1, 15],\n [0, 0, 0, -6, -6, 0],\n [0, 0, 0, 0, -11, 7],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-96", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-11, 8, -4, -12, -1, -7],\n [0, -6, 13, 12, 7, 15],\n [0, 0, -8, -4, 6, 8],\n [0, 0, 0, 14, -15, 0],\n [0, 0, 0, 0, 2, -5],\n [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": "340", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, 7, 6, -6, -5],\n [9, -3, -7, 15, -9, -7],\n [-3, 10, -13, -13, -15, 5],\n [15, 4, -14, 9, -13, -1],\n [8, -10, 14, -3, 5, -15],\n [4, 3, -15, 12, 15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, 2, 6, 6, 2],\n [0, -1, -12, 6, 2, 1],\n [2, -12, -10, 6, -4, 4],\n [6, 6, 6, -7, 4, 0],\n [6, 2, -4, 4, 12, 3],\n [2, 1, 4, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, 8, 4, 3, -2, 8],\n [8, -3, 0, -2, 8, 6],\n [4, 0, -6, 13, 8, -6],\n [3, -2, 13, 11, 0, -11],\n [-2, 8, 8, 0, -1, -2],\n [8, 6, -6, -11, -2, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 4, 10, -9, 8, -14],\n [0, 7, 0, -3, -8, -10],\n [0, 0, -12, 11, -5, -11],\n [0, 0, 0, -9, 11, -1],\n [0, 0, 0, 0, -5, 12],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, 0, 6, 4, 4],\n [-2, -5, -3, -3, 11, -9],\n [0, -3, -7, -1, 7, 0],\n [6, -3, -1, 6, -4, 0],\n [4, 11, 7, -4, 8, 3],\n [4, -9, 0, 0, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -10, 14, 11, -9, 15],\n [-1, 10, -15, 8, -12, 13],\n [9, -15, -5, 2, -2, 6],\n [-5, -6, 11, 14, 1, -12],\n [8, -1, 10, 0, 5, -3],\n [-7, -5, -5, -10, -15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 6, 8, 15, 6],\n [0, -1, 11, 2, 4, -2],\n [0, 0, -11, 10, -12, -14],\n [0, 0, 0, -6, 2, 1],\n [0, 0, 0, 0, -15, -15],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1937", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -15, -11, 15, -7],\n [14, 9, 1, 0, -8, 1],\n [-1, 8, -15, -4, -11, 8],\n [-10, 9, -15, 9, -15, -6],\n [-6, -13, 1, 3, 12, -5],\n [13, 2, -14, -7, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-222", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[12, -2, -12, 13, 1, 1],\n [-4, 12, 4, 2, -13, -5],\n [9, 2, -12, 1, 2, -11],\n [-2, -6, -1, -15, 0, -5],\n [7, 4, -10, 8, 13, 6],\n [0, 14, -14, -15, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-59", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 6, -4, 1, 14, 9],\n [0, 13, -1, 14, 3, 11],\n [0, 0, 13, 10, 15, 11],\n [0, 0, 0, -7, 11, -3],\n [0, 0, 0, 0, 5, -6],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -5, 2, 1, -4],\n [10, 6, 10, 5, 1, 4],\n [-5, 10, -13, -4, -12, 8],\n [2, 5, -4, 3, 0, -12],\n [1, 1, -12, 0, 0, 2],\n [-4, 4, 8, -12, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1269", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 6, 2, 6, 4, 1],\n [6, 8, 0, -1, -2, -8],\n [2, 0, -14, -3, 2, 2],\n [6, -1, -3, -3, -10, 4],\n [4, -2, 2, -10, -6, -4],\n [1, -8, 2, 4, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "566", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, 8, -13, 14, 4],\n [0, 3, -9, -7, 3, -3],\n [0, 0, 6, 2, 13, 7],\n [0, 0, 0, -5, 15, -15],\n [0, 0, 0, 0, 14, -9],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 5, -5, 0, 3],\n [1, 11, 10, -10, -5, 1],\n [-7, 2, 1, 15, -4, 7],\n [6, 6, 14, -11, -5, -12],\n [11, -12, -13, 10, 8, 7],\n [9, 1, -9, 10, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, -15, 5, 3, 5],\n [4, 2, -5, 4, -13, 13],\n [1, -4, -6, -8, -1, -11],\n [-12, 10, 12, 5, 4, 3],\n [5, -12, -1, 1, -4, -13],\n [-6, -1, -6, 8, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-114", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, -13, 5, 10, 15, 11],\n [0, -15, -13, -13, -11, 3],\n [0, 0, -15, -12, 13, 13],\n [0, 0, 0, 1, -2, 2],\n [0, 0, 0, 0, -13, 7],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 15, 5, 10, -7, 10],\n [-13, -10, 8, -5, -7, 13],\n [-1, 7, 12, -13, -15, 4],\n [13, 6, 3, -2, 1, 6],\n [-2, 1, 9, 11, -2, -4],\n [0, -15, -3, -10, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 3, -10, -9, -15, -15],\n [13, -11, -10, 15, 0, 15],\n [9, 0, -2, -15, -3, 4],\n [-6, 8, -6, -7, 15, -3],\n [-13, 11, 2, 4, -14, 1],\n [12, 3, 7, -3, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-14, -15, 8, -11, 8, -13],\n [0, 12, -9, 8, 15, 6],\n [0, 0, 7, 14, 12, 2],\n [0, 0, 0, -15, -11, 1],\n [0, 0, 0, 0, 4, -12],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-14, 8, 5, -2, -9, 2],\n [8, 10, -5, -4, -6, 4],\n [5, -5, -3, 4, -4, 12],\n [-2, -4, 4, 14, 4, -2],\n [-9, -6, -4, 4, -7, -10],\n [2, 4, 12, -2, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[0, -3, -6, 4, 2, -2],\n [-3, -15, -4, 4, -2, 3],\n [-6, -4, 0, 10, -2, -6],\n [4, 4, 10, -5, -10, -4],\n [2, -2, -2, -10, -11, -2],\n [-2, 3, -6, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-165", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[4, -6, -7, -6, 13, -10],\n [0, 12, 9, -10, -12, 14],\n [0, 0, 7, 3, 2, 10],\n [0, 0, 0, 1, 15, -11],\n [0, 0, 0, 0, -3, -12],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-77", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-9, -15, 15, 7, 13, -4],\n [-5, 8, -8, 9, -10, 12],\n [6, -14, 3, 4, 4, 8],\n [-2, -15, -6, 0, 14, -12],\n [11, 12, 13, -5, 0, 11],\n [4, -15, 0, 3, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, 1, 2, 9, 2, -8],\n [1, -3, -12, -6, -6, 12],\n [2, -12, -15, 4, -4, 1],\n [9, -6, 4, 0, 4, 6],\n [2, -6, -4, 4, 13, -10],\n [-8, 12, 1, 6, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -3, -8, 8, -11, -4],\n [0, -13, -13, -15, 9, 6],\n [0, 0, -4, -7, -7, 2],\n [0, 0, 0, 11, -12, -3],\n [0, 0, 0, 0, -13, -11],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "281", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 13, 7, 11, 6, -6],\n [9, -3, 0, -7, -14, 7],\n [-11, 13, 6, 1, 7, 6],\n [-12, 1, -7, 4, -14, 8],\n [2, 5, 11, 6, -5, -3],\n [-8, 11, -15, 1, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[5, -3, 15, 13, -7, 11],\n [14, -9, 7, 8, 15, -11],\n [-11, 1, 14, -7, -10, 9],\n [3, 0, 5, -14, -6, 0],\n [-11, -1, -3, -3, -3, -1],\n [-2, -8, -5, 2, 8, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16181", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the inverse of matrix 1/180 * A where A =\n[[10, -6, 15, -15, 13, -11],\n [0, -15, 7, -8, -13, -13],\n [0, 0, -13, -1, -8, -13],\n [0, 0, 0, 2, -5, -5],\n [0, 0, 0, 0, -15, 13],\n [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": "-12", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (5, 3) rounded to the nearest integer?\n[[-12, -1, 2, -2, -2, -1],\n [-1, -3, 4, 4, -4, 0],\n [2, 4, -15, -6, -6, 6],\n [-2, 4, -6, -8, -3, -8],\n [-2, -4, -6, -3, -12, 10],\n [-1, 0, 6, -8, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-162", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-2, 7, 12, -2, 6, -6],\n [0, 15, -11, 7, 11, -10],\n [0, 0, -3, 13, -3, 3],\n [0, 0, 0, -15, -8, 6],\n [0, 0, 0, 0, -10, 0],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 2) rounded to the nearest integer?\n[[-14, -6, -15, -12, 9, -4],\n [0, -12, -7, 15, 12, -10],\n [0, 0, 13, -2, 6, 9],\n [0, 0, 0, 2, 4, 0],\n [0, 0, 0, 0, 7, -5],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, 7, 8, 2, -3, -6],\n [7, 14, 3, 8, 2, -3],\n [8, 3, -11, 0, -10, 2],\n [2, 8, 0, -9, -8, 0],\n [-3, 2, -10, -8, -10, -4],\n [-6, -3, 2, 0, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-9, -2, 10, 7, -6, -4],\n [-2, 13, 8, -6, 9, 2],\n [10, 8, -15, -10, 2, 1],\n [7, -6, -10, -13, 4, -1],\n [-6, 9, 2, 4, 7, 2],\n [-4, 2, 1, -1, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-6, 6, 5, 0, 2, -10],\n [6, 12, 0, 13, -4, 4],\n [5, 0, 10, 6, 1, -2],\n [0, 13, 6, -15, 10, 2],\n [2, -4, 1, 10, -14, 0],\n [-10, 4, -2, 2, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[1, -4, 2, -2, 0, 6],\n [-4, -13, 5, -1, 1, 4],\n [2, 5, 9, 2, 4, 0],\n [-2, -1, 2, -12, -4, 2],\n [0, 1, 4, -4, -13, -6],\n [6, 4, 0, 2, -6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[14, -14, 5, 6, -10, -2],\n [-14, 8, 0, -4, 3, 6],\n [5, 0, -9, -5, -8, -5],\n [6, -4, -5, -9, -6, 2],\n [-10, 3, -8, -6, -14, -6],\n [-2, 6, -5, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1889", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 7, 10, 15, 0, -6],\n [13, 8, -4, 9, -10, 12],\n [-4, -6, 2, 2, -12, 15],\n [-7, -9, 2, -8, -5, -9],\n [-7, -8, -13, 1, -14, -1],\n [-2, 13, 2, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 9, 4, -10, -10, 10],\n [-5, 10, 1, 8, 12, -13],\n [15, -3, 6, -13, 0, -1],\n [-5, 2, -1, -11, 0, 14],\n [0, 1, -7, 11, 7, -13],\n [4, -3, 6, -13, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 1, -7, 13, 10, 7],\n [0, -5, 13, 4, -10, -15],\n [0, 0, 15, 6, 4, 7],\n [0, 0, 0, -13, -15, 2],\n [0, 0, 0, 0, -15, 4],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-47", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[8, -1, -10, -15, 7, 3],\n [0, -3, 13, 13, -10, -1],\n [0, 0, 7, 0, -6, 6],\n [0, 0, 0, 1, 1, 8],\n [0, 0, 0, 0, -2, -6],\n [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": "-1116", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, 10, -1, -1, 8, -10],\n [0, -10, 15, 0, -14, 15],\n [0, 0, 14, -5, 10, 14],\n [0, 0, 0, 8, 4, -9],\n [0, 0, 0, 0, 7, 13],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -1, 8, 0, -4, 6],\n [-1, 11, 10, -3, 1, 14],\n [8, 10, -7, 6, 2, 4],\n [0, -3, 6, 15, -10, 0],\n [-4, 1, 2, -10, 4, 4],\n [6, 14, 4, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21189", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[-8, 9, 0, 0, 8, 7],\n [9, -4, -10, -2, -2, 1],\n [0, -10, -13, 1, -1, -2],\n [0, -2, 1, 4, 11, 11],\n [8, -2, -1, 11, 1, 7],\n [7, 1, -2, 11, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[4, -3, -14, 8, 15, 11],\n [0, 9, -2, -12, 1, -3],\n [0, 0, -4, 6, 7, -8],\n [0, 0, 0, 6, -6, -4],\n [0, 0, 0, 0, -13, 4],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-14, -11, 4, 13, 13, -8],\n [-9, -10, -5, -4, 2, 3],\n [-6, 9, 13, 9, 15, 5],\n [-2, -13, 2, 8, -1, -10],\n [-6, 11, -4, -9, 1, -15],\n [10, 2, 10, -1, 3, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, 14, -11, -1, 15, -13],\n [0, -8, -4, 11, 6, 9],\n [0, 0, 9, 15, -4, 15],\n [0, 0, 0, 3, -10, -8],\n [0, 0, 0, 0, 12, -9],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-120", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[11, 8, 0, 9, 0, -8],\n [8, -9, 4, -7, 6, -1],\n [0, 4, -14, 4, -14, -1],\n [9, -7, 4, 15, 10, 1],\n [0, 6, -14, 10, -1, 0],\n [-8, -1, -1, 1, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, 12, -7, 2, -12, -7],\n [0, -12, 0, 3, -15, 7],\n [0, 0, -6, 0, -12, 6],\n [0, 0, 0, 4, 14, 13],\n [0, 0, 0, 0, 13, -13],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-15, 4, -5, 10, 10, -4],\n [-2, 9, -8, -5, -12, 12],\n [-9, -6, 3, 9, 10, -12],\n [-14, 10, 5, 2, -2, 10],\n [0, 6, -5, -6, 1, -2],\n [6, -12, 3, -14, -9, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, 2, -4, 8, -2, 7],\n [2, 7, -4, 8, -6, -10],\n [-4, -4, 9, 12, 5, 0],\n [8, 8, 12, 13, -13, 4],\n [-2, -6, 5, -13, -10, -11],\n [7, -10, 0, 4, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-12, 13, -7, 13, 6, 11],\n [-6, 0, -6, 13, -6, 13],\n [3, -6, -10, 14, 1, -11],\n [10, -10, 15, 11, 8, 11],\n [15, -1, 9, 11, 3, 2],\n [13, -12, -8, 11, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 4, -13, -6, -14, -12],\n [-10, -5, -2, 0, 11, 5],\n [3, -14, 9, 15, 1, -7],\n [1, -1, 14, -9, 6, 7],\n [15, 3, 14, -13, 13, 11],\n [-15, -12, 12, 2, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[3, 7, 7, 12, 9, -10],\n [-15, -8, -15, 3, -5, 5],\n [8, 9, -1, 7, 9, -5],\n [3, 13, 5, -6, 8, -4],\n [-15, 8, -9, 1, 13, 13],\n [10, 12, -6, 15, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, 1, -6, 2, 10],\n [2, 6, 4, -12, 9, -8],\n [1, 4, 0, -2, -6, 1],\n [-6, -12, -2, -11, -1, -6],\n [2, 9, -6, -1, -15, 10],\n [10, -8, 1, -6, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[8, 0, 0, 12, 0, -5],\n [0, 0, 2, 12, 0, 7],\n [0, 2, -4, 6, -10, 12],\n [12, 12, 6, -14, 0, -2],\n [0, 0, -10, 0, -13, 8],\n [-5, 7, 12, -2, 8, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-10, 4, -1, 8, 5, -9],\n [0, 13, 13, 14, 5, 11],\n [0, 0, 14, -12, 6, 2],\n [0, 0, 0, 2, 8, 8],\n [0, 0, 0, 0, -1, -11],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 6) of the inverse. Round your answer to the nearest integer:\n[[-13, 4, 7, 12, 12, 12],\n [14, 2, 10, 4, -12, -15],\n [10, 0, -8, 1, -8, -9],\n [9, -8, 5, 8, 14, 15],\n [11, 10, -4, 0, 15, -4],\n [3, 15, -6, -9, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 5, 3, 0, -5, 4],\n [5, -2, -6, 3, 5, -8],\n [3, -6, -12, 0, 1, -4],\n [0, 3, 0, -7, -5, -6],\n [-5, 5, 1, -5, -9, 2],\n [4, -8, -4, -6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-303", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the inverse of matrix 1/180 * A where A =\n[[13, -4, 0, 11, 0, -4],\n [-4, 15, 8, -5, -5, -2],\n [0, 8, 8, 0, -4, 14],\n [11, -5, 0, -13, 3, -1],\n [0, -5, -4, 3, -3, -5],\n [-4, -2, 14, -1, -5, -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"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 3) rounded to the nearest integer?\n[[-4, -15, -4, 6, -10, 3],\n [3, 0, 15, 3, -13, 7],\n [-6, 11, 2, 10, -3, 10],\n [2, -13, 10, 12, 7, -13],\n [7, 9, 11, 10, -4, 15],\n [11, 4, -9, 9, 14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -7, -2, -11, 14, 5],\n [3, 5, 0, 8, -4, 5],\n [-12, -8, -9, -1, 14, 14],\n [-10, -11, -2, 5, -3, -6],\n [2, 13, 15, -12, -8, 8],\n [-5, 1, 2, 5, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-158", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 9, 8, 9, 0, 4],\n [0, -10, -11, 5, -12, -14],\n [0, 0, -7, 12, 1, -2],\n [0, 0, 0, -15, 13, 4],\n [0, 0, 0, 0, 2, -13],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -13, -9, -8, 3, 2],\n [-3, -3, 8, 3, 7, -4],\n [1, 14, 15, 12, 6, -4],\n [12, -3, 9, -4, 3, -2],\n [-9, -3, -10, 8, 3, 3],\n [-12, 3, -7, 0, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-167", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, -8, 11, 13, 8, 0],\n [15, -11, 5, 6, -6, 7],\n [-3, 13, 10, -2, -9, 13],\n [4, -10, -9, -11, 5, 2],\n [7, -4, -10, 11, -15, -12],\n [3, -4, -1, -13, 7, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1118", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[12, 10, 4, 15, 12, -8],\n [-5, 0, -7, -13, -11, 4],\n [-2, 12, 10, -1, -10, 11],\n [10, -12, -8, 3, 11, -11],\n [-3, 0, -15, -3, 15, 6],\n [-5, 5, -8, 9, -8, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, 4, 1, 0, -10, 3],\n [4, 4, -2, -2, 7, 5],\n [1, -2, -7, 5, 4, 1],\n [0, -2, 5, -15, -8, 0],\n [-10, 7, 4, -8, 0, 8],\n [3, 5, 1, 0, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3854", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -3, -7, 8, 8, -1],\n [9, 10, -13, 8, -15, 0],\n [-8, 13, 7, -3, 15, -8],\n [1, 6, 7, -2, 11, 5],\n [14, 5, -9, 15, 11, -1],\n [0, 3, -10, 7, -15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-62", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, 0, -4, 4, -3, -8],\n [11, 13, 14, 10, 6, -15],\n [10, 5, -9, -1, 13, 6],\n [-3, -3, 12, -7, 8, -1],\n [-12, -3, 11, -4, -11, -9],\n [-8, -11, -7, -2, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-12, 4, 13, -8, 1, -8],\n [0, 13, 14, 11, -15, 4],\n [0, 0, 8, 5, -15, -9],\n [0, 0, 0, -4, 3, -1],\n [0, 0, 0, 0, 6, 13],\n [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": "704", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 6, 8, 13, 1, 5],\n [3, 2, -5, 8, -9, -6],\n [-9, -11, -4, 0, 13, 9],\n [5, 2, -13, 4, -1, -11],\n [-3, 3, -4, 14, 7, 5],\n [-11, -10, -9, 10, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-8, -1, -1, -9, 5, 10],\n [-1, -8, 5, -5, 2, -3],\n [-1, 5, -5, 2, -12, 0],\n [-9, -5, 2, 13, -3, 1],\n [5, 2, -12, -3, -15, 8],\n [10, -3, 0, 1, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-421", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -9, -12, -10, 0, 4],\n [-1, -2, 7, -4, 13, -4],\n [0, -1, 13, -3, -5, 14],\n [1, 5, -1, -2, -6, -4],\n [0, -1, -6, 15, -12, 11],\n [7, 13, -7, 5, 4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, 5, 9, 8, 4, -5],\n [0, -9, 5, -6, -12, -11],\n [0, 0, 15, -7, 12, 0],\n [0, 0, 0, -12, 15, -14],\n [0, 0, 0, 0, -10, -5],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-150", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -1, 4, 1, -12, 2],\n [-1, 15, -6, -6, 12, 1],\n [4, -6, -7, -2, 2, -6],\n [1, -6, -2, 12, -8, -12],\n [-12, 12, 2, -8, 11, -5],\n [2, 1, -6, -12, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[6, -15, -13, -1, 10, 5],\n [15, 10, 7, 14, -6, -8],\n [-4, 9, 6, -1, 11, -7],\n [8, 9, -6, 4, -7, -1],\n [7, 5, 5, -15, -14, 10],\n [3, 14, -2, -8, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[10, 11, 13, -1, -2, 5],\n [0, -15, 12, -5, 12, 9],\n [0, 0, 2, 4, 12, -14],\n [0, 0, 0, 10, -9, -8],\n [0, 0, 0, 0, 6, 13],\n [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": "1758", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 3, -6, 11, -1, -5],\n [-1, 10, 11, 8, -3, -11],\n [-12, -3, -7, 9, 1, -14],\n [8, -11, 0, -9, -15, 12],\n [10, -4, 5, -5, -4, 3],\n [10, -4, -4, -2, -14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, 13, -12, 4, 7, 10],\n [0, -6, -3, -14, -13, 3],\n [-10, 3, 11, 5, 4, 3],\n [-8, -2, -6, -13, -10, 13],\n [-1, 7, 7, 2, -2, 3],\n [12, 10, -6, -1, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-14, -13, -9, 7, 0, 15],\n [0, 3, 12, 1, 12, 3],\n [0, 0, 4, -3, -3, -5],\n [0, 0, 0, 1, 6, 2],\n [0, 0, 0, 0, 6, 7],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-248", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, -1, -2, 6],\n [-10, 6, -4, 2, -4, -2],\n [-4, -4, 4, -5, -8, 8],\n [-1, 2, -5, 6, -10, 2],\n [-2, -4, -8, -10, -3, 2],\n [6, -2, 8, 2, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 0, -2, -2, 12, -2],\n [0, -13, -5, -4, -6, -3],\n [-2, -5, 13, 6, -13, 4],\n [-2, -4, 6, 8, 10, -6],\n [12, -6, -13, 10, -4, 0],\n [-2, -3, 4, -6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, -5, -3, 11],\n [0, -6, -8, 4, -8, -7],\n [0, 0, 12, -14, 9, -5],\n [0, 0, 0, -1, 12, -13],\n [0, 0, 0, 0, -14, 13],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-408", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -8, 10, 4, 1, -2],\n [-8, -11, 6, 8, 6, 8],\n [10, 6, -6, -2, -4, 0],\n [4, 8, -2, 6, 7, -7],\n [1, 6, -4, 7, 12, 10],\n [-2, 8, 0, -7, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, 5, -2, -7],\n [1, -1, 5, 15, -9, 11],\n [6, 6, -4, 7, -10, 5],\n [0, 10, -11, -7, -2, -8],\n [-2, -4, 15, -6, 14, 4],\n [4, 10, 5, -3, 13, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2440", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 4, 4, 6, 2, -12],\n [4, 5, -12, -2, 1, -2],\n [4, -12, 10, 4, 8, -4],\n [6, -2, 4, -1, 2, -6],\n [2, 1, 8, 2, -4, -1],\n [-12, -2, -4, -6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 8, 4, 6, -2, -11],\n [0, -8, -14, 12, 0, -3],\n [0, 0, -9, 11, -2, -2],\n [0, 0, 0, -4, 4, 5],\n [0, 0, 0, 0, -13, -9],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "467", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, 7, 6, -10, -6, 0],\n [-5, -3, 13, -10, 8, -15],\n [5, 3, -4, 8, 11, -10],\n [14, 2, 15, -3, -9, 7],\n [-3, 5, -8, 14, 5, 1],\n [-7, 4, -3, -14, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 6) of the inverse of matrix 1/180 * A where A =\n[[13, 9, -14, -12, 2, -11],\n [0, -6, 2, 14, 9, 5],\n [0, 0, 1, 6, -3, 7],\n [0, 0, 0, -4, -2, -2],\n [0, 0, 0, 0, 15, 12],\n [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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -8, -2, 6, 12, -2],\n [0, -2, 5, 15, -8, -13],\n [0, 0, 13, 7, 2, -13],\n [0, 0, 0, -1, 2, -11],\n [0, 0, 0, 0, -5, 11],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-334", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-2, -7, 2, -9, 12, 0],\n [-7, 14, -6, 4, 2, 2],\n [2, -6, -10, -8, 2, -4],\n [-9, 4, -8, 14, -12, 4],\n [12, 2, 2, -12, 4, -11],\n [0, 2, -4, 4, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-394", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[5, 10, -2, 2, -4, -6],\n [10, 11, 0, -2, -3, 8],\n [-2, 0, -2, 2, 10, 4],\n [2, -2, 2, 10, 0, -6],\n [-4, -3, 10, 0, -10, 2],\n [-6, 8, 4, -6, 2, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-4, 1, -3, 3, -4, 0],\n [0, 15, 11, -11, 9, 0],\n [0, 0, -5, 1, 10, 7],\n [0, 0, 0, 7, 14, 12],\n [0, 0, 0, 0, -9, -14],\n [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": "510", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-11, 13, -12, -14, -6, 6],\n [0, 2, -6, 7, 6, 12],\n [0, 0, 11, -7, -5, 10],\n [0, 0, 0, 13, 1, 5],\n [0, 0, 0, 0, 6, -5],\n [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": "367", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 5, 2, 6, -2, -1],\n [5, -12, 12, 3, 6, -4],\n [2, 12, -3, -6, -4, -2],\n [6, 3, -6, -5, 9, -10],\n [-2, 6, -4, 9, -4, 8],\n [-1, -4, -2, -10, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[13, -12, 7, 12, 0, 15],\n [-4, 5, 5, -3, 1, -8],\n [-3, 4, 10, -11, 2, -1],\n [-4, 13, 1, 9, -1, -14],\n [-10, 1, 0, 1, 9, 4],\n [-7, 11, -11, 7, -15, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[8, -2, 1, 9, 3, -15],\n [-15, -3, -2, 11, -10, 11],\n [-10, -15, 14, -2, -13, 7],\n [-6, 3, 3, 3, 12, 7],\n [-12, 4, 3, -6, 11, 9],\n [-14, -12, 8, -10, 14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[0, 12, -8, 4, -2, 3],\n [12, 6, 0, -5, 9, -2],\n [-8, 0, 2, -2, 6, -6],\n [4, -5, -2, -6, -6, 10],\n [-2, 9, 6, -6, -14, 5],\n [3, -2, -6, 10, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 2) of the inverse of matrix 1/180 * A where A =\n[[14, 3, -7, 6, -14, 2],\n [3, 0, 0, -8, -4, 3],\n [-7, 0, 7, 3, 0, 2],\n [6, -8, 3, 14, 2, 0],\n [-14, -4, 0, 2, 8, 3],\n [2, 3, 2, 0, 3, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, -4, -1, 11],\n [0, 15, -14, 1, 11, 13],\n [0, 0, 6, 3, 8, -9],\n [0, 0, 0, 7, -1, 15],\n [0, 0, 0, 0, -10, -3],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-180", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 9, -3, 6, -11, 12],\n [3, 5, 8, 12, 2, 5],\n [6, -6, 8, -8, -1, 5],\n [9, 4, 12, 9, 11, 7],\n [6, -12, -14, 8, -10, 12],\n [15, -13, -9, -6, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -12, 5, 0, -4, -8],\n [-12, -11, 11, -9, 8, -4],\n [5, 11, -4, 1, 5, 0],\n [0, -9, 1, 0, 0, 14],\n [-4, 8, 5, 0, 7, 5],\n [-8, -4, 0, 14, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "134", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, -3, -15, -10, -3, -5],\n [-6, 0, 11, 10, 8, 7],\n [4, 1, 1, -12, -11, 12],\n [7, -2, 4, -6, -2, 12],\n [-15, -5, 10, 7, 2, 0],\n [13, 11, 2, -8, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[10, 1, -9, -2, -6, 0],\n [1, -10, -12, -7, 2, 6],\n [-9, -12, 13, -9, -8, -10],\n [-2, -7, -9, -14, -5, 6],\n [-6, 2, -8, -5, -5, 7],\n [0, 6, -10, 6, 7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-11, -6, 3, -12, -4, -6],\n [-6, -2, -7, -1, 10, -4],\n [3, -7, 1, 8, 4, -10],\n [-12, -1, 8, -12, 2, -6],\n [-4, 10, 4, 2, -5, 6],\n [-6, -4, -10, -6, 6, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3238", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[3, -8, -4, 0, 4, -10],\n [-8, -7, 12, -5, 2, 11],\n [-4, 12, -14, -9, 1, 8],\n [0, -5, -9, -7, -8, 0],\n [4, 2, 1, -8, 15, -3],\n [-10, 11, 8, 0, -3, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 6) of the inverse of matrix 1/180 * A where A =\n[[8, -4, 14, 4, 0, -13],\n [0, -15, -6, 15, -1, -9],\n [0, 0, 8, 0, -2, -13],\n [0, 0, 0, 2, -13, 14],\n [0, 0, 0, 0, 6, -11],\n [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": "-168", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 0, -10, 8, -13, 3],\n [-10, -8, 6, -3, -4, 14],\n [-6, -13, -12, -15, -3, 8],\n [-12, 6, -5, 3, -5, -4],\n [-5, -10, -4, 11, -7, 9],\n [-6, -13, -13, 4, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[7, 15, -1, 12, 13, -1],\n [0, 3, 10, 4, -10, 3],\n [0, 0, -8, -10, 4, 7],\n [0, 0, 0, -13, -6, -1],\n [0, 0, 0, 0, -5, 0],\n [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": "167", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-8, -6, -4, 8, 7, 10],\n [-6, -11, 8, 3, -2, -7],\n [-4, 8, 1, -6, -6, -11],\n [8, 3, -6, -10, -8, -2],\n [7, -2, -6, -8, -7, -2],\n [10, -7, -11, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[15, -12, 2, -3, -3, -2],\n [0, 2, -15, 5, 0, -1],\n [0, 0, -11, 13, -10, -10],\n [0, 0, 0, -12, -15, -12],\n [0, 0, 0, 0, 11, -8],\n [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": "3336", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, 0, -6, 0, -12],\n [-4, -5, -5, 10, 0, 8],\n [0, -5, -5, 2, 8, 4],\n [-6, 10, 2, 11, -5, 2],\n [0, 0, 8, -5, -11, 1],\n [-12, 8, 4, 2, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -9, 2, -2, -10, -8],\n [0, -1, -1, 0, -15, -5],\n [0, 0, 9, -11, -11, 13],\n [0, 0, 0, -14, -10, -2],\n [0, 0, 0, 0, 11, 9],\n [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": "-2978", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[11, -12, -15, 9, 5, 6],\n [0, 3, 0, -5, 10, -8],\n [0, 0, -15, 10, 12, 5],\n [0, 0, 0, 11, -4, 6],\n [0, 0, 0, 0, 11, -9],\n [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": "65", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 6) rounded to the nearest integer?\n[[12, 12, 3, 2, -1, -14],\n [-2, 5, -6, 12, 0, -9],\n [-8, -6, -1, -8, -3, -4],\n [-8, -1, 10, -4, -5, 3],\n [-2, 11, 2, -3, -12, 15],\n [1, 3, 11, -7, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, -13, 12, 15, 1, 15],\n [0, 1, 6, 14, 14, 1],\n [0, 0, 5, 7, -10, -4],\n [0, 0, 0, 4, 1, 1],\n [0, 0, 0, 0, 13, -3],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 3, 0, 6, -7, -7],\n [3, 1, 4, 0, 9, 1],\n [0, 4, 5, 0, 4, 8],\n [6, 0, 0, 2, 4, -10],\n [-7, 9, 4, 4, 6, 2],\n [-7, 1, 8, -10, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-95", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, 6, 6, 0, 0, -2],\n [-10, -14, 15, -2, 0, 7],\n [14, 4, -3, -1, -4, -7],\n [10, 2, 5, -2, 4, 9],\n [-12, -8, -8, 6, 6, 0],\n [11, 8, 12, 13, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "383", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 15, 5, 11, 1, -15],\n [15, 2, -6, 10, 5, -12],\n [-15, -12, -12, 10, -12, 1],\n [-7, 14, 3, -3, -12, -11],\n [13, -3, 7, 0, 6, -11],\n [-8, 0, 14, -15, 7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "412", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, -5, 0, -11, 0, -9],\n [3, -15, -7, 2, -3, 10],\n [-1, -13, 8, 12, -6, -7],\n [-3, 0, -13, 6, 7, -1],\n [1, -2, -9, 4, 0, 5],\n [-8, -12, 15, 4, 8, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-48", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[-11, -3, -10, 12, 11, 14],\n [-11, 1, -9, -10, -14, -5],\n [-9, 6, 5, -8, -11, 11],\n [2, 6, 0, -2, -4, 1],\n [-11, -2, -10, -1, -9, -2],\n [2, -15, -10, -13, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 9, -14, 7, 10, 14],\n [0, -3, 13, -13, -5, 0],\n [0, 0, -5, -7, -2, 15],\n [0, 0, 0, -13, 13, 3],\n [0, 0, 0, 0, -4, 14],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-109", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, -6, -4, -8, 3],\n [0, -15, -13, 11, 2, 2],\n [0, 0, -14, -11, 13, -15],\n [0, 0, 0, -6, -11, 2],\n [0, 0, 0, 0, -8, 1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-178", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, -15, 10, 10, -12],\n [-8, -15, 11, -1, 2, -15],\n [-5, 7, -14, -15, 15, -4],\n [0, 6, 6, -6, 2, -1],\n [1, 14, -6, -13, 10, 14],\n [5, 0, -10, -13, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6671", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 2, 10, 6, 12],\n [0, 11, 6, -12, 6, 8],\n [0, 0, -6, -14, -8, -10],\n [0, 0, 0, -10, -3, 7],\n [0, 0, 0, 0, 14, -6],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, 8, 4, -10, 2],\n [10, -7, -4, -2, 6, 1],\n [8, -4, 10, 0, -2, -9],\n [4, -2, 0, 5, -1, 8],\n [-10, 6, -2, -1, 1, -1],\n [2, 1, -9, 8, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[-9, 6, 4, 1, -1, -5],\n [6, 9, -2, -7, -14, -12],\n [4, -2, 0, -1, -2, -1],\n [1, -7, -1, 3, -7, -12],\n [-1, -14, -2, -7, 7, -4],\n [-5, -12, -1, -12, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[3, -8, 2, -13, 8, 8],\n [1, -8, -6, -14, -4, 7],\n [-10, -14, 5, 7, 8, -13],\n [1, 13, -9, 13, 5, -11],\n [7, -15, -8, -4, -2, 0],\n [-6, -1, 5, 8, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 5, 12, -9, 10, -13],\n [-14, -10, 5, -7, -6, -12],\n [11, -13, -7, 8, 6, 1],\n [-2, -6, -3, -4, 11, -15],\n [12, 6, 13, 3, 3, -10],\n [-3, 3, -3, 11, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, 1, 8, -5, 0, 2],\n [1, 11, -6, 8, 0, 8],\n [8, -6, 1, -8, 4, -8],\n [-5, 8, -8, -13, -2, 4],\n [0, 0, 4, -2, -15, -2],\n [2, 8, -8, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-1, 2, -2, 5, 10, -13],\n [0, -8, -12, -12, 3, -5],\n [0, 0, -1, -15, -9, 5],\n [0, 0, 0, -5, 11, 13],\n [0, 0, 0, 0, -4, 1],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[12, -12, -4, -5, -13, 15],\n [0, 14, -11, -10, 3, 2],\n [0, 0, -5, -11, -7, 15],\n [0, 0, 0, -8, -10, -12],\n [0, 0, 0, 0, 5, 0],\n [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": "634", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-3, -7, -9, -4, -11, 2],\n [-12, -14, -13, 10, -4, -13],\n [-12, -10, -4, 3, -6, 14],\n [-15, 1, 0, -7, 9, 5],\n [-7, 11, 7, -7, -4, 7],\n [-7, -1, -14, -5, -5, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[7, -10, 5, 4, -9, -13],\n [0, 2, 1, -5, -14, 9],\n [0, 0, 8, 3, -9, 15],\n [0, 0, 0, -9, 12, 5],\n [0, 0, 0, 0, -11, -4],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-549", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, -5, -11, 10, 12],\n [-2, -15, -6, 10, -10, 6],\n [-5, -6, -3, -11, 1, -4],\n [-11, 10, -11, 12, -3, -4],\n [10, -10, 1, -3, -2, -4],\n [12, 6, -4, -4, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-12, 2, -9, -10, -3, 2],\n [2, -3, -2, -4, 2, 2],\n [-9, -2, -2, 4, -10, 8],\n [-10, -4, 4, -9, -5, 12],\n [-3, 2, -10, -5, -12, 2],\n [2, 2, 8, 12, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 6, 0, -4, 0, 1],\n [6, -4, 8, -3, -15, 2],\n [0, 8, -1, -2, 6, -8],\n [-4, -3, -2, 5, -2, 4],\n [0, -15, 6, -2, -7, 2],\n [1, 2, -8, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-544", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-6, 5, 8, 0, 1, -9],\n [5, 1, 2, 2, 4, 8],\n [8, 2, -9, -8, 2, 0],\n [0, 2, -8, -2, -8, -6],\n [1, 4, 2, -8, -8, 2],\n [-9, 8, 0, -6, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-15, -8, -10, 7, -2, 12],\n [-8, -7, -7, 0, 0, -6],\n [-10, -7, -3, 0, -4, -2],\n [7, 0, 0, 3, -2, 7],\n [-2, 0, -4, -2, 9, -1],\n [12, -6, -2, 7, -1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-281", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -7, -3, 13, -12, -7],\n [0, -2, 3, -4, 5, 10],\n [0, 0, -13, 10, 9, 6],\n [0, 0, 0, 4, 8, 7],\n [0, 0, 0, 0, 3, 14],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[1, 4, 10, -8, -5, 4],\n [4, 5, 6, -4, -10, 12],\n [10, 6, 11, -14, -8, 14],\n [-8, -4, -14, -7, -8, 11],\n [-5, -10, -8, -8, -9, 0],\n [4, 12, 14, 11, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[14, 9, -3, 0, -9, 0],\n [-3, -2, 1, -4, 13, 8],\n [8, 4, -3, 8, 4, -1],\n [8, 5, -12, 6, -14, 12],\n [2, -14, 9, -1, 14, 10],\n [3, -1, 10, 4, -6, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 4, -5, 10, -6, 13],\n [7, -11, -7, 4, 3, -3],\n [2, 1, 11, -10, -6, -14],\n [8, -10, 12, 12, 5, -3],\n [2, -9, -14, 13, -2, -11],\n [2, -5, -6, -5, 11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-1, -9, -7, -11, -9, 4],\n [-14, -13, -14, 5, 6, 15],\n [15, 7, 3, -12, 8, 4],\n [-9, 12, 6, -9, 1, 3],\n [6, 0, -13, -1, -2, -1],\n [-2, -9, 9, -13, 14, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, 0, 1, -4, 8, 2],\n [0, -2, 10, -1, 8, 2],\n [1, 10, -8, -4, 2, -12],\n [-4, -1, -4, -2, 2, 6],\n [8, 8, 2, 2, -10, 5],\n [2, 2, -12, 6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[6, -13, 4, -7, 5, 6],\n [-13, -5, 2, 2, 0, 0],\n [4, 2, 5, 8, 2, 6],\n [-7, 2, 8, -8, -12, 0],\n [5, 0, 2, -12, 11, 6],\n [6, 0, 6, 0, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, 2, -6, 11],\n [-4, -3, -13, 0, 5, 0],\n [2, -13, -15, 8, 12, -6],\n [2, 0, 8, 1, 6, -1],\n [-6, 5, 12, 6, -8, -9],\n [11, 0, -6, -1, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "711", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[6, 4, -3, 4, -14, -13],\n [0, 7, 3, -3, -11, 10],\n [0, 0, -2, -12, 6, 3],\n [0, 0, 0, -14, 11, -9],\n [0, 0, 0, 0, -6, 0],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-2, 4, -5, 0, 6, 2],\n [4, 4, -3, 6, 1, 2],\n [-5, -3, 4, 8, -2, 0],\n [0, 6, 8, -15, 8, -10],\n [6, 1, -2, 8, -12, -4],\n [2, 2, 0, -10, -4, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "580", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 9, 14, 6, 4, 6],\n [-1, 4, 7, -7, -13, -13],\n [-14, -15, -2, 1, -3, 3],\n [14, 7, -1, 11, 9, -2],\n [-14, -9, 1, 2, -10, 11],\n [5, -8, 12, 11, -14, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[0, -5, 7, 8, -4, 6],\n [-5, -3, 2, 0, -13, 3],\n [7, 2, -7, 10, 0, 8],\n [8, 0, 10, -12, 4, -2],\n [-4, -13, 0, 4, 8, -2],\n [6, 3, 8, -2, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-3, 2, 2, 4, -4, 4],\n [2, 13, 6, -6, 10, 4],\n [2, 6, 9, 2, -10, 2],\n [4, -6, 2, 5, 1, -6],\n [-4, 10, -10, 1, 5, 0],\n [4, 4, 2, -6, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[9, -13, 4, 13, -9, 2],\n [0, 3, 0, 6, 11, 8],\n [0, 0, 4, -1, -15, -14],\n [0, 0, 0, -14, 3, -7],\n [0, 0, 0, 0, -1, 3],\n [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": "5269", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-8, -10, -8, -13, 4, 2],\n [-10, -6, -6, 8, -4, 3],\n [-8, -6, -12, -2, -6, 2],\n [-13, 8, -2, -7, -8, -2],\n [4, -4, -6, -8, 2, -2],\n [2, 3, 2, -2, -2, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1498", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[5, 5, 11, 3, 7, 3],\n [2, 3, -5, -13, -8, 4],\n [3, -6, 0, -11, 4, -7],\n [-8, -5, 0, -9, -1, 8],\n [13, 5, 4, 7, 1, -10],\n [-1, -8, -9, -14, 14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, 7, 13, -10, 13, -11],\n [0, -15, 13, 2, -1, 7],\n [0, 0, -11, 8, 13, -3],\n [0, 0, 0, 13, -14, -7],\n [0, 0, 0, 0, -15, -4],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 5) of the inverse. Round your answer to the nearest integer:\n[[-1, 11, -13, -10, 12, -3],\n [0, 3, 13, 2, 8, -15],\n [0, 0, -9, -4, -6, 13],\n [0, 0, 0, -12, 3, -10],\n [0, 0, 0, 0, -6, -11],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 10, 6, -8, -10, 0],\n [10, -7, -8, 2, 2, 2],\n [6, -8, -5, -1, -8, -3],\n [-8, 2, -1, 0, -6, 4],\n [-10, 2, -8, -6, -13, 3],\n [0, 2, -3, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[7, 4, 14, -2, 6, 7],\n [0, 15, -10, -5, -3, 15],\n [0, 0, -14, 5, -13, 7],\n [0, 0, 0, 12, 6, -10],\n [0, 0, 0, 0, 15, -13],\n [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": "-90", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-7, 0, 2, -6, 10, 10],\n [0, 10, 0, -4, 8, -3],\n [2, 0, 0, 4, -5, 3],\n [-6, -4, 4, -14, 0, -3],\n [10, 8, -5, 0, -3, 3],\n [10, -3, 3, -3, 3, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, 12, -9, 10, 10],\n [-15, 9, -1, 4, 5, 2],\n [14, 12, 10, -3, 8, 14],\n [-14, 3, -1, -4, -1, 9],\n [2, -2, -10, -4, 4, 7],\n [14, 14, -10, 10, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[14, 8, 3, -9, -13, -8],\n [0, -15, -2, -10, -6, 9],\n [0, 0, -12, -10, 0, 12],\n [0, 0, 0, -15, -10, -7],\n [0, 0, 0, 0, -5, -1],\n [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": "-22", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -4, -14, 1, -13, -6],\n [0, 6, -7, -5, 5, -1],\n [-13, 0, 14, 5, 5, 5],\n [12, -4, 7, -11, -9, -7],\n [5, 2, 5, -8, -4, 4],\n [-14, -6, 3, -7, 9, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 8, 8, 8, -15, -10],\n [0, 9, 8, 3, 11, 1],\n [0, 0, 15, 2, 7, 12],\n [0, 0, 0, -8, -1, -7],\n [0, 0, 0, 0, -3, -15],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-133", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-14, 12, 10, 7, -1, -12],\n [0, -10, -13, -9, -10, -13],\n [0, 0, 14, 5, -7, 14],\n [0, 0, 0, 11, -5, -9],\n [0, 0, 0, 0, -12, 11],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 6, -2, 8, 8, 11],\n [0, 10, -5, -12, -9, 13],\n [0, 0, -10, 11, -10, -14],\n [0, 0, 0, 11, -9, 11],\n [0, 0, 0, 0, -1, 9],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4035", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 9, -6, 14, -6, -14],\n [-2, -3, 6, 13, -10, -7],\n [-3, -7, 15, -3, -11, -2],\n [-11, -7, -8, -9, -8, 6],\n [-13, 7, 8, -1, -8, -15],\n [-9, 3, -14, -2, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-93", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 0, 10, 6, -1, 12],\n [0, 6, 7, -2, -5, -1],\n [10, 7, 11, 2, 9, 2],\n [6, -2, 2, -9, 7, 2],\n [-1, -5, 9, 7, -5, 1],\n [12, -1, 2, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[10, 2, -6, 3, 4, 1],\n [4, 0, -11, -13, 14, 11],\n [-1, 10, -14, -3, 6, -8],\n [7, 11, 14, 1, -12, 3],\n [6, 9, -7, 7, -1, 12],\n [-7, 8, 5, -7, -2, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[5, 4, 7, 0, 14, -2],\n [4, 10, -4, 6, -6, -6],\n [7, -4, -15, -12, -6, 6],\n [0, 6, -12, 12, -6, 12],\n [14, -6, -6, -6, 11, -4],\n [-2, -6, 6, 12, -4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 10, -2, 12, 7, 4],\n [10, -10, 4, 8, -2, -4],\n [-2, 4, 4, 7, -6, -3],\n [12, 8, 7, -7, 8, 2],\n [7, -2, -6, 8, -10, 0],\n [4, -4, -3, 2, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, 8, 1, 13, 13, 4],\n [8, -7, 2, 7, -2, 6],\n [1, 2, 4, -3, 0, 0],\n [13, 7, -3, -12, -10, -3],\n [13, -2, 0, -10, 12, 15],\n [4, 6, 0, -3, 15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[15, -10, 6, -3, -7, -7],\n [0, -7, 15, -1, -3, 6],\n [0, 0, 10, -2, 11, -10],\n [0, 0, 0, 5, 8, -2],\n [0, 0, 0, 0, -4, 0],\n [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": "-25", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -7, -14, 1, 4, -3],\n [-11, -6, -4, 1, 5, -10],\n [-13, 12, -1, -9, 14, -10],\n [-12, 3, -11, -13, 10, 9],\n [-7, -10, -3, 11, 6, 12],\n [14, 4, -12, -14, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, -9, 4, 1, 2, 9],\n [-9, -3, 8, 3, -10, 2],\n [4, 8, -2, 10, -6, 3],\n [1, 3, 10, -1, 2, 8],\n [2, -10, -6, 2, -5, 0],\n [9, 2, 3, 8, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, 10, -11, -8, -6, 0],\n [10, -8, 9, 1, 2, -4],\n [-11, 9, 1, 7, -2, 6],\n [-8, 1, 7, -2, -8, 5],\n [-6, 2, -2, -8, 4, 14],\n [0, -4, 6, 5, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-12, -1, -5, -15, 2, 13],\n [0, -8, 9, 0, 10, 12],\n [0, 0, 6, -7, -4, 3],\n [0, 0, 0, -11, 11, -14],\n [0, 0, 0, 0, 9, -9],\n [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": "116", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, -9, 12, 3, 15, 4],\n [0, -9, -8, -9, -10, 9],\n [0, 0, -3, -9, -8, 6],\n [0, 0, 0, 6, -14, 14],\n [0, 0, 0, 0, 8, 12],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 2, 2, 9, 10],\n [0, -2, -2, -2, 9, -12],\n [0, 0, -1, 2, -2, 10],\n [0, 0, 0, 4, -6, -6],\n [0, 0, 0, 0, 12, 11],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-713", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 5) of the inverse of matrix 1/180 * A where A =\n[[-7, -2, -2, -8, 2, 2],\n [-2, 2, 2, 12, 6, 4],\n [-2, 2, 4, 7, 7, -10],\n [-8, 12, 7, 4, -12, -3],\n [2, 6, 7, -12, 3, -8],\n [2, 4, -10, -3, -8, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 10, 0, -2, -7, 2],\n [10, 0, -1, 0, 6, -2],\n [0, -1, -2, -2, 3, -3],\n [-2, 0, -2, 5, 4, 1],\n [-7, 6, 3, 4, 12, -10],\n [2, -2, -3, 1, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6916", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-14, 0, 0, -2, 10, -2],\n [0, 15, -2, -8, 0, -3],\n [0, -2, -1, 4, -4, 7],\n [-2, -8, 4, -2, 5, -8],\n [10, 0, -4, 5, -5, 1],\n [-2, -3, 7, -8, 1, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-266", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[11, -1, 0, -2, 12, 7],\n [-1, 13, -8, 2, 0, -12],\n [0, -8, -15, 4, 2, 6],\n [-2, 2, 4, -11, 0, -4],\n [12, 0, 2, 0, -5, 4],\n [7, -12, 6, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[3, -4, 0, -10, -13, -14],\n [0, -11, -5, 10, 9, -13],\n [0, 0, -11, 6, 7, -5],\n [0, 0, 0, 5, -8, 4],\n [0, 0, 0, 0, 3, -12],\n [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": "-848", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[9, -11, -4, 6, -6, -8],\n [-11, 5, -5, -2, 10, -5],\n [-4, -5, -11, -1, 0, 4],\n [6, -2, -1, -1, -2, 0],\n [-6, 10, 0, -2, -8, -6],\n [-8, -5, 4, 0, -6, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-109", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[14, 6, 4, 0, -9, -9],\n [0, 2, -14, -1, -2, 15],\n [0, 0, -7, -2, -11, -5],\n [0, 0, 0, -5, -11, 1],\n [0, 0, 0, 0, 6, -14],\n [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": "-5118", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -10, 0, 4, 8, -13],\n [0, 3, 3, 8, -12, -15],\n [0, 0, 14, 10, 13, -3],\n [0, 0, 0, 3, 6, 8],\n [0, 0, 0, 0, 1, -6],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10281", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-1, -7, -6, 7, 4, 4],\n [0, -10, -12, -11, -7, -4],\n [0, 0, 5, -11, 13, -5],\n [0, 0, 0, -2, 12, -8],\n [0, 0, 0, 0, 3, -4],\n [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": "8340", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -2, -1, 0, -14, 14],\n [0, 2, 15, -4, 0, -3],\n [0, 0, 2, -13, 7, -6],\n [0, 0, 0, 3, -12, 13],\n [0, 0, 0, 0, -8, 11],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12645", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 4) of the inverse. Round your answer to the nearest integer:\n[[0, -6, -12, -3, -6, 5],\n [-2, -7, -5, 7, 2, -5],\n [1, -14, -13, -5, 2, 11],\n [-13, 10, -1, -5, -5, 15],\n [12, 14, 12, 9, 4, 12],\n [9, -5, 3, 12, -15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -6, -2, -14, -12],\n [-14, 2, -3, 3, -11, 4],\n [-14, 15, -5, 14, 14, 10],\n [2, 14, -10, 7, 12, -6],\n [6, 7, 1, 6, -5, 3],\n [1, 8, -12, 10, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-2, 11, 4, -12, 12, -2],\n [0, -12, -10, 14, -7, 5],\n [0, 0, 10, 14, 15, -8],\n [0, 0, 0, 11, 10, 9],\n [0, 0, 0, 0, 3, 11],\n [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": "-36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-9, -2, 6, 9, -7, -4],\n [-2, -9, -4, 3, 8, 10],\n [6, -4, -6, 1, 1, 14],\n [9, 3, 1, -6, -2, 6],\n [-7, 8, 1, -2, 9, -2],\n [-4, 10, 14, 6, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-1, -9, -6, 5, 7, 14],\n [0, 13, -6, -3, -1, 7],\n [0, 0, 15, -12, 4, 1],\n [0, 0, 0, 5, -14, -12],\n [0, 0, 0, 0, -10, -9],\n [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": "722", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -4, 6, 0, -2],\n [11, -2, 8, 14, 2, -2],\n [-4, 8, -10, 10, -5, -6],\n [6, 14, 10, -7, -12, -4],\n [0, 2, -5, -12, -15, 2],\n [-2, -2, -6, -4, 2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-15, -11, 2, 0, 15, 10],\n [0, 14, -12, -15, 7, -8],\n [0, 0, 8, 1, 15, -9],\n [0, 0, 0, 13, 6, -1],\n [0, 0, 0, 0, 9, 5],\n [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": "1892", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[5, -13, 0, 9, -3, 8],\n [-13, -2, -4, 0, -10, -10],\n [0, -4, -9, 0, -3, -1],\n [9, 0, 0, -3, 3, -8],\n [-3, -10, -3, 3, 6, -4],\n [8, -10, -1, -8, -4, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[7, -8, 1, -3, -9, -7],\n [-4, 13, -2, -2, -1, -13],\n [-1, 3, 8, 4, -2, -8],\n [-11, 14, 3, 15, -12, -2],\n [0, 4, 8, -10, 7, 9],\n [15, -10, -13, -1, 13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, -10, -7, -15, -4, 10],\n [0, -10, -15, 6, -14, 8],\n [0, 0, -6, 14, -10, -10],\n [0, 0, 0, -14, 10, 15],\n [0, 0, 0, 0, 10, -10],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 1, -14, -7, -4, 3],\n [0, 15, -9, -7, 5, 0],\n [0, 0, -4, -1, 2, 3],\n [0, 0, 0, -5, -1, 13],\n [0, 0, 0, 0, -12, 0],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-86", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -2, -4, -2, 5, 0],\n [-2, 3, 4, -4, 8, 1],\n [-4, 4, 7, 0, -2, 4],\n [-2, -4, 0, 4, 13, 4],\n [5, 8, -2, 13, -7, -6],\n [0, 1, 4, 4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 6) rounded to the nearest integer?\n[[-9, 6, 10, -8, 8, -8],\n [3, -1, 0, 14, 10, 6],\n [7, -7, 10, 10, 14, -4],\n [15, 0, -12, -11, -8, -15],\n [12, -10, -1, -12, 5, -5],\n [-11, 2, 8, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2552", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, -11, 14, -15, 6],\n [2, -2, -11, 15, -10, 11],\n [8, 9, 13, 15, 12, 0],\n [6, 5, -4, 4, 2, -14],\n [7, 5, 7, -3, 11, 1],\n [1, 0, 5, 2, -8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[15, -13, 1, 13, 2, 10],\n [10, 7, -10, 12, -8, 7],\n [14, 10, -3, -8, 3, -10],\n [13, 7, -1, -6, 11, 1],\n [-15, -9, 13, 11, -3, -13],\n [3, -1, -11, 15, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -13, -10, -13, 14, -11],\n [0, 12, 3, 12, 11, -3],\n [0, 0, -5, 5, 5, 11],\n [0, 0, 0, -10, 1, -5],\n [0, 0, 0, 0, 8, -9],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-208", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[13, 7, -13, -1, 12, -13],\n [0, 14, 2, -2, 2, 3],\n [0, 0, -10, 13, -8, 10],\n [0, 0, 0, 2, 2, -1],\n [0, 0, 0, 0, 5, 5],\n [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": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-3, 15, -7, -7, 1, -9],\n [0, 6, -15, -14, -12, -2],\n [0, 0, -8, 2, 3, -2],\n [0, 0, 0, 1, -8, 12],\n [0, 0, 0, 0, -8, 15],\n [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": "-2390", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -6, -3, -4, -7],\n [8, 5, 6, -6, -4, -14],\n [-6, 6, 15, 0, -6, 4],\n [-3, -6, 0, 3, 2, 6],\n [-4, -4, -6, 2, -2, 2],\n [-7, -14, 4, 6, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[13, -12, 6, 9, -6, 8],\n [-12, -14, 6, 1, 13, 12],\n [6, 6, 10, -5, -10, 1],\n [9, 1, -5, -5, 0, -4],\n [-6, 13, -10, 0, 14, -11],\n [8, 12, 1, -4, -11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, -12, -1, 3, 11, -8],\n [12, 12, 7, -1, 11, 15],\n [-9, -1, -8, 14, 10, 7],\n [-6, 2, -12, -1, -5, 6],\n [-13, -1, -13, -1, -10, -15],\n [-2, 0, -15, 5, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-8, 2, 0, -10, -6, -6],\n [-11, 10, 12, -4, 4, 1],\n [-2, -2, -13, 13, -4, 4],\n [2, -4, -14, -14, 11, 1],\n [-6, 2, 6, 3, 10, 5],\n [-15, 8, 13, -12, 9, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[14, 10, 14, 12, -11, -2],\n [10, -4, 0, 1, 3, 2],\n [14, 0, 7, 6, -1, 5],\n [12, 1, 6, 4, 10, -8],\n [-11, 3, -1, 10, -8, 0],\n [-2, 2, 5, -8, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, -11, -9, 14, -7, -9],\n [-7, 4, -6, 14, 10, -12],\n [-10, 8, -2, -7, -15, 1],\n [-3, 8, 11, -9, -7, -5],\n [-13, 10, -4, 5, -13, -1],\n [5, -6, -15, -2, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, -14, 13, 7, -8, -15],\n [0, -12, 11, -12, 13, -11],\n [0, 0, 12, 4, -7, 7],\n [0, 0, 0, 9, -15, 6],\n [0, 0, 0, 0, 4, 6],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the inverse of matrix 1/180 * A where A =\n[[-9, -13, 0, 2, -2, 2],\n [-13, -3, 2, 1, 6, 1],\n [0, 2, 2, 1, 3, -4],\n [2, 1, 1, 4, -5, 1],\n [-2, 6, 3, -5, -4, -12],\n [2, 1, -4, 1, -12, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, -7, 12, 10, 15, 1],\n [0, 7, -3, 7, -6, 0],\n [0, 0, -5, 10, 4, -13],\n [0, 0, 0, -1, 12, -3],\n [0, 0, 0, 0, 1, -9],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15820", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-12, 10, 5, 4, 5, 4],\n [10, 15, -9, -4, -7, 8],\n [5, -9, 14, 5, 0, 8],\n [4, -4, 5, 7, 2, -6],\n [5, -7, 0, 2, -7, -1],\n [4, 8, 8, -6, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 5, -15, 1, -5, 4],\n [12, -1, -12, -1, 6, 6],\n [10, -2, 6, -15, 10, -7],\n [11, -9, 7, -5, 7, -14],\n [-14, -10, 7, 3, 13, 4],\n [-2, 12, -13, -9, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-114", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[13, 7, -11, 1, 10, -12],\n [7, -3, 0, 0, 15, -14],\n [2, -15, 2, 10, 14, -8],\n [-5, 8, 8, -1, 0, 1],\n [1, -4, -6, 4, -10, -8],\n [-3, -14, 13, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, 2, -9, 4, 8],\n [8, 7, 10, 9, -12, -9],\n [-6, 10, -1, -4, -15, 4],\n [2, 9, 0, -11, 3, -12],\n [-10, 10, 1, -9, 8, 7],\n [-9, -7, -3, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the inverse of matrix 1/180 * A where A =\n[[7, -1, -4, -10, -6, 6],\n [-1, 4, -2, -6, 0, 10],\n [-4, -2, 13, 2, 11, 10],\n [-10, -6, 2, 13, -4, -11],\n [-6, 0, 11, -4, -1, 3],\n [6, 10, 10, -11, 3, 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"}
{"messages": [{"content": "Find the value at position (3, 2) of the inverse of matrix 1/180 * A where A =\n[[3, -9, 12, -13, 14, -13],\n [10, 9, 13, 2, 14, 4],\n [6, -2, -13, 12, 10, 14],\n [10, -9, -9, 15, -11, -13],\n [2, -1, 15, 4, -2, 15],\n [13, -12, 11, 8, -8, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[5, -3, 6, -8, -1, 1],\n [0, 4, -12, -5, 2, -6],\n [0, 0, -1, -10, 7, 5],\n [0, 0, 0, -7, -5, 11],\n [0, 0, 0, 0, 11, -7],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the inverse of matrix 1/180 * A where A =\n[[12, 2, 11, 9, -6, 3],\n [0, -3, -1, 0, -14, 13],\n [0, 0, 2, 13, 15, 1],\n [0, 0, 0, -7, -1, 12],\n [0, 0, 0, 0, 11, 10],\n [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": "-60", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -12, 4, 1, 3, -13],\n [0, -2, 1, -3, -7, 11],\n [0, 0, 1, 0, 2, -14],\n [0, 0, 0, 11, 1, -13],\n [0, 0, 0, 0, -14, -14],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2908", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[13, 11, 9, -10, 10, -4],\n [9, -7, -9, 14, -4, 10],\n [9, -11, 0, -11, -4, 8],\n [10, 4, -7, 7, -9, 13],\n [15, 3, 4, 7, -5, 11],\n [14, 5, -4, -13, 1, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, -6, 15, 7, -1, 14],\n [0, -3, 12, -12, 2, 8],\n [0, 0, -14, -14, -12, -13],\n [0, 0, 0, -14, 0, -5],\n [0, 0, 0, 0, 7, -14],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1018", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[10, 10, 13, 12, -13, 4],\n [0, 4, 2, 5, 15, 5],\n [0, 0, 15, 11, -6, -15],\n [0, 0, 0, -9, 4, 15],\n [0, 0, 0, 0, 5, 3],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the inverse of matrix 1/180 * A where A =\n[[8, -3, 14, 15, 11, 12],\n [0, 1, -15, -10, 3, 4],\n [0, 0, 1, 5, 6, -1],\n [0, 0, 0, -9, 1, -12],\n [0, 0, 0, 0, -15, -15],\n [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": "427", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -2, -4, -6, -3, -7],\n [-2, 7, -1, -2, -4, -10],\n [-4, -1, -9, 10, -6, -6],\n [-6, -2, 10, 11, 0, 8],\n [-3, -4, -6, 0, -1, -7],\n [-7, -10, -6, 8, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -9, -4, 0, 3],\n [12, 6, -2, 8, 14, -8],\n [-9, -2, 4, 4, -4, 4],\n [-4, 8, 4, -15, -2, 8],\n [0, 14, -4, -2, -3, -4],\n [3, -8, 4, 8, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, -15, -4, -1, -5, -6],\n [0, 10, 13, -12, 1, 1],\n [0, 0, -8, 7, -2, 8],\n [0, 0, 0, 15, 13, 3],\n [0, 0, 0, 0, -13, 4],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-4, -2, 2, 2, 2, -8],\n [-2, -8, -2, -4, 2, -2],\n [2, -2, 13, 0, 2, -2],\n [2, -4, 0, 7, 8, -2],\n [2, 2, 2, 8, -8, -1],\n [-8, -2, -2, -2, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[14, -2, 2, -7, 0, 1],\n [-2, -9, 0, 1, 0, -5],\n [2, 0, -2, -2, -2, -2],\n [-7, 1, -2, 1, 2, -6],\n [0, 0, -2, 2, -8, 8],\n [1, -5, -2, -6, 8, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2273", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[15, -8, 15, 0, -1, -3],\n [0, 4, -1, 2, -3, 8],\n [0, 0, 12, -5, -10, 14],\n [0, 0, 0, -15, 9, -14],\n [0, 0, 0, 0, 8, 11],\n [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": "654", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[14, 10, 4, 0, -13, 1],\n [0, 10, -8, -4, 9, 7],\n [0, 0, -15, -15, -1, 1],\n [0, 0, 0, 10, -7, -4],\n [0, 0, 0, 0, -2, 11],\n [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": "-68", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-15, 7, -2, -13, 10, 0],\n [7, -1, -4, 2, 1, -6],\n [-2, -4, 12, 4, -10, -10],\n [-13, 2, 4, -9, 0, -1],\n [10, 1, -10, 0, -3, 8],\n [0, -6, -10, -1, 8, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3122", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[5, 14, 4, 4, -9, -7],\n [0, 11, -3, -2, -4, -8],\n [0, 0, 2, 0, 13, -5],\n [0, 0, 0, 5, -14, -13],\n [0, 0, 0, 0, 4, 13],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-141", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[11, 8, -7, -13, 3, -3],\n [8, -4, 10, 6, 0, 6],\n [-7, 10, -6, 8, -2, 8],\n [-13, 6, 8, 9, -13, 4],\n [3, 0, -2, -13, -10, -7],\n [-3, 6, 8, 4, -7, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, -9, 2, -5, 0],\n [0, 6, -4, 2, 4, 8],\n [-9, -4, -11, -9, -2, 2],\n [2, 2, -9, -5, 6, 0],\n [-5, 4, -2, 6, -9, 3],\n [0, 8, 2, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[9, 12, 6, 4, -9, -13],\n [-11, -15, -1, 10, -13, -8],\n [9, -7, -1, -6, -14, 4],\n [-11, 15, 3, -3, -5, -15],\n [6, 14, -1, 10, 2, 0],\n [-7, -15, -5, -7, 7, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-78", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-3, 12, -9, -8, 2, -4],\n [12, 2, -2, 15, -5, 1],\n [-9, -2, -10, -9, 6, 12],\n [-8, 15, -9, 6, -2, -4],\n [2, -5, 6, -2, -15, -2],\n [-4, 1, 12, -4, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-4, -6, -8, 7, 3, -10],\n [-6, -14, -4, -11, -6, 0],\n [-8, -4, -2, 2, -5, -3],\n [7, -11, 2, -6, -4, 6],\n [3, -6, -5, -4, -9, 10],\n [-10, 0, -3, 6, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, 12, -15, -12, 10, 11],\n [-10, 6, 10, 6, -11, -13],\n [-14, -13, -7, 3, 3, 1],\n [2, -5, -4, -13, 2, 8],\n [-10, -9, -15, -10, 2, -3],\n [15, 6, 3, -9, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-13, 4, -5, 3, 6, 6],\n [4, -8, -3, 2, -12, 2],\n [-5, -3, -9, -6, 6, 4],\n [3, 2, -6, -13, 9, 1],\n [6, -12, 6, 9, -6, -2],\n [6, 2, 4, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1468", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[5, -6, 7, -13, 2, 5],\n [3, -11, 9, -5, -6, 1],\n [-12, 10, 15, 5, 2, 12],\n [2, -15, -2, -8, -14, 3],\n [-1, 12, -14, -12, 14, -15],\n [3, 5, -6, -15, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -12, -9, 14, -9, 6],\n [0, 2, -3, -6, 8, -8],\n [0, 0, -2, -2, 11, 4],\n [0, 0, 0, 5, 14, -15],\n [0, 0, 0, 0, -13, 4],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2678", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[8, 14, -14, 6, -12, 9],\n [-6, -14, -8, -15, 11, -10],\n [-5, 11, 14, 12, -6, -3],\n [-15, -14, -13, -7, -11, -6],\n [-6, -4, 2, 10, 5, 5],\n [-15, -13, -11, 9, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, 3, 2, -10, 4, -6],\n [3, -9, -8, -1, -4, 2],\n [2, -8, -7, 7, -8, 0],\n [-10, -1, 7, 6, -4, -9],\n [4, -4, -8, -4, -13, -2],\n [-6, 2, 0, -9, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 1) rounded to the nearest integer?\n[[0, -2, 2, 0, 8, 2],\n [-2, 2, -1, -6, -4, 10],\n [2, -1, 0, -2, 1, 7],\n [0, -6, -2, 10, 15, 6],\n [8, -4, 1, 15, -12, 8],\n [2, 10, 7, 6, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[1, -13, 3, -15, 13, 7],\n [-15, 7, 4, -7, 7, -11],\n [-9, 9, 10, -10, 1, 6],\n [1, -3, -4, -12, 14, -8],\n [-11, 15, -11, -3, 10, -5],\n [-8, -8, -15, -3, 13, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, 1, -4, 2, 2, 10],\n [1, -7, 0, 9, 2, 6],\n [-4, 0, -9, 11, 10, -12],\n [2, 9, 11, -7, -4, 14],\n [2, 2, 10, -4, 10, -8],\n [10, 6, -12, 14, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -12, 14, 8, -8],\n [2, 15, 0, 0, 12, -4],\n [-12, 0, 9, 8, -6, 4],\n [14, 0, 8, -12, 8, 4],\n [8, 12, -6, 8, -12, -8],\n [-8, -4, 4, 4, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[-12, -3, 0, -4, -8, -1],\n [-3, 9, -8, -10, 2, 10],\n [0, -8, -15, 15, -2, 0],\n [-4, -10, 15, 9, -8, -4],\n [-8, 2, -2, -8, 14, -8],\n [-1, 10, 0, -4, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[7, 7, -4, 9, -4, 1],\n [0, -1, -6, -13, 7, 4],\n [0, 0, -4, -15, -15, -6],\n [0, 0, 0, 1, -8, 6],\n [0, 0, 0, 0, 5, 15],\n [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": "-42036", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[10, -1, 1, 11, 2, 3],\n [0, -4, 8, -11, 8, 11],\n [0, 0, -1, -1, 11, -10],\n [0, 0, 0, 11, 4, -7],\n [0, 0, 0, 0, -8, 6],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-11, 6, 4, -10, -3, -4],\n [6, -6, -10, 7, 0, 3],\n [4, -10, 15, -2, 0, 2],\n [-10, 7, -2, -12, 10, 2],\n [-3, 0, 0, 10, 13, 6],\n [-4, 3, 2, 2, 6, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-103", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, 3, 12, -15, 15],\n [0, -9, -14, -9, 3, 15],\n [0, 0, 8, -11, 7, 3],\n [0, 0, 0, 11, 2, 8],\n [0, 0, 0, 0, -7, -4],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[6, 9, -6, -14, -9, 15],\n [4, -14, 3, -10, -6, -7],\n [-8, 10, 14, -5, -7, 4],\n [12, 4, 15, -7, -8, 12],\n [-1, -14, 8, -15, -7, -7],\n [-3, 15, -8, 11, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -13, 5, -12, 1, 0],\n [0, 9, 15, 10, 14, 4],\n [-13, -10, -15, 5, 0, -1],\n [-9, -14, -6, 9, 12, -1],\n [-10, -14, 8, 8, 1, 12],\n [-15, -15, 12, -12, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -15, 10, 3, -5, 1],\n [0, -6, -4, -7, -9, 13],\n [0, 0, -8, 1, -11, 15],\n [0, 0, 0, 13, 1, -13],\n [0, 0, 0, 0, 2, -12],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, -11, 4, -4],\n [0, -1, -4, -12, 14, 15],\n [0, 0, 1, 3, 0, -5],\n [0, 0, 0, 1, 2, 13],\n [0, 0, 0, 0, -11, 9],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3122", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/180 * A where A =\n[[-11, 12, -15, 7, 10, 14],\n [0, 8, 8, -9, 2, 5],\n [0, 0, -6, 9, -1, -12],\n [0, 0, 0, -4, -8, -8],\n [0, 0, 0, 0, -14, -4],\n [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": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[0, -7, 10, 12, -15, -1],\n [-4, -11, 7, 8, 2, 4],\n [-14, -12, -1, -10, 6, -4],\n [13, 2, 11, 4, -12, 14],\n [-15, -1, 14, 2, -2, -13],\n [13, -1, 11, -11, 11, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, 6, -13, 6, -9, -10],\n [0, 6, -15, 3, -9, -12],\n [0, 0, 7, 9, 14, 11],\n [0, 0, 0, 2, -7, 3],\n [0, 0, 0, 0, 11, -1],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[6, 2, 0, -14, -12, 4],\n [0, -13, 8, 14, 7, -14],\n [0, 0, 9, 13, -11, -14],\n [0, 0, 0, 14, -14, -14],\n [0, 0, 0, 0, 2, 9],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -2, 1, 6, 2, -6],\n [-2, -11, 14, 0, -2, -2],\n [1, 14, -1, -1, 11, -6],\n [6, 0, -1, -6, 10, 5],\n [2, -2, 11, 10, 5, 10],\n [-6, -2, -6, 5, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 6) of the inverse. Round your answer to the nearest integer:\n[[2, 6, -2, 11, -2, -10],\n [6, 13, -6, 2, -2, 11],\n [-2, -6, 15, 6, -5, -2],\n [11, 2, 6, 5, -6, 14],\n [-2, -2, -5, -6, -7, -3],\n [-10, 11, -2, 14, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[5, -3, 5, -8, 15, -3],\n [0, 4, 4, -3, 7, 11],\n [0, 0, 6, 12, -10, 14],\n [0, 0, 0, 13, -11, 9],\n [0, 0, 0, 0, 7, -8],\n [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": "73", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 2) of the inverse. Round your answer to the nearest integer:\n[[4, -1, 10, 6, -6, -5],\n [0, -7, 13, -5, 11, 14],\n [0, 0, -10, 13, 7, 5],\n [0, 0, 0, 12, -2, 4],\n [0, 0, 0, 0, 1, -1],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -8, 3, 15, 13, -7],\n [0, -3, -3, 11, 8, 3],\n [0, 0, 3, -11, 0, -7],\n [0, 0, 0, 6, -13, 3],\n [0, 0, 0, 0, -13, 8],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-162", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[15, 13, 15, 10, 2, 10],\n [0, 9, -9, 0, -10, 0],\n [0, 0, 8, 12, -15, 8],\n [0, 0, 0, -12, -12, -12],\n [0, 0, 0, 0, 1, 1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the value at position (6, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -13, 8, 14, -8, 6],\n [9, 12, -6, 1, 13, -8],\n [6, -15, 4, 5, -9, 8],\n [-7, 12, -4, 6, 10, -7],\n [4, 8, -13, -12, -6, -12],\n [6, 15, -7, 6, -15, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-47", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-7, -11, -10, 3, -8, -6],\n [-5, -3, 4, -12, -5, -4],\n [-11, 14, -6, 15, 9, 13],\n [8, -9, 5, -7, -7, -6],\n [-6, -14, -12, -8, 13, -2],\n [1, -3, 15, 5, 8, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, 2, -3, 12, -8, 11],\n [2, 8, -4, -10, 1, 10],\n [-3, -4, -4, 1, 0, 0],\n [12, -10, 1, 4, -11, -4],\n [-8, 1, 0, -11, 13, 4],\n [11, 10, 0, -4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 13, -6, 8, 1, 15],\n [0, -14, 15, -10, 9, -11],\n [0, 0, -14, -4, -13, -10],\n [0, 0, 0, 5, 5, 10],\n [0, 0, 0, 0, -1, -9],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3372", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 6) of the inverse. Round your answer to the nearest integer:\n[[6, 11, 6, 11, -2, -1],\n [0, -4, 3, 6, 12, -6],\n [0, 0, 9, -7, -14, -12],\n [0, 0, 0, -3, 4, -8],\n [0, 0, 0, 0, 9, 0],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -13, 14, -5, 2, -13],\n [0, 11, 11, 12, -2, -10],\n [0, 0, -9, -6, -1, 15],\n [0, 0, 0, 1, 11, 3],\n [0, 0, 0, 0, 10, -4],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5666", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, 13, -15, 10, 1, 1],\n [0, -6, 14, -8, -8, -2],\n [0, 0, -12, -15, -1, 15],\n [0, 0, 0, 4, -13, 7],\n [0, 0, 0, 0, 5, 4],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-76", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-15, 13, -12, 3, -11, 13],\n [0, 5, 12, 4, 8, 3],\n [0, 0, -15, -9, 1, 15],\n [0, 0, 0, 1, 11, -13],\n [0, 0, 0, 0, -5, 13],\n [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": "572", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[7, 7, 5, 8, 10, 6],\n [-1, 5, 4, 7, -12, 5],\n [5, -15, -1, 1, 3, 15],\n [-2, 11, 3, 2, 12, -14],\n [-10, -3, 1, -10, 5, 6],\n [-11, -9, -15, -3, 3, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-15, -3, -5, 11, -9, 4],\n [0, 10, 9, -15, -8, 1],\n [0, 0, -11, 10, 8, 6],\n [0, 0, 0, 13, -10, 11],\n [0, 0, 0, 0, -8, -3],\n [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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 15, -4, 4, -13, 12],\n [0, -2, 2, 11, 3, 13],\n [0, 0, -6, 1, -1, 3],\n [0, 0, 0, 3, 0, -8],\n [0, 0, 0, 0, 5, 15],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1787", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-1, -9, 12, 1, -13, -5],\n [15, -10, 15, -10, -1, -9],\n [-5, 14, 11, 1, 7, 2],\n [6, 13, 8, 13, 5, 10],\n [3, 11, -8, 8, 4, -8],\n [5, 13, -5, 5, -13, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[7, 11, -2, 11, -7, 9],\n [-15, -15, 10, 12, -4, -5],\n [15, 5, -15, 4, -4, 1],\n [-1, -14, 2, 0, -12, -8],\n [-14, -2, 9, -1, 12, -7],\n [-14, 1, 10, 15, -6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, -14, 8, 14, 3, 1],\n [0, 1, -6, 2, 7, 12],\n [0, 0, 12, 11, 2, 4],\n [0, 0, 0, -13, -1, 4],\n [0, 0, 0, 0, 7, -2],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1933", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-11, 0, 0, 2, 2, 4],\n [0, 6, -1, -2, -5, 1],\n [0, -1, 0, 2, -8, 2],\n [2, -2, 2, 12, 7, 0],\n [2, -5, -8, 7, 13, 2],\n [4, 1, 2, 0, 2, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[14, 7, -4, 4, -2, 3],\n [0, 4, -1, 11, 4, 8],\n [0, 0, -2, 7, 15, 12],\n [0, 0, 0, 6, 8, 11],\n [0, 0, 0, 0, -8, 13],\n [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": "-5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 5) rounded to the nearest integer?\n[[9, -10, -4, -1, -4, -7],\n [3, 5, -14, 12, -3, -3],\n [-8, 11, -3, -12, -10, -10],\n [5, -4, -4, 1, 11, -9],\n [10, -1, 8, 1, -6, 7],\n [4, -10, -7, -1, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -7, -6, -2, 4, 4],\n [-7, 7, 10, 10, 6, -12],\n [-6, 10, -9, 6, -4, -14],\n [-2, 10, 6, -2, 3, 6],\n [4, 6, -4, 3, -15, 10],\n [4, -12, -14, 6, 10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-14, -2, 4, 2, 10, -2],\n [-2, 14, -2, -7, -6, 5],\n [4, -2, 9, 2, -7, 6],\n [2, -7, 2, -2, -2, 0],\n [10, -6, -7, -2, 4, -14],\n [-2, 5, 6, 0, -14, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-3, 10, -7, -9, 0, 2],\n [0, 4, 4, -6, 8, 10],\n [0, 0, 6, 0, -13, -5],\n [0, 0, 0, -8, -7, -1],\n [0, 0, 0, 0, -3, -4],\n [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": "949", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[0, 10, 10, 3, -8, 4],\n [10, -6, 2, 2, -2, 6],\n [10, 2, -5, -4, -2, -6],\n [3, 2, -4, 7, -12, 4],\n [-8, -2, -2, -12, -9, -6],\n [4, 6, -6, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-11, 4, 2, 15, -15, -12],\n [7, -5, 4, -7, 14, -8],\n [-8, -11, -4, 15, -15, -1],\n [9, 2, -10, -6, -2, 5],\n [10, 13, 15, -8, 11, -13],\n [6, 6, 10, 3, -4, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2564", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, -9, 11, -12, 5],\n [0, 6, 0, 10, 15, -3],\n [0, 0, -7, 10, 5, 2],\n [0, 0, 0, -5, 15, 12],\n [0, 0, 0, 0, 8, 9],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-204", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 15, -1, -14, -14, -6],\n [-13, 14, -8, 4, -9, -4],\n [10, 3, 10, 12, 14, -1],\n [-2, 0, 13, 11, -2, -13],\n [2, 13, 12, 6, -10, 1],\n [7, 12, -2, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, -13, -3, 13, 8],\n [-14, -7, -3, -8, 0, 8],\n [13, -13, -3, -12, 2, -14],\n [4, 6, 5, -1, 1, 13],\n [-6, -15, 15, -10, -13, 3],\n [-9, -3, -3, 1, -15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 10, -13, -2, 8, -15],\n [0, -6, -3, -12, -7, -2],\n [0, 0, -8, 7, -13, 7],\n [0, 0, 0, -13, -14, -1],\n [0, 0, 0, 0, -9, 4],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[7, 5, 14, 10, -8, 14],\n [-14, -14, -11, 15, -15, 6],\n [-12, -10, 7, -3, 3, -5],\n [-3, -8, -9, -3, -15, -10],\n [-9, 0, 14, 11, -1, 4],\n [14, -14, 10, 9, 7, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 8, -1, -13, -12, -4],\n [0, 1, 15, -10, -6, 6],\n [0, 0, -6, -10, 8, -10],\n [0, 0, 0, 9, 0, 6],\n [0, 0, 0, 0, 10, 1],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5373", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 12, -6, -3, 2, 14],\n [0, -5, -3, 3, 13, 8],\n [0, 0, 13, 8, 6, -11],\n [0, 0, 0, -3, -11, -4],\n [0, 0, 0, 0, -7, 1],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "594", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, 6, 1, -13, 12, -10],\n [0, -1, -2, -5, -5, -7],\n [0, 0, -4, 13, -10, -15],\n [0, 0, 0, -1, -14, 1],\n [0, 0, 0, 0, 7, 13],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32083", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, -1, -9, 3, 4, 6],\n [0, -5, 7, -2, -3, 4],\n [0, 0, 9, -7, -7, 0],\n [0, 0, 0, 2, -14, 11],\n [0, 0, 0, 0, -14, -1],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-6, 2, -6, -7, 12, 8],\n [0, -15, -12, 8, -13, -6],\n [0, 0, 7, 4, -10, 5],\n [0, 0, 0, 14, -7, 11],\n [0, 0, 0, 0, 1, 1],\n [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": "2417", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-7, 7, 4, 4, -4, 6],\n [7, -14, 2, -10, 5, 2],\n [4, 2, 0, 2, 2, 6],\n [4, -10, 2, -8, -9, -2],\n [-4, 5, 2, -9, 6, -1],\n [6, 2, 6, -2, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-130", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[15, 4, -7, -8, -2, 3],\n [3, -8, -14, 9, -12, 15],\n [-10, -13, -13, 3, -5, 13],\n [-6, -4, -2, 14, 14, 12],\n [2, 8, -7, -1, 8, 15],\n [10, -13, 7, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-12, 12, -3, 14, 13, -10],\n [11, 5, -3, 9, 10, 4],\n [-11, 4, -2, -3, -2, -8],\n [0, -3, 8, -1, 3, -15],\n [6, -14, 2, 3, -8, -13],\n [7, 10, -2, 10, -7, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, 1, 7, 7, 8, 0],\n [-6, 5, -6, 9, 9, 8],\n [-10, 6, 1, 13, 0, -1],\n [6, -2, -12, -12, 14, -14],\n [13, -5, 14, -12, 5, 13],\n [12, 5, 0, 5, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, 10, 8, 3, -14, -7],\n [7, 9, -3, 2, 0, 0],\n [9, -6, -7, -5, 9, 10],\n [13, 10, -12, -6, -13, -10],\n [-13, 11, -7, -13, 2, -8],\n [6, -8, -1, -3, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, -6, 1, -15, -3, 13],\n [10, -3, 8, 0, 13, -7],\n [-6, -10, -11, -14, -5, -7],\n [-10, -8, -7, -7, -8, -4],\n [10, -8, -13, -3, 3, -14],\n [1, 0, -12, 2, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-14, -1, 0, 11, -4, 2],\n [-1, 15, -5, 10, 9, -3],\n [0, -5, 2, -2, -8, 6],\n [11, 10, -2, -3, 4, -3],\n [-4, 9, -8, 4, 8, 6],\n [2, -3, 6, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-185", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[7, 13, 10, -12, -14, 15],\n [0, 2, 1, -8, 10, -1],\n [0, 0, 7, -14, -10, 13],\n [0, 0, 0, -14, 2, -6],\n [0, 0, 0, 0, 1, 11],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[5, -14, -14, 15, 7, -9],\n [0, -15, -4, -3, -4, 3],\n [0, 0, 1, 2, -8, -9],\n [0, 0, 0, -1, 15, -1],\n [0, 0, 0, 0, -15, 10],\n [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": "1380", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, -4, 3, -15, 12, 5],\n [10, -2, -12, -11, -15, -15],\n [5, -10, -11, -14, 9, 5],\n [11, 11, -11, 10, -7, 3],\n [5, -1, -3, -4, -11, -14],\n [11, -12, 11, 11, 2, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-6, -3, -4, -14, 10, -1],\n [-2, 9, -6, 6, -8, 9],\n [-1, -3, -8, 5, 5, 6],\n [-2, -15, -3, 11, -8, 2],\n [6, 14, 14, -7, -3, -13],\n [2, -6, -11, 11, 9, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-597", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -8, 8, -9, 5, 2],\n [0, -1, -6, 10, 5, -4],\n [0, 0, 12, -9, -5, -3],\n [0, 0, 0, -10, 7, -5],\n [0, 0, 0, 0, -8, 3],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1972", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[2, -10, -2, -13, 0, -15],\n [0, 14, 15, 15, -2, 3],\n [0, 0, -7, -9, -2, -11],\n [0, 0, 0, 5, -9, -7],\n [0, 0, 0, 0, -10, 2],\n [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": "118", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -7, -8, 11, -12, -14],\n [0, 13, -14, -14, 14, 11],\n [0, 0, -9, -4, -10, 2],\n [0, 0, 0, -3, 4, 5],\n [0, 0, 0, 0, 11, -14],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "735", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[15, 0, 3, -6, -10, 0],\n [0, -3, -7, -9, -12, 3],\n [0, 0, 3, 12, 3, -4],\n [0, 0, 0, -12, 9, 12],\n [0, 0, 0, 0, 14, -11],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-9, 2, 10, 9, -10, 2],\n [0, -14, 3, -15, 9, 14],\n [0, 0, 4, -11, 0, 7],\n [0, 0, 0, -13, -14, 8],\n [0, 0, 0, 0, -15, -1],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 4, 11, 7, 2, -2],\n [4, 9, 0, -6, 8, 0],\n [11, 0, -5, 8, -4, 0],\n [7, -6, 8, 4, -4, 1],\n [2, 8, -4, -4, 7, 12],\n [-2, 0, 0, 1, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-4, 11, -8, -13, -14, 12],\n [-10, 0, 4, 8, 13, -1],\n [-2, -14, 4, 2, -2, 2],\n [-14, -15, 4, -14, -7, -7],\n [0, -5, 11, 7, -10, -4],\n [-13, 14, -4, 14, 15, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-15, -7, 4, 6, -10, -5],\n [-13, -12, 13, 11, -6, 3],\n [13, -10, -15, -8, -8, 9],\n [-10, 1, 3, 15, -15, -1],\n [-3, 15, 5, -13, 14, -14],\n [-13, -7, 11, 0, 8, -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"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[3, 12, 4, 3, -6, 10],\n [12, -4, -2, 8, -8, -4],\n [4, -2, 4, 0, -8, -4],\n [3, 8, 0, -12, 10, 3],\n [-6, -8, -8, 10, 10, 4],\n [10, -4, -4, 3, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[6, -4, 1, -2, 2, 14],\n [-4, -1, 4, -8, 2, 14],\n [1, 4, -6, 4, 2, 0],\n [-2, -8, 4, -3, 2, -7],\n [2, 2, 2, 2, -14, 6],\n [14, 14, 0, -7, 6, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-210", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 3) of the inverse of matrix 1/180 * A where A =\n[[-14, 1, -2, 8, 12, 0],\n [0, -6, 1, -3, 0, -7],\n [0, 0, 8, 13, 12, 13],\n [0, 0, 0, 11, 15, -5],\n [0, 0, 0, 0, -12, -2],\n [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"}
{"messages": [{"content": "Find the inverse of 1/180 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, 7, -7, 13, -11, -8],\n [0, -2, -9, -9, -7, -13],\n [0, 0, 2, -4, 6, -2],\n [0, 0, 0, -3, -2, -7],\n [0, 0, 0, 0, 1, -14],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62916", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[7, 10, 8, 8, 13, 0],\n [0, -8, 10, -1, 9, -15],\n [0, 0, 14, -1, -2, -2],\n [0, 0, 0, 15, -10, 14],\n [0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, 2, 0, -2, 2, -2],\n [2, -1, 10, 10, -8, 0],\n [0, 10, 0, 4, 4, 4],\n [-2, 10, 4, -7, -2, 6],\n [2, -8, 4, -2, 4, 4],\n [-2, 0, 4, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7594", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 3) of the inverse. Round your answer to the nearest integer:\n[[-3, 6, -12, -12, 5, -2],\n [0, -11, 0, -2, 14, -2],\n [0, 0, 8, 9, 13, -2],\n [0, 0, 0, 1, -2, -6],\n [0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[13, 15, -11, -3, -15, -9],\n [0, -6, -10, 4, -4, -3],\n [0, 0, -5, 2, -14, 0],\n [0, 0, 0, -15, -5, 2],\n [0, 0, 0, 0, 12, -15],\n [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": "-35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 7, 5, -7, -14, 1],\n [0, 8, -6, -10, 15, -11],\n [0, 0, 14, -11, -4, -9],\n [0, 0, 0, -12, 2, -6],\n [0, 0, 0, 0, -5, 2],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -13, -13, -10, -6, 8],\n [6, 2, 2, -2, 0, -9],\n [-15, 1, 7, 9, -11, 11],\n [-15, 5, 11, 1, -6, 15],\n [-4, 9, 4, 9, -14, 7],\n [0, -1, 12, -3, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[4, -4, -2, 0, -10, -7],\n [-4, -11, 2, 6, 9, 9],\n [-2, 2, 14, -1, 1, 14],\n [0, 6, -1, 0, -2, -8],\n [-10, 9, 1, -2, -13, -7],\n [-7, 9, 14, -8, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -15, -6, 7, 0, 11],\n [0, 3, 8, 9, -13, 12],\n [0, 0, -1, 1, 2, -9],\n [0, 0, 0, 10, -8, 5],\n [0, 0, 0, 0, -1, -9],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62126", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[7, 11, -7, -15, 4, -15],\n [0, -13, -14, 14, -12, 11],\n [0, 0, -11, 15, 13, 8],\n [0, 0, 0, 7, -8, -3],\n [0, 0, 0, 0, 11, -4],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, 6, -10, 15, -5, -3],\n [0, 4, -15, -5, 10, -5],\n [0, 0, -13, 12, 3, -4],\n [0, 0, 0, 7, -8, -11],\n [0, 0, 0, 0, 1, -10],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 1, 14, 11, 9, 0],\n [0, -14, 0, -15, -13, 7],\n [0, 0, 10, 2, -1, -7],\n [0, 0, 0, 2, -11, 8],\n [0, 0, 0, 0, -8, -13],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-15, 14, 11, 6, -3, 7],\n [0, 1, -13, -7, -11, -10],\n [0, 0, 14, 5, 5, 5],\n [0, 0, 0, 6, -5, -14],\n [0, 0, 0, 0, -6, -10],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-250", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, -10, -2, 10, 7, 0],\n [9, -9, -14, -10, -7, -9],\n [-14, 3, -8, -5, 9, -12],\n [0, 9, 2, -3, 11, -11],\n [11, -14, -5, -15, -3, 14],\n [-11, 2, -2, -3, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, -9, 4, 1, 0, -5],\n [15, 3, 11, 12, -15, 5],\n [15, 13, -8, -15, 14, -7],\n [3, 5, -7, 5, 9, -6],\n [8, 7, -5, -15, 4, 9],\n [10, -8, 4, -4, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[-12, -1, 3, -10, 11, -11],\n [-11, 2, 12, -13, 11, 6],\n [-14, 15, -12, 2, -7, 3],\n [10, -6, 6, -1, -15, 13],\n [-5, -2, 15, 15, -6, 3],\n [8, 5, 0, -8, 15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[7, 9, -9, 3, -9, -1],\n [-8, -2, -15, 13, -3, -13],\n [5, 12, -10, 3, -1, -12],\n [5, 15, -13, -12, -11, 2],\n [10, 9, -6, -8, -4, 6],\n [10, 11, -13, 11, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-8, 10, -15, -2, 15, 6],\n [0, 15, -3, 9, -4, -13],\n [0, 0, -3, -1, -6, -15],\n [0, 0, 0, -6, -1, -7],\n [0, 0, 0, 0, 15, 8],\n [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": "-123", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 13, 3, 3, -10, 12],\n [0, 13, -6, 7, -2, 1],\n [0, 0, 12, -15, -6, -13],\n [0, 0, 0, -6, 14, 10],\n [0, 0, 0, 0, -7, 12],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-647", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 8, -9, 1, 9, 8],\n [8, 11, -5, 14, -8, -6],\n [-9, -5, -10, 2, -7, 2],\n [1, 14, 2, -8, -3, -6],\n [9, -8, -7, -3, -9, 10],\n [8, -6, 2, -6, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-249", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 1, 8, 2, -9, 6],\n [0, 2, 12, 13, 3, 4],\n [0, 0, -3, 11, 2, 8],\n [0, 0, 0, -15, 6, -8],\n [0, 0, 0, 0, -1, 5],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-7, 0, 4, -4, 8, 3],\n [0, -8, 0, 10, -4, -5],\n [4, 0, 10, -4, -8, 6],\n [-4, 10, -4, -12, 4, -4],\n [8, -4, -8, 4, 8, -2],\n [3, -5, 6, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -5, -4, -3, -8, -15],\n [0, 12, -14, -2, -3, 0],\n [0, 0, -4, 0, -6, -13],\n [0, 0, 0, -11, 2, -13],\n [0, 0, 0, 0, 5, 12],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-500", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, -2, -4, 1, -6, 2],\n [-2, 13, -5, 6, 0, -13],\n [-4, -5, 15, -6, -2, -2],\n [1, 6, -6, 7, -6, -4],\n [-6, 0, -2, -6, -1, -2],\n [2, -13, -2, -4, -2, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-82", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, -4, -10, -10, 2],\n [-2, 14, 6, 1, 4, 2],\n [-4, 6, 8, -11, -12, -6],\n [-10, 1, -11, 10, 2, 10],\n [-10, 4, -12, 2, 0, 6],\n [2, 2, -6, 10, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "461", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[8, 15, 3, 9, 3, 8],\n [0, -7, 7, -12, -6, 15],\n [0, 0, -1, 3, -14, -6],\n [0, 0, 0, 15, 4, 8],\n [0, 0, 0, 0, 2, 1],\n [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": "3058", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, -2, 0, -1, 8, 8],\n [-2, -12, 6, 10, -3, 8],\n [0, 6, 10, 2, -6, -4],\n [-1, 10, 2, 8, -7, 12],\n [8, -3, -6, -7, -8, -10],\n [8, 8, -4, 12, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, 9, -11, -7, -1],\n [-4, 1, 0, -6, -1, 3],\n [9, 0, -5, 0, -8, 4],\n [-11, -6, 0, -12, 3, -4],\n [-7, -1, -8, 3, -1, 11],\n [-1, 3, 4, -4, 11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[10, -2, -4, 2, -12, 11],\n [0, 3, 13, -3, 9, 14],\n [0, 0, -5, 12, -10, -7],\n [0, 0, 0, -1, -5, -10],\n [0, 0, 0, 0, 9, -5],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-102", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[1, 7, -13, -2, 11, -9],\n [9, 3, -13, -14, 10, 1],\n [-7, 6, -10, 8, 11, 5],\n [-7, 15, 11, -11, -14, 6],\n [-1, -7, 3, -6, -12, -6],\n [11, -8, 6, -3, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -1, -4, 0, -10, 12],\n [0, -13, -8, -9, -12, 10],\n [0, 0, 14, -9, -6, 9],\n [0, 0, 0, 15, 10, 9],\n [0, 0, 0, 0, -1, -8],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "973", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, -3, 9, -9, -8, 7],\n [0, -5, 10, -12, 1, 0],\n [3, 7, 11, -5, -9, 11],\n [-3, 3, 1, 10, 9, 12],\n [6, -3, 13, -4, -9, -15],\n [-15, 4, 7, -2, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[7, -5, 14, 4, 3, -12],\n [0, 10, -6, 8, -3, 13],\n [0, 0, 5, -14, 13, -12],\n [0, 0, 0, 14, 1, 0],\n [0, 0, 0, 0, 7, 15],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, 9, -15, -1, -13, -10],\n [-2, 7, -10, -15, 4, -10],\n [-8, 10, -1, -2, 0, 4],\n [7, 0, 11, 3, 8, -15],\n [-12, 8, -6, 4, 2, -14],\n [-12, -1, 13, -12, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[2, -8, -2, 10, -6, -5],\n [-8, 8, -10, -10, -2, 8],\n [-2, -10, 5, 3, 4, 8],\n [10, -10, 3, 1, 4, -4],\n [-6, -2, 4, 4, 3, 11],\n [-5, 8, 8, -4, 11, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3431", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, -5, 8, -11, -9, -10],\n [14, 10, -3, -14, 3, -5],\n [11, 4, -11, -7, -10, 1],\n [3, 7, -8, -9, -11, -1],\n [-6, 8, 0, -7, -9, -5],\n [-7, 1, 14, -7, -13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 4, 0, -9, 12],\n [0, 4, 9, -3, -13, -4],\n [0, 0, -3, 4, 0, -9],\n [0, 0, 0, 1, -15, 14],\n [0, 0, 0, 0, 10, -5],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-549", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -2, 0, 15, 15, -4],\n [-7, 4, 13, 7, 5, 0],\n [5, 3, 0, -7, -3, 10],\n [-11, 6, 3, -6, -9, -7],\n [9, -2, -1, -3, -6, -2],\n [10, 5, 7, 13, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "266", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 4) of the inverse. Round your answer to the nearest integer:\n[[13, 3, -10, -4, 8, -3],\n [-8, 0, -14, 6, -9, -4],\n [-9, 3, -2, 14, -7, 2],\n [-5, 0, 3, 15, -5, 2],\n [-5, 9, -12, 2, 3, -3],\n [-12, 15, 14, -6, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-119", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, -13, 0, 10, -8, 8],\n [-9, 3, -2, -1, 1, 5],\n [-15, -10, 11, 7, -1, 15],\n [-4, 5, 4, -14, -11, -7],\n [4, -2, 2, 13, 15, 6],\n [-8, -14, -7, -9, 14, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-149", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, -1, 8, -7, 10],\n [12, -1, -1, -8, 8, 6],\n [-1, -1, 3, 0, -3, -2],\n [8, -8, 0, 10, -7, -14],\n [-7, 8, -3, -7, -11, 0],\n [10, 6, -2, -14, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "389", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[4, 7, -13, -11, -5, -7],\n [-11, 9, -15, 9, -2, -11],\n [-8, 5, -2, 12, 0, -10],\n [-8, -14, 3, 11, -7, -11],\n [-11, 9, 10, 3, 14, -12],\n [0, 0, 0, -9, 2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "603", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/180 * A where A =\n[[5, 15, -15, -13, 15, 9],\n [5, -8, -15, 14, -9, -9],\n [-8, 3, 1, -5, -1, -7],\n [1, -5, -10, -7, 14, 2],\n [4, -14, -12, 2, 12, -15],\n [-5, -13, -8, -11, 4, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[6, 6, -11, 12, -5, -4],\n [6, -7, 5, -3, 6, 4],\n [13, -13, -3, 12, 6, -5],\n [-5, 5, 4, 5, -9, 1],\n [0, -2, 15, -15, -5, -3],\n [-15, -14, -7, -3, -11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 4) of the inverse of matrix 1/180 * A where A =\n[[7, -10, 8, 9, 8, 5],\n [0, -6, 15, -1, 10, -7],\n [0, 0, -14, 2, -4, -13],\n [0, 0, 0, 9, -10, -15],\n [0, 0, 0, 0, -12, 13],\n [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": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, 0, 4, 6, 4],\n [-9, 6, 10, -4, -8, 2],\n [0, 10, 6, -2, -2, -1],\n [4, -4, -2, 13, -6, -6],\n [6, -8, -2, -6, -8, -4],\n [4, 2, -1, -6, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 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, 5, -15, 13],\n [0, 14, -8, -13, -15, 4],\n [0, 0, -7, 15, 1, 11],\n [0, 0, 0, -10, 14, 7],\n [0, 0, 0, 0, -6, -2],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-483", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[4, -3, -1, 11, 10, -4],\n [-3, -8, 0, 14, 13, 13],\n [-13, 12, 13, 15, -3, -4],\n [3, 13, -14, -15, -8, 14],\n [-7, 9, 11, -8, 5, 1],\n [-7, -10, 12, -1, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, 5, 6, -4, -3, -9],\n [0, 2, -2, -5, 12, -2],\n [0, 0, 5, 10, 15, -14],\n [0, 0, 0, -6, 6, -8],\n [0, 0, 0, 0, -3, 0],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[6, 2, -2, -10, -4, -12],\n [2, 0, 2, 0, 4, -7],\n [-2, 2, -4, 7, -4, -6],\n [-10, 0, 7, -3, 9, 2],\n [-4, 4, -4, 9, -15, -7],\n [-12, -7, -6, 2, -7, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "383", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, 6, 6, -2, 4, -4],\n [6, -6, -6, 5, 2, 2],\n [6, -6, 4, -8, -10, -2],\n [-2, 5, -8, 10, -4, -2],\n [4, 2, -10, -4, -2, -10],\n [-4, 2, -2, -2, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9607", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[8, -14, -9, 3, -2, 3],\n [14, -9, -4, -13, 15, -1],\n [-11, -8, -2, 13, -12, -9],\n [-9, 2, -2, -8, 10, -4],\n [-6, 15, -2, -7, -10, 14],\n [-11, -15, -15, 9, 14, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4735", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[4, -2, 9, -6, 7, -14],\n [0, 14, 2, 5, -14, 5],\n [0, 0, -14, 9, -9, -9],\n [0, 0, 0, 7, 6, 2],\n [0, 0, 0, 0, -7, -3],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[11, -8, -1, 5, 14, 7],\n [3, -1, -8, -8, 3, -7],\n [14, 8, 1, -8, -4, 11],\n [-1, -12, -10, 14, 13, 0],\n [10, 9, -11, 7, -3, -1],\n [1, 9, 14, 6, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[6, -6, 4, 3, -2, 0],\n [-6, 0, 3, -6, -1, -7],\n [4, 3, -11, 5, -10, -4],\n [3, -6, 5, -2, 12, 0],\n [-2, -1, -10, 12, 1, -1],\n [0, -7, -4, 0, -1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "274", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-11, -15, -7, 8, -8, -13],\n [-14, -15, -4, 6, -3, -6],\n [1, 14, -5, -11, 9, 11],\n [-7, -3, 12, 15, 4, 7],\n [14, -5, 7, -12, 5, -5],\n [-7, -9, 0, 7, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 10, -13, -5, 3, -12],\n [10, 0, 3, 5, 8, -4],\n [-13, 3, -9, -4, -8, 9],\n [-5, 5, -4, 6, 5, -6],\n [3, 8, -8, 5, -8, -2],\n [-12, -4, 9, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 10, -13, 11, -14, 0],\n [0, 8, -1, 1, 0, 4],\n [0, 0, -11, -14, -15, 6],\n [0, 0, 0, -11, -13, 11],\n [0, 0, 0, 0, 9, 3],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "581", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -9, 4, -4, -6, -8],\n [-9, 12, 6, -6, 0, -4],\n [4, 6, 0, 0, 8, 0],\n [-4, -6, 0, 0, 4, 6],\n [-6, 0, 8, 4, 12, 8],\n [-8, -4, 0, 6, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-179", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -9, -15, -8, 3, 13],\n [4, 4, 15, -6, 14, -4],\n [8, -15, 8, 9, 9, 5],\n [-12, -12, -7, -1, 8, 10],\n [-1, 10, 12, -9, -4, -13],\n [4, 15, -7, -2, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "318", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[12, -4, -4, 4, 0, 7],\n [-4, -6, -12, -5, -8, 9],\n [-4, -12, -4, -2, 6, 8],\n [4, -5, -2, -5, -4, -5],\n [0, -8, 6, -4, -12, -3],\n [7, 9, 8, -5, -3, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -12, -2, 4, 10, 0],\n [-12, 4, 6, -8, 2, 4],\n [-2, 6, 9, 2, -8, 11],\n [4, -8, 2, -11, -2, 3],\n [10, 2, -8, -2, 13, 5],\n [0, 4, 11, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, 6, 13, 9, 10, -2],\n [-2, -14, 6, -3, -13, 14],\n [2, 6, -12, 5, 5, 3],\n [0, 12, -12, 3, 7, -1],\n [-15, 0, -1, 0, 6, 4],\n [-15, 1, -11, 14, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 2) rounded to the nearest integer?\n[[-9, -3, -4, -12, 14, 9],\n [-12, 7, 5, 15, 5, -10],\n [8, -1, 5, 15, 3, -10],\n [14, -4, -2, 2, 12, -4],\n [8, 8, -1, 3, 12, -8],\n [-7, -11, -11, -10, 7, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[-11, -15, -5, 10, 5, 4],\n [-15, -9, -1, 1, 13, -8],\n [14, 10, 12, -14, 10, -3],\n [-4, -11, -3, -10, 9, -1],\n [14, 7, 6, 5, 6, 15],\n [14, -5, -12, -15, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the inverse of matrix 1/180 * A where A =\n[[-7, -10, -8, 10, -2, -6],\n [-10, 9, -15, -12, -11, 6],\n [-8, -15, -2, -14, -1, 1],\n [10, -12, -14, -6, 6, -9],\n [-2, -11, -1, 6, 12, -3],\n [-6, 6, 1, -9, -3, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, 6, 0, -7, 6, 0],\n [6, 9, -6, -12, -2, -8],\n [0, -6, -12, 6, -4, 10],\n [-7, -12, 6, -15, 8, 12],\n [6, -2, -4, 8, -15, 4],\n [0, -8, 10, 12, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-143", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-14, -6, -2, -12, 8, -12],\n [-6, -1, -8, 12, -11, -6],\n [-2, -8, -7, -12, 2, -5],\n [-12, 12, -12, -6, -4, -6],\n [8, -11, 2, -4, 8, -12],\n [-12, -6, -5, -6, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-5, -4, -7, 0, 6, -9],\n [-4, -13, -2, -2, -11, -7],\n [-7, -2, 4, -1, -2, -12],\n [0, -2, -1, 12, -2, -3],\n [6, -11, -2, -2, 2, -13],\n [-9, -7, -12, -3, -13, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -13, -6, -6, -6, 0],\n [-13, 5, -2, -4, 4, -1],\n [-6, -2, -6, -10, 0, -14],\n [-6, -4, -10, 12, 7, 6],\n [-6, 4, 0, 7, -6, 0],\n [0, -1, -14, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -11, -7, 15, 9, 14],\n [0, 8, 4, 0, 14, 4],\n [0, 0, -12, 0, -12, -10],\n [0, 0, 0, -8, 2, 8],\n [0, 0, 0, 0, 10, 14],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "639", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, -9, 6, 11, -1, -9],\n [-3, 9, -13, 10, 7, -3],\n [10, -13, 13, -14, 12, 7],\n [-12, 1, -10, -5, -10, 6],\n [-14, 1, -13, -4, -2, -14],\n [6, 13, 12, 6, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, 2, -6, 10, -2],\n [-4, -6, 2, -9, -14, 6],\n [2, 2, 15, -4, -2, -10],\n [-6, -9, -4, -9, -8, -8],\n [10, -14, -2, -8, -2, -8],\n [-2, 6, -10, -8, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, -8, -4, 6, 4, -6],\n [-8, -14, 11, -8, 7, 1],\n [-4, 11, 0, 4, -10, 10],\n [6, -8, 4, -10, 2, 6],\n [4, 7, -10, 2, -7, 1],\n [-6, 1, 10, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "437", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-7, -1, -2, -15, 1, -15],\n [0, 13, 5, 6, -3, 15],\n [0, 0, 14, -3, 0, -14],\n [0, 0, 0, -3, 3, -3],\n [0, 0, 0, 0, 9, -10],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-9, 15, -9, 10, 7, 10],\n [0, 11, 0, -11, -1, 7],\n [0, 0, 9, -3, 12, 3],\n [0, 0, 0, -7, 1, -14],\n [0, 0, 0, 0, 2, -9],\n [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": "94", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, 12, -8, 4, -6, 8],\n [12, 9, -3, 2, 2, -8],\n [-8, -3, 6, -6, 0, -2],\n [4, 2, -6, 15, 3, 10],\n [-6, 2, 0, 3, 7, 0],\n [8, -8, -2, 10, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-5, 4, -5, 1, 13, 10],\n [5, -2, 0, 8, -6, 15],\n [15, -12, -6, 10, 4, 13],\n [-4, 14, -7, -1, -7, -9],\n [10, 8, -4, 12, 4, 8],\n [-2, 6, 0, 13, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[-13, -5, 7, 5, 4, 3],\n [-8, 4, -8, 10, -13, -6],\n [-3, -7, -10, -1, 0, -11],\n [5, -3, 3, -14, -10, 11],\n [-15, -1, -1, -2, -9, 15],\n [-11, 4, 9, 10, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -1, 4, 0, -13, -10],\n [0, 7, -3, -15, 13, 5],\n [0, 0, -14, 11, -1, 11],\n [0, 0, 0, -13, -12, -1],\n [0, 0, 0, 0, -11, -6],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 6, -5, 12, 14, 3],\n [0, -6, 4, -13, 6, -1],\n [0, 0, -14, 9, 8, -10],\n [0, 0, 0, 15, -12, 7],\n [0, 0, 0, 0, -14, 15],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-134", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, 10, 0, 2, 12],\n [10, 9, 0, 4, -13, 2],\n [10, 0, -12, -6, 8, -3],\n [0, 4, -6, -12, 6, -4],\n [2, -13, 8, 6, -1, 10],\n [12, 2, -3, -4, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -11, -7, 4, -11, -12],\n [13, 0, -14, 10, 0, 2],\n [-14, 0, 13, -15, 0, -13],\n [-1, 14, -5, -6, 1, -12],\n [1, -12, 3, 9, -15, -2],\n [8, -5, 9, 12, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-12, -6, 1, -12, 15, 3],\n [2, 1, -10, 12, -9, -10],\n [9, -4, -7, 2, 15, 15],\n [-14, 9, 1, 5, -15, 7],\n [-7, -10, 14, -14, -10, -7],\n [-13, 0, 9, 8, -1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 6) rounded to the nearest integer?\n[[-4, 7, -8, 10, -10, -13],\n [0, -12, 11, -6, -2, 5],\n [0, 0, -9, -9, -8, -6],\n [0, 0, 0, -1, -15, -6],\n [0, 0, 0, 0, -4, 8],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-926", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[7, -6, 9, -2, -1, 12],\n [7, 8, -12, 9, 15, 14],\n [-15, -8, -13, -2, 1, -14],\n [-1, -10, -11, -2, 3, -7],\n [-8, 13, -13, 2, -8, 0],\n [14, -1, 5, -1, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-135", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-15, -6, 3, -11, 2, -13],\n [-12, -12, -5, -7, -15, 12],\n [9, 15, 0, -7, -5, -10],\n [11, 1, 11, 13, -4, 6],\n [-8, 0, -11, 5, -15, 1],\n [8, 13, 5, -8, -6, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, 4, -3, 11, 14, -6],\n [0, -3, -13, 6, 11, 7],\n [0, 0, -14, -5, -2, -6],\n [0, 0, 0, -15, 10, -9],\n [0, 0, 0, 0, 11, 6],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-428", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 14, -8, 8, 3, -13],\n [0, -1, -12, -10, 9, -6],\n [0, 0, 2, -10, 3, 1],\n [0, 0, 0, -9, 4, -4],\n [0, 0, 0, 0, 8, -12],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4572", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, -10, 7, -3, -7, 5],\n [-7, -8, 1, 0, 0, 11],\n [12, 3, 8, 0, 9, -2],\n [4, -2, -2, -2, -4, -10],\n [4, -3, 0, 15, -7, -14],\n [6, 11, 13, -13, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-14, 11, 8, -6, -8, 1],\n [10, 6, -15, -10, -9, -1],\n [2, -7, -8, 9, 15, -6],\n [13, -12, 4, 12, -8, -15],\n [-8, 7, -4, 7, 9, -1],\n [-3, 0, 10, 7, 15, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, 3, -3, -2, -8, 6],\n [3, -6, 8, 1, -1, 12],\n [-3, 8, 1, -1, -2, 5],\n [-2, 1, -1, 11, 3, -10],\n [-8, -1, -2, 3, 2, 0],\n [6, 12, 5, -10, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[15, -7, 12, 8, 2, 15],\n [-8, 3, -13, -7, -3, -7],\n [15, 9, 4, -4, 14, 7],\n [-3, -8, -1, 15, 13, 15],\n [-3, 5, -3, 15, 15, 1],\n [-1, 9, 6, 3, -13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[14, -5, 4, 6, 2, 8],\n [-5, 1, 8, 4, -6, -2],\n [4, 8, 8, 2, 0, 2],\n [6, 4, 2, -5, 5, -8],\n [2, -6, 0, 5, -1, -10],\n [8, -2, 2, -8, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, -6, 2, -4, -4, -11],\n [-6, -12, 4, 4, -6, 2],\n [2, 4, 12, 3, -2, 4],\n [-4, 4, 3, -7, 2, -2],\n [-4, -6, -2, 2, -12, -8],\n [-11, 2, 4, -2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-48", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, 13, -2, -2, 4, 12],\n [7, -13, -15, 13, -7, -7],\n [6, 15, -14, 0, -8, 10],\n [-10, 7, -3, -15, 3, -1],\n [-15, -6, -15, 12, -4, -5],\n [13, 1, -12, 13, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-4, 1, -6, 12, -9, -3],\n [1, -9, -4, 4, -2, -2],\n [-6, -4, -12, 0, -2, 2],\n [12, 4, 0, -10, -3, -4],\n [-9, -2, -2, -3, -3, -6],\n [-3, -2, 2, -4, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 3, -11, 5, -2, 15],\n [0, 12, -12, -4, -10, 3],\n [0, 0, 7, 7, 12, 0],\n [0, 0, 0, 2, 15, 13],\n [0, 0, 0, 0, 9, 2],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1264", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-15, -8, -4, 0, 0, 7],\n [-8, 2, -7, 4, -2, 2],\n [-4, -7, -4, -1, -3, 7],\n [0, 4, -1, -13, 3, -11],\n [0, -2, -3, 3, 4, 2],\n [7, 2, 7, -11, 2, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 11, -6, 3, 4, 11],\n [0, 6, 14, 1, -7, -7],\n [0, 0, -9, -5, -8, 9],\n [0, 0, 0, 5, 8, 0],\n [0, 0, 0, 0, -5, -10],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, 8, -7, 8, -13, -10],\n [9, 1, -13, -14, -4, 8],\n [-10, -6, -5, 0, 11, 0],\n [8, 2, 11, 6, 7, 8],\n [-7, 5, 11, 3, -14, 8],\n [-15, 10, 15, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-13, 6, -11, -1, -6, 0],\n [6, -5, 5, 0, -4, 9],\n [-11, 5, 5, 2, -1, 1],\n [-1, 0, 2, 4, 4, 2],\n [-6, -4, -1, 4, -14, 2],\n [0, 9, 1, 2, 2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, -2, 15, -5, -7, -9],\n [0, 4, 1, -13, -1, -2],\n [0, 0, 10, -6, -14, -2],\n [0, 0, 0, -6, 9, 2],\n [0, 0, 0, 0, 2, 15],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[14, -12, -1, -8, -1, -2],\n [15, 13, 11, 5, -7, 4],\n [-13, 10, -1, 8, 1, 9],\n [0, -12, -5, 9, -8, -13],\n [3, -2, -7, -13, -12, 9],\n [12, -12, -5, 3, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[7, 6, 1, 14, -6, 8],\n [1, 0, 4, 6, -10, -9],\n [-2, -5, -4, -2, -11, -11],\n [4, 6, 7, 10, -1, 10],\n [-15, 9, 15, 14, 8, 7],\n [-7, -13, 10, -12, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[6, -2, 0, 13, 2, 0],\n [0, -14, -6, -9, 9, 11],\n [-1, 12, -7, -9, 11, 8],\n [0, 10, -13, 1, 7, -8],\n [-14, 15, 9, 4, 10, 11],\n [9, 13, -13, -8, 11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, 15, 2, 6, 0, -15],\n [0, -6, 3, 0, -2, 9],\n [0, 0, -10, 12, 6, 7],\n [0, 0, 0, -12, 6, 8],\n [0, 0, 0, 0, -3, -12],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1008", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-8, -9, -11, -13, -1, 15],\n [0, 1, 13, 7, -3, -1],\n [0, 0, 4, -2, 5, -3],\n [0, 0, 0, 13, 7, -7],\n [0, 0, 0, 0, -6, -15],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-14, -14, -9, -7, 8, 15],\n [0, -14, 3, 10, -11, -7],\n [0, 0, -4, 14, 3, -7],\n [0, 0, 0, -4, -2, -8],\n [0, 0, 0, 0, -10, -4],\n [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": "-81", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[11, -2, -10, 14, -2, -4],\n [14, 11, 6, 10, -4, -8],\n [-6, 0, 4, 10, -8, -7],\n [-3, 13, 4, 1, 3, 1],\n [-9, 12, -15, 11, 4, 13],\n [-2, 1, -3, 13, -14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "418", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[15, -2, -15, 13, -11, -9],\n [3, -2, 8, -2, -1, -11],\n [-11, 13, 5, 8, -14, 2],\n [15, 14, 12, 8, -7, 11],\n [12, -6, 10, 2, -12, -8],\n [2, 4, 10, 13, 13, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the inverse of matrix 1/180 * A where A =\n[[13, -11, -3, 9, -6, -13],\n [0, 9, 11, -3, 11, -4],\n [0, 0, 10, -13, 1, -7],\n [0, 0, 0, -7, 5, 4],\n [0, 0, 0, 0, 12, 0],\n [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": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, 2, -10, -10, 2, -10],\n [-10, 6, 12, -3, -2, 5],\n [-9, -3, -1, -4, 5, 11],\n [-15, 12, 9, -13, 2, 10],\n [6, -8, -14, -12, 2, 12],\n [12, 9, 10, -3, -1, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-6, -12, 12, 8, 6, 0],\n [-12, -4, 4, -2, 3, -4],\n [12, 4, 11, 3, -12, -5],\n [8, -2, 3, -10, -6, 1],\n [6, 3, -12, -6, -10, -5],\n [0, -4, -5, 1, -5, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "519", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -11, 7, 1, 13, 1],\n [0, -3, 15, 6, 15, -9],\n [0, 0, -10, 13, -2, 0],\n [0, 0, 0, 5, 2, 14],\n [0, 0, 0, 0, 7, -13],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3729", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 4) of the inverse. Round your answer to the nearest integer:\n[[-12, 1, -13, 7, -12, 15],\n [-14, -2, -11, 15, 5, 15],\n [-14, 15, -1, -5, 6, -6],\n [4, 14, -15, 3, -2, 9],\n [10, 7, 13, 6, -2, -15],\n [9, 13, -7, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 15, -10, -9, -14, 10],\n [0, 8, -10, 9, -13, 2],\n [0, 0, 7, -10, -5, -13],\n [0, 0, 0, 6, -14, -1],\n [0, 0, 0, 0, -12, 12],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[2, -10, 2, 12, -9, -14],\n [0, -7, 13, 15, -12, -2],\n [0, 0, -9, -8, -1, 11],\n [0, 0, 0, 4, 7, -12],\n [0, 0, 0, 0, 9, 0],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "398", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, 8, 3, 9, 9, -2],\n [8, -4, 11, -6, -10, -6],\n [3, 11, -6, -6, 10, -2],\n [9, -6, -6, -14, -4, 8],\n [9, -10, 10, -4, 12, -8],\n [-2, -6, -2, 8, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -11, 11, 11, 8, -10],\n [0, -5, 5, -6, -12, -7],\n [0, 0, 11, -2, -11, -15],\n [0, 0, 0, -11, -11, 13],\n [0, 0, 0, 0, 2, 12],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1626", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 4, 6, 2, 9, 6],\n [4, 11, 1, 10, 9, -10],\n [6, 1, -4, 7, -4, 8],\n [2, 10, 7, -15, 6, -4],\n [9, 9, -4, 6, -6, 2],\n [6, -10, 8, -4, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-126", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-13, -12, 0, 8, -12, 9],\n [4, 13, 14, 4, -3, 5],\n [1, 7, 9, 0, 12, 9],\n [1, 15, -10, -13, 4, 8],\n [15, -12, -8, 4, -7, 6],\n [-15, -3, 10, -14, 7, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[7, 6, 8, -2, 4, 3],\n [6, -2, 1, 6, -3, 2],\n [8, 1, -6, -3, -12, -4],\n [-2, 6, -3, 1, -2, -4],\n [4, -3, -12, -2, 10, 0],\n [3, 2, -4, -4, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 3, 6, 2, -11, 2],\n [-4, -12, -1, -5, 11, 3],\n [-11, -10, -3, 7, -6, 8],\n [9, -2, -12, 4, 7, -4],\n [-1, 10, -6, -5, -7, -5],\n [-14, -3, 11, 6, 10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "737", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-8, 13, 5, 5, -8, -15],\n [-10, 10, -3, -7, 12, -10],\n [-1, 7, 0, -12, 12, 10],\n [1, -7, -4, 6, 3, 4],\n [10, -4, 6, -10, -4, -7],\n [4, -11, 5, -13, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 4) of the inverse. Round your answer to the nearest integer:\n[[-6, -1, -7, -6, -5, 13],\n [0, -2, -11, 11, -7, -12],\n [0, 0, -15, 5, -15, -4],\n [0, 0, 0, 11, -5, 13],\n [0, 0, 0, 0, 6, 4],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, -13, 4, -2, -7, -7],\n [5, 12, 9, -10, -8, -5],\n [-8, -4, -6, 15, 7, -12],\n [0, 4, -10, 14, -7, 7],\n [-11, 5, 8, -10, 1, 1],\n [9, 8, 6, -3, 1, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-14, 10, 3, 10, 12, -13],\n [0, 12, -14, 6, -9, -12],\n [0, 0, -9, 4, -10, -7],\n [0, 0, 0, 14, 10, -12],\n [0, 0, 0, 0, -6, 2],\n [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": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-8, 4, 9, -2, 6, 1],\n [4, 3, 12, 0, 2, 6],\n [9, 12, 6, 3, -7, -3],\n [-2, 0, 3, -12, -1, -1],\n [6, 2, -7, -1, -5, 4],\n [1, 6, -3, -1, 4, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -6, 5, -3, 10, 2],\n [-6, 14, 8, 0, 0, -7],\n [5, 8, -10, 0, -2, 12],\n [-3, 0, 0, -10, -8, -11],\n [10, 0, -2, -8, -5, 4],\n [2, -7, 12, -11, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-13, 5, 7, -11, -10, -14],\n [0, -11, 6, 1, 10, -14],\n [0, 0, -5, -7, -10, 8],\n [0, 0, 0, -11, 12, -4],\n [0, 0, 0, 0, -15, -5],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 13, 4, -9, 7],\n [0, -4, 13, -13, 7, 6],\n [0, 0, -9, 7, 10, -11],\n [0, 0, 0, 12, 14, 3],\n [0, 0, 0, 0, 5, 8],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[3, 12, -12, 10, -15, 11],\n [-12, -12, -7, -8, -14, 13],\n [7, -10, 7, -5, -12, 14],\n [-2, 5, 6, -7, -14, 11],\n [9, 10, -15, -12, -4, -11],\n [-7, 15, 6, -12, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[0, -2, 10, 6, -3, 1],\n [-2, -15, 0, 6, -6, 12],\n [10, 0, 1, 2, 4, 6],\n [6, 6, 2, -6, 14, -10],\n [-3, -6, 4, 14, -13, 8],\n [1, 12, 6, -10, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -9, -6, 2, 15, 6],\n [-10, -9, 12, 1, 14, -4],\n [1, 15, 2, -2, -5, -14],\n [5, -15, -5, -14, 0, 6],\n [-13, 4, -15, 5, 4, -8],\n [3, 10, -15, 14, 13, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1615", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-11, 4, 12, -4, -5, -2],\n [4, -11, -2, -4, 2, 0],\n [12, -2, -4, 1, -8, 2],\n [-4, -4, 1, -14, -10, 6],\n [-5, 2, -8, -10, -6, 8],\n [-2, 0, 2, 6, 8, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-85", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-10, -4, 12, 4, 8, 4],\n [-4, 4, 10, 8, -10, -2],\n [12, 10, -2, -2, 2, 11],\n [4, 8, -2, -5, 0, 7],\n [8, -10, 2, 0, 6, 2],\n [4, -2, 11, 7, 2, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[10, -4, -6, -1, -11, -2],\n [-4, -10, -8, -2, 4, -14],\n [-6, -8, 15, 8, -12, 2],\n [-1, -2, 8, 6, 0, -2],\n [-11, 4, -12, 0, 11, 3],\n [-2, -14, 2, -2, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-1, 2, -7, -3, 12, -3],\n [0, -3, 11, -6, -6, 6],\n [0, 0, 6, 15, 15, -11],\n [0, 0, 0, -6, -6, 10],\n [0, 0, 0, 0, -3, -1],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "335", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, -10, -15, -14, 7, -1],\n [-12, -11, -1, -5, -6, 1],\n [-14, 4, 8, -6, 4, 14],\n [-13, 3, 12, -11, -13, -8],\n [-11, 12, 14, -4, -2, -9],\n [-5, -8, -11, -8, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -4, 12, 2, 11, 2],\n [-4, -9, 8, 2, 2, -3],\n [12, 8, -12, 9, -5, -2],\n [2, 2, 9, -1, 0, 0],\n [11, 2, -5, 0, -5, 2],\n [2, -3, -2, 0, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[2, 4, -10, 12, -3, 0],\n [4, 7, 6, 2, 0, 0],\n [-10, 6, 15, -2, -4, -1],\n [12, 2, -2, 5, 4, -2],\n [-3, 0, -4, 4, 2, 6],\n [0, 0, -1, -2, 6, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/180 * A where A =\n[[-3, -5, -6, 1, -2, 1],\n [-5, -15, 1, -4, -8, 2],\n [-6, 1, -12, -4, 2, 10],\n [1, -4, -4, -1, -8, -6],\n [-2, -8, 2, -8, 10, -4],\n [1, 2, 10, -6, -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"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, -6, 9, 8, 6, 12],\n [0, 4, 14, 13, -6, 9],\n [0, 0, 2, -7, 14, 0],\n [0, 0, 0, 9, -6, -11],\n [0, 0, 0, 0, -6, -8],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5406", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-14, -1, 2, -10, 3, -6],\n [-1, -1, -8, -1, -6, 0],\n [2, -8, -8, 3, -10, -6],\n [-10, -1, 3, -10, -12, -4],\n [3, -6, -10, -12, 9, -12],\n [-6, 0, -6, -4, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "356", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, 1, -7, 6, 6, 14],\n [1, -6, 8, -10, 7, -8],\n [-7, 8, -2, 2, 0, -10],\n [6, -10, 2, 1, 5, -8],\n [6, 7, 0, 5, 11, 0],\n [14, -8, -10, -8, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[12, 0, -3, 12, -7, 10],\n [0, 4, 9, 15, 5, -3],\n [0, 0, -13, -4, 3, -8],\n [0, 0, 0, 9, 8, 1],\n [0, 0, 0, 0, -4, 9],\n [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": "623", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[13, 0, 8, -9, 1, -8],\n [0, 2, -2, 8, 5, 0],\n [8, -2, 7, 6, 0, 6],\n [-9, 8, 6, 11, 4, 10],\n [1, 5, 0, 4, -11, 14],\n [-8, 0, 6, 10, 14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9646", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -7, 2, 8, -10, -7],\n [-7, -9, -9, 6, -2, 1],\n [2, -9, -13, 12, -10, -7],\n [8, 6, 12, 3, 4, 7],\n [-10, -2, -10, 4, -14, -9],\n [-7, 1, -7, 7, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (2, 6) of the inverse. Round your answer to the nearest integer:\n[[-8, -2, 13, -1, 0, -5],\n [0, -14, -12, 14, -13, -7],\n [0, 0, -9, -12, -10, 3],\n [0, 0, 0, 6, -12, 2],\n [0, 0, 0, 0, 12, 15],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-138", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[12, -14, -4, 6, -7, 12],\n [0, 13, -4, 13, -3, 11],\n [0, 0, 1, -11, 4, -3],\n [0, 0, 0, -1, -1, 2],\n [0, 0, 0, 0, -3, -5],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1980", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[2, 6, -2, -4, 6, -8],\n [6, 5, 4, -2, -6, 2],\n [-2, 4, -5, -7, 5, -2],\n [-4, -2, -7, -11, -10, -6],\n [6, -6, 5, -10, -1, -4],\n [-8, 2, -2, -6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, -7, -2, 13, -8],\n [-2, -6, -2, 8, 2, 6],\n [-7, -2, -12, -10, -10, -6],\n [-2, 8, -10, -9, 4, -1],\n [13, 2, -10, 4, 4, 2],\n [-8, 6, -6, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, -5, 2, 12, -2],\n [0, -10, 15, 13, -7, 6],\n [0, 0, 12, -4, 15, -12],\n [0, 0, 0, 8, -6, 10],\n [0, 0, 0, 0, -9, 7],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -2, -7, 0, -12, 0],\n [-2, -7, -8, 8, 4, 3],\n [-7, -8, 3, 2, -2, -5],\n [0, 8, 2, 10, -8, 4],\n [-12, 4, -2, -8, 1, -5],\n [0, 3, -5, 4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, 7, 0, 2, 5, 2],\n [7, 14, -11, -10, -4, -4],\n [0, -11, 12, 5, 4, 6],\n [2, -10, 5, 15, -6, 0],\n [5, -4, 4, -6, -12, -9],\n [2, -4, 6, 0, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, 3, -15, 1, 11, 15],\n [0, -10, -9, 9, -10, -11],\n [0, 0, 2, 8, 15, 1],\n [0, 0, 0, 11, 7, -9],\n [0, 0, 0, 0, -9, 0],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 4) of the inverse. Round your answer to the nearest integer:\n[[3, 4, 12, 9, 10, -1],\n [0, -15, -1, 15, -4, -9],\n [0, 0, 4, 13, -5, 1],\n [0, 0, 0, 12, -14, 7],\n [0, 0, 0, 0, 12, -6],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[1, -5, 0, -4, -6, 4],\n [-5, 1, 10, -4, 9, 2],\n [0, 10, 13, -3, -9, 6],\n [-4, -4, -3, 9, 8, 1],\n [-6, 9, -9, 8, 13, -4],\n [4, 2, 6, 1, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[11, 11, 10, -5, -2, 2],\n [-9, -11, 0, -5, 6, -13],\n [0, -5, -6, 7, 7, -14],\n [0, 1, -6, 2, -4, -8],\n [11, 10, -13, 11, 4, 8],\n [-13, -10, -14, -13, 1, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1504", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (1, 5) rounded to the nearest integer?\n[[-12, 6, 15, 7, -14, 8],\n [12, -7, -2, 10, -5, -14],\n [5, -14, 11, -11, -9, 6],\n [-12, -2, -14, 7, -4, -6],\n [9, -15, 3, 7, 0, -1],\n [-2, -7, 13, 5, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -6, -12, -3, -6, 2],\n [-6, -1, -5, 8, -8, 2],\n [-12, -5, -10, -7, 0, 12],\n [-3, 8, -7, 15, 3, -2],\n [-6, -8, 0, 3, -14, -4],\n [2, 2, 12, -2, -4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[3, 3, 5, -13, -10, -14],\n [8, -3, 11, 12, 11, -7],\n [-3, 15, 7, -2, 3, -5],\n [-2, 0, -6, 4, 0, 12],\n [10, -14, 9, 0, -2, 5],\n [12, 2, 10, -10, -9, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-14, -1, 1, -3, -9, -15],\n [-13, 4, 2, -9, 5, 1],\n [12, -4, 0, 8, -6, 7],\n [0, 4, 2, -1, 7, -5],\n [2, -10, -15, 14, 7, -9],\n [-4, 4, -12, 15, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-14, -4, -8, -3, 3, 6],\n [-4, -13, 4, -14, -2, -11],\n [-8, 4, 14, -9, 2, 3],\n [-3, -14, -9, 8, 4, -14],\n [3, -2, 2, 4, -3, -11],\n [6, -11, 3, -14, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, -2, -2, -8, -5],\n [0, -8, 11, -2, 4, 10],\n [-2, 11, -5, 0, 4, 6],\n [-2, -2, 0, 11, -8, -6],\n [-8, 4, 4, -8, 10, -3],\n [-5, 10, 6, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-12, 0, -6, -3, -10, 1],\n [0, -7, 11, -9, -3, -3],\n [-6, 11, -2, 12, -8, 9],\n [-3, -9, 12, -15, 6, 9],\n [-10, -3, -8, 6, 13, 2],\n [1, -3, 9, 9, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 11, 9, 15, -4, -5],\n [9, 13, -2, 6, 4, -3],\n [-14, 11, 4, -9, -15, 14],\n [9, -13, 13, 13, 4, -4],\n [-11, -4, 13, -13, 4, -11],\n [12, -15, 0, 14, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -6, -3, 0, 14, 4],\n [13, 9, -12, -2, 1, 12],\n [-11, -3, 9, -13, -11, 0],\n [3, 12, 3, 1, 2, 2],\n [9, 7, -8, 2, -7, 13],\n [3, -6, 13, -14, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-190", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[9, 4, -2, 12, 7, -6],\n [4, 4, -3, 8, 4, 0],\n [-2, -3, 4, -3, -10, 6],\n [12, 8, -3, 3, 6, 2],\n [7, 4, -10, 6, 4, 14],\n [-6, 0, 6, 2, 14, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, -12, -3, -10, 10, 6],\n [-12, 4, -6, 4, 11, -10],\n [-3, -6, 12, 3, 4, -10],\n [-10, 4, 3, 0, 3, -4],\n [10, 11, 4, 3, 9, 3],\n [6, -10, -10, -4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1618", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 2, -4, 2, 4],\n [10, -10, -6, -4, -1, -1],\n [2, -6, 12, 2, 7, -2],\n [-4, -4, 2, -10, 14, -10],\n [2, -1, 7, 14, 4, 5],\n [4, -1, -2, -10, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-3, 2, 2, 4, 0, -8],\n [2, -9, 2, 2, -11, 0],\n [2, 2, 2, 14, 2, 8],\n [4, 2, 14, -14, -10, -11],\n [0, -11, 2, -10, 11, -8],\n [-8, 0, 8, -11, -8, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-3, 0, -3, -14, 3, 3],\n [13, 3, 2, 9, -10, -14],\n [3, 10, -10, 4, 7, 6],\n [-1, -10, 12, -13, -5, -8],\n [9, 6, 2, 1, 3, 3],\n [8, 5, 1, 11, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, 10, 15, 13, 0, -10],\n [0, 10, 4, -14, 9, 15],\n [0, 0, -3, 12, 2, 1],\n [0, 0, 0, -13, 6, -9],\n [0, 0, 0, 0, -15, -12],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2904", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, 4, 0, 1],\n [1, 2, -2, 2, -12, 14],\n [0, -2, -4, 3, 0, -2],\n [4, 2, 3, 14, -10, -11],\n [0, -12, 0, -10, -9, 2],\n [1, 14, -2, -11, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-134", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 7, 15, 10, 6, -10],\n [0, -9, 6, -14, -5, 5],\n [0, 0, -8, 10, -5, 2],\n [0, 0, 0, -12, -12, 12],\n [0, 0, 0, 0, 13, -1],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[4, 11, -9, -8, -8, 14],\n [0, -14, -2, -6, 2, 2],\n [0, 0, 4, -11, 4, 15],\n [0, 0, 0, -6, 1, 14],\n [0, 0, 0, 0, 1, 12],\n [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": "2833", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[14, -5, -13, 6, -6, -5],\n [0, -15, -10, -11, -9, 6],\n [0, 0, -9, -14, 12, -15],\n [0, 0, 0, 2, -4, -9],\n [0, 0, 0, 0, -6, 13],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -8, 7, -10, -15],\n [8, -15, -8, -5, 2, 8],\n [-6, -4, 4, 7, 0, -11],\n [0, 8, -4, 15, -10, 14],\n [15, -11, -15, 3, -6, 9],\n [15, -2, 9, 5, -13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, 15, 1, 2, -4, -11],\n [14, -7, -4, 4, -7, -13],\n [-15, 6, -1, -6, -2, -9],\n [-12, 10, -11, 4, 0, -13],\n [1, -3, -10, 10, -11, 0],\n [-5, 1, -11, -10, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-15, 14, 5, -6, 1, 11],\n [-13, 12, 13, -14, 13, 1],\n [-12, -14, -11, -6, -15, 12],\n [10, -15, 11, 10, -12, -9],\n [-2, -2, 2, -14, -15, 5],\n [6, 0, 13, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, -3, 4, 6, -2],\n [10, -6, -5, -6, -4, 1],\n [-3, -5, -4, -10, 2, -6],\n [4, -6, -10, 11, 0, -6],\n [6, -4, 2, 0, 5, 2],\n [-2, 1, -6, -6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 4, -10, -4, 9, 14],\n [7, 2, 11, -14, 3, 8],\n [-6, 15, 9, 13, 14, -13],\n [9, 12, -4, 10, 0, -4],\n [-8, -11, -5, -6, -13, 11],\n [7, -7, -4, -10, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-73", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 7, 8, 13, -2, 12],\n [0, 2, -6, 2, -4, 3],\n [0, 0, -2, 7, -10, -2],\n [0, 0, 0, -4, -11, -14],\n [0, 0, 0, 0, 1, 15],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13236", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, 0, 7, -6, -4],\n [0, 8, -3, 4, 8, 8],\n [0, -3, 7, -2, 6, -3],\n [7, 4, -2, 7, 6, 0],\n [-6, 8, 6, 6, 13, 6],\n [-4, 8, -3, 0, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-165", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-6, -8, 9, 10, 2, 10],\n [-8, -2, -3, 2, 3, 2],\n [9, -3, -7, -2, -1, 1],\n [10, 2, -2, -5, 2, -5],\n [2, 3, -1, 2, -10, 5],\n [10, 2, 1, -5, 5, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[9, -13, -8, 12, -13, -14],\n [0, -2, 4, 13, 5, 6],\n [0, 0, -15, -1, 4, 6],\n [0, 0, 0, -7, -13, -14],\n [0, 0, 0, 0, -7, 9],\n [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": "455", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, 12, 14, -12, -13, -1],\n [0, 15, 15, -15, 2, 7],\n [0, 0, 14, -3, 1, 2],\n [0, 0, 0, 9, -9, -9],\n [0, 0, 0, 0, -4, -4],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-92", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[8, 13, 0, -11, -11, 4],\n [0, 5, 2, 2, -11, -5],\n [0, 0, 1, 9, 2, -2],\n [0, 0, 0, 2, 14, 4],\n [0, 0, 0, 0, -6, -1],\n [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": "-2200", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 5, -2, 1, 4, 11],\n [5, 1, -4, 6, 0, 4],\n [-2, -4, 7, -4, -4, 2],\n [1, 6, -4, -11, -2, 0],\n [4, 0, -4, -2, -3, 2],\n [11, 4, 2, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-77", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, 11, -11, -11, -9, 0],\n [0, 15, -10, -14, 15, -3],\n [0, 0, 4, -5, 10, 5],\n [0, 0, 0, 6, 3, 4],\n [0, 0, 0, 0, -11, -2],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-1, 12, -7, -13, 7, -7],\n [0, -12, 3, 8, -12, -7],\n [0, 0, 4, 3, -13, -6],\n [0, 0, 0, -6, -6, 2],\n [0, 0, 0, 0, -8, 10],\n [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": "10422", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[14, -11, -3, 6, 4, -9],\n [0, -9, 11, 9, 6, 0],\n [-3, 1, -7, -4, -3, 10],\n [-7, -11, -9, -15, -12, 12],\n [10, -12, 0, -11, 6, -12],\n [-10, 10, 7, -13, 9, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[1, 13, 2, 2, 10, 9],\n [-4, 9, 9, -15, 7, 15],\n [-4, -5, -3, -13, 11, 9],\n [-8, -13, 1, 9, -3, -6],\n [1, 15, -13, -3, 6, -10],\n [-2, 11, -6, 4, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, -6, -10, -6, -11, 13],\n [0, -9, -5, 0, 9, -4],\n [0, 0, 7, 4, 10, -11],\n [0, 0, 0, -10, 13, -7],\n [0, 0, 0, 0, 2, 3],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3212", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[2, 2, -7, -6, 6, 12],\n [2, -2, -9, 10, -2, -2],\n [-7, -9, 3, 2, 1, 4],\n [-6, 10, 2, 11, 4, -10],\n [6, -2, 1, 4, -15, -12],\n [12, -2, 4, -10, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, 3, 0, -6, -8, -6],\n [3, 6, 8, 3, -7, 1],\n [0, 8, 5, 6, 8, 10],\n [-6, 3, 6, 4, 7, 0],\n [-8, -7, 8, 7, -15, 9],\n [-6, 1, 10, 0, 9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "270", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-13, -14, -10, -5, 13, -13],\n [0, -15, -5, -3, -11, 2],\n [0, 0, -1, 4, 4, 4],\n [0, 0, 0, -8, 12, -3],\n [0, 0, 0, 0, 13, -2],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-10, 11, 1, 5, 8, 15],\n [0, -4, 10, 9, -12, -6],\n [0, 0, 5, 15, 11, -8],\n [0, 0, 0, 14, 5, -15],\n [0, 0, 0, 0, -9, 15],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3879", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, -6, -12, -10, 2],\n [2, -5, 0, 12, -3, -2],\n [-6, 0, 12, 4, -6, -2],\n [-12, 12, 4, -9, 9, 6],\n [-10, -3, -6, 9, -5, -9],\n [2, -2, -2, 6, -9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 6, -2, -6, 12, 0],\n [6, 6, 6, 3, 6, 0],\n [-2, 6, -10, -8, 2, 1],\n [-6, 3, -8, -5, 0, -6],\n [12, 6, 2, 0, 12, -2],\n [0, 0, 1, -6, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1536", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, -2, -2, -8, -8, -10],\n [-2, 5, -1, 4, -4, 2],\n [-2, -1, -7, 4, 6, 1],\n [-8, 4, 4, 3, 2, -10],\n [-8, -4, 6, 2, 3, 4],\n [-10, 2, 1, -10, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-302", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, -3, 5, -11, -7, 13],\n [-13, -6, -1, 4, 5, 1],\n [7, 8, 15, -10, 9, -13],\n [2, -11, -3, 9, 11, -15],\n [1, 10, -13, 10, 3, 5],\n [4, 6, -4, -8, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 4) rounded to the nearest integer?\n[[-5, 4, -15, 13, 0, 14],\n [0, -9, -10, 5, -12, 6],\n [0, 0, 3, 9, -13, -12],\n [0, 0, 0, -14, -5, 0],\n [0, 0, 0, 0, -14, -10],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, 0, -2, -6, -3, -15],\n [0, 14, 6, -4, 14, 1],\n [0, 0, -11, 3, -11, -1],\n [0, 0, 0, 12, -2, -12],\n [0, 0, 0, 0, -13, -3],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-14, -13, 13, 8, -8, -5],\n [0, -12, -7, 8, 1, 8],\n [0, 0, -1, 4, 10, 6],\n [0, 0, 0, -12, 8, 8],\n [0, 0, 0, 0, -2, 6],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3934", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[11, -3, -4, 3, 3, 4],\n [-14, 13, 13, 5, -13, -6],\n [-11, -4, 13, -9, -7, -14],\n [9, -6, -10, -4, -10, 11],\n [-13, 14, -6, 13, -7, 4],\n [-11, -13, -11, -8, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-106", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 6, 15, 15, 1, -5],\n [10, 0, 12, -10, 12, -5],\n [-6, 7, 14, -7, 12, 8],\n [11, 12, 8, -1, -9, 2],\n [-15, -1, -14, 15, 6, 13],\n [-14, -6, 4, -1, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[6, 4, 9, 4, 6, 2],\n [4, 6, -2, -3, 8, -6],\n [9, -2, 6, 8, 6, -11],\n [4, -3, 8, 6, -2, 0],\n [6, 8, 6, -2, -10, 8],\n [2, -6, -11, 0, 8, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1190", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, -5, 8, 8, -1, -7],\n [-13, 1, 9, 1, -13, 3],\n [-7, 15, 1, 7, 2, 7],\n [15, -1, -15, 13, 10, -6],\n [-8, -6, 13, 10, -14, 3],\n [-2, -8, 3, -15, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-219", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 5) of the inverse. Round your answer to the nearest integer:\n[[8, -1, 4, 8, 14, -11],\n [0, 1, 13, -6, -11, -5],\n [0, 0, -9, 3, -9, -2],\n [0, 0, 0, -3, 11, -15],\n [0, 0, 0, 0, -15, -12],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 5) of the inverse. Round your answer to the nearest integer:\n[[1, -4, -1, -4, 12, 4],\n [-4, -13, -2, 8, 14, 1],\n [-1, -2, -4, -4, 6, -6],\n [-4, 8, -4, 9, -1, 8],\n [12, 14, 6, -1, -6, 6],\n [4, 1, -6, 8, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -11, 0, 7, -9, 0],\n [0, -15, -13, 9, -8, 2],\n [0, 0, 2, 8, 3, -9],\n [0, 0, 0, 15, 11, -10],\n [0, 0, 0, 0, -4, -15],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-100", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, 0, -6, -9],\n [1, 7, -2, 13, -8, -4],\n [-4, -2, -4, 6, -7, 10],\n [0, 13, 6, 9, 4, 2],\n [-6, -8, -7, 4, -11, 7],\n [-9, -4, 10, 2, 7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, -1, 2, -2, 12, 8],\n [-1, 4, 8, 6, 1, 0],\n [2, 8, 4, 7, -8, 0],\n [-2, 6, 7, -14, 3, 6],\n [12, 1, -8, 3, 7, 4],\n [8, 0, 0, 6, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, 2, 1, 12, -1, 11],\n [2, -7, -4, 4, 4, 2],\n [1, -4, 14, 0, -8, 2],\n [12, 4, 0, 8, -6, 7],\n [-1, 4, -8, -6, -11, 1],\n [11, 2, 2, 7, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-118", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 0, -2, -4, -2, 8],\n [0, -6, 14, 10, -2, 0],\n [-2, 14, 4, -8, 0, 2],\n [-4, 10, -8, 13, 4, 1],\n [-2, -2, 0, 4, 10, -8],\n [8, 0, 2, 1, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[0, -2, 5, 0, 15, 11],\n [-12, -15, -15, 13, 6, -1],\n [4, 4, -13, -2, -7, 3],\n [-8, -14, -12, -15, -5, -11],\n [-14, 11, -3, 1, 1, 2],\n [5, 12, 15, 15, -7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[12, 4, 15, -13, -8, -13],\n [-15, 4, 11, -3, 5, -11],\n [0, 5, 8, 0, 8, -4],\n [-3, -12, 15, -7, 0, -15],\n [-11, 5, -11, 8, 9, 3],\n [-7, 13, 11, -8, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/180 * A where A =\n[[-1, -12, -1, -3, 12, 2],\n [4, -11, 2, 12, -8, -15],\n [3, 7, 10, 1, 13, 11],\n [15, -14, 3, 14, 0, 14],\n [2, -14, 12, 11, -10, -9],\n [-10, 11, -10, 15, -7, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/180 * A where A =\n[[14, 8, 6, 5, -7, -4],\n [0, 7, -10, 7, 12, -12],\n [0, 0, 2, 13, 4, -11],\n [0, 0, 0, -15, -1, -13],\n [0, 0, 0, 0, 5, -8],\n [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": "129", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 5) of the inverse. Round your answer to the nearest integer:\n[[14, -10, -8, -9, 3, -9],\n [-10, -12, 1, -4, -3, 4],\n [-8, 1, -7, 11, -2, 2],\n [-9, -4, 11, 3, 10, 4],\n [3, -3, -2, 10, 14, 4],\n [-9, 4, 2, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -13, 10, -3, -4, -10],\n [6, 5, 13, -3, -2, -9],\n [-11, -2, 2, -12, -15, -9],\n [4, -3, -12, -3, -12, -13],\n [-8, 4, -8, 9, 1, -1],\n [-12, -10, 8, 14, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, -3, 2, -2, 2],\n [-4, 11, 0, -8, 7, 6],\n [-3, 0, -1, -5, 6, 4],\n [2, -8, -5, -15, 2, -14],\n [-2, 7, 6, 2, -11, 0],\n [2, 6, 4, -14, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1946", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-8, -5, -2, 13, 9, 7],\n [-3, 3, -4, 6, 3, 10],\n [-12, 12, -12, -13, 10, -10],\n [-11, -5, 9, -7, -13, 13],\n [-7, 13, -4, -13, 4, 1],\n [5, -4, 9, 15, 2, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "353", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-6, 2, 14, -8, -7, 3],\n [-3, 15, 9, -10, 6, -9],\n [12, 5, -10, -5, 1, 3],\n [12, 9, -4, 5, 5, 8],\n [11, 11, -3, 2, 13, -9],\n [9, 7, 12, -11, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (6, 3) rounded to the nearest integer?\n[[6, -12, 14, 12, 7, -15],\n [-12, -13, 13, -12, -15, -4],\n [-3, -14, 12, 11, 13, -7],\n [15, -9, -3, 6, -14, -15],\n [2, -9, 2, 3, -8, 7],\n [-4, -5, 11, 14, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -13, 0, -4, 4, 8],\n [-13, 7, 6, 8, -2, 0],\n [0, 6, -7, -10, -10, 4],\n [-4, 8, -10, 8, 3, 4],\n [4, -2, -10, 3, -5, -8],\n [8, 0, 4, 4, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[5, -1, 13, -10, -11, 6],\n [0, -13, -5, -5, 0, -13],\n [0, 0, 3, -5, -2, -14],\n [0, 0, 0, 4, -15, -10],\n [0, 0, 0, 0, -10, -15],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[6, -5, -12, 14, 1, -11],\n [0, 9, 8, 15, -8, 5],\n [0, 0, -6, -9, 1, 12],\n [0, 0, 0, 3, -7, 8],\n [0, 0, 0, 0, 11, -10],\n [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": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-6, -2, -4, -4, 0, 2],\n [-2, -9, -3, 2, 2, 0],\n [-4, -3, 12, 13, 4, 2],\n [-4, 2, 13, 9, -2, -4],\n [0, 2, 4, -2, -13, 1],\n [2, 0, 2, -4, 1, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, 11, -1, -10, -4, -14],\n [0, 4, 9, 9, 5, -4],\n [0, 0, -10, 8, 1, 11],\n [0, 0, 0, 7, -9, -14],\n [0, 0, 0, 0, -3, 8],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1317", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[11, 8, -7, 13, -2, -3],\n [0, -5, -4, 6, -13, -15],\n [0, 0, 10, 3, -3, -9],\n [0, 0, 0, -13, -10, 12],\n [0, 0, 0, 0, 14, 9],\n [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": "55", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[4, 1, -7, -3, 9, -3],\n [-11, -2, -5, 9, 15, 10],\n [-2, 9, -9, 8, 1, -12],\n [-6, -6, -1, 4, -4, -7],\n [-13, -1, -4, 10, -1, 10],\n [-15, -1, -5, -11, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[4, 9, -10, 6, -13, -6],\n [10, 5, 10, 6, 14, -12],\n [-3, 3, -11, 7, 11, 6],\n [2, -15, 5, 5, 12, 0],\n [0, 0, 12, 6, 3, 0],\n [-15, 15, 4, 4, -6, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-2, -4, -3, 12, -1, 0],\n [-4, 1, -8, 6, 8, -4],\n [-3, -8, -3, 8, 2, 9],\n [12, 6, 8, 4, -13, -12],\n [-1, 8, 2, -13, 12, 4],\n [0, -4, 9, -12, 4, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-88", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the value at position (2, 5) rounded to the nearest integer?\n[[-10, -10, 9, 1, 10, 6],\n [0, -8, 8, -4, -1, 15],\n [0, 0, 5, 10, 4, 12],\n [0, 0, 0, 2, 12, -14],\n [0, 0, 0, 0, 5, 2],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, 2, -2, 8, -2, 3],\n [2, 9, 9, -8, -7, -4],\n [-2, 9, -5, 2, -8, -2],\n [8, -8, 2, 12, -8, -4],\n [-2, -7, -8, -8, -11, 10],\n [3, -4, -2, -4, 10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-100", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -8, 3, 5, -5, 2],\n [-6, 10, 12, 4, -4, 4],\n [12, 13, -8, 3, 5, 0],\n [11, 5, 2, -7, -12, -7],\n [9, -14, -7, -7, 2, -5],\n [-3, -10, -7, 0, -12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, -1, 9, -10, -5, 11],\n [14, 4, 1, -12, 3, -9],\n [-5, -3, 11, 10, 5, 12],\n [-13, -2, -14, 13, 2, -11],\n [-3, -3, 8, 8, -2, -4],\n [5, -3, 2, -3, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, -1, -3, 10, -5, 6],\n [-1, -2, 14, -12, 14, -6],\n [-3, 14, -9, -12, 8, -12],\n [10, -12, -12, -7, 2, -1],\n [-5, 14, 8, 2, -2, 9],\n [6, -6, -12, -1, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[-1, 14, 2, -5, -12, 12],\n [4, -5, -6, 6, -3, 6],\n [-8, 12, -3, -7, 14, -15],\n [-15, -1, 6, -12, 11, 4],\n [-15, 9, -4, -5, 3, -1],\n [5, -6, -15, 8, -13, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, -15, -6, 6, -15, 15],\n [-1, -13, 5, 4, 7, 6],\n [-4, 3, 0, 11, -8, 8],\n [-2, 2, 7, 14, -15, -14],\n [8, -4, 1, -14, 12, 1],\n [5, -9, -10, -10, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-11, -1, 10, -9, -13, 9],\n [0, -13, 14, -2, 6, -13],\n [0, 0, 3, -12, 14, -14],\n [0, 0, 0, 8, -4, -3],\n [0, 0, 0, 0, 4, 5],\n [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": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, -8, -14, -9, -5],\n [1, 8, 13, -2, 12, 14],\n [-3, -1, 6, 12, 5, 9],\n [-7, -13, 9, -3, 15, -3],\n [-7, 2, -11, -5, -14, 1],\n [7, 4, 5, -12, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[2, 8, 4, -8, 3, -4],\n [12, -5, 0, -11, 12, -13],\n [-4, -1, 0, -3, -9, -1],\n [-13, 15, -4, -8, 9, 13],\n [-4, 2, -13, -4, 13, 7],\n [5, 10, 7, -14, -2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[14, 11, -9, 9, 9, -4],\n [0, 1, -7, -8, 7, -10],\n [0, 0, -6, 7, 11, 9],\n [0, 0, 0, -2, 10, 3],\n [0, 0, 0, 0, 10, 13],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10575", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -2, -8, -5, -6, 2],\n [0, -12, -4, 2, 13, -8],\n [0, 0, -9, 15, -15, 15],\n [0, 0, 0, -13, 13, -13],\n [0, 0, 0, 0, 12, -12],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, 14, 10, 4, -14, 2],\n [9, -5, -15, 0, 1, 0],\n [-6, 1, 14, -13, 2, 3],\n [-2, 5, 9, -14, -4, -5],\n [15, 14, 1, 11, -10, 3],\n [-3, -9, 6, -5, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 5, -15, 14, 3, 3],\n [7, -1, -2, 13, -13, 11],\n [5, 4, -12, 13, -9, -15],\n [7, 15, 8, 3, 15, -13],\n [4, -1, -3, 6, -2, -9],\n [-15, 15, -3, -12, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -14, 1, -15, 10, -2],\n [0, 6, 12, 5, -15, 10],\n [0, 0, -5, -9, 12, 9],\n [0, 0, 0, 6, -13, -15],\n [0, 0, 0, 0, 5, 8],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -2, -6, 5, -9, 13],\n [15, -8, 14, -8, -9, -3],\n [-2, 3, -5, -14, 1, -10],\n [13, -7, 3, -11, -7, 14],\n [14, 9, -9, 14, -12, 11],\n [2, 2, 4, 1, 14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, 10, 13, 6, -6, 7],\n [10, -11, -2, -2, -10, -8],\n [13, -2, 4, 2, -3, -2],\n [6, -2, 2, 15, -13, 8],\n [-6, -10, -3, -13, 1, -2],\n [7, -8, -2, 8, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2248", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[4, -12, -1, -7, -10, -4],\n [2, 7, -1, 13, 3, -7],\n [6, 8, -3, 0, -3, -15],\n [2, 6, -13, 1, 6, -11],\n [13, 9, -10, 5, 1, 15],\n [1, 11, -15, -9, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "469", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[0, -11, 0, -12, -5, -2],\n [13, -3, 11, 8, 11, -8],\n [5, 15, 4, -1, 2, -9],\n [5, 3, 9, -7, -5, 15],\n [11, -6, -2, 0, 11, -8],\n [-15, -4, -13, -14, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-14, 0, 10, 1, 6, -4],\n [0, 14, -2, -2, -4, -4],\n [10, -2, 2, 8, 0, -4],\n [1, -2, 8, -6, 2, 3],\n [6, -4, 0, 2, 7, 0],\n [-4, -4, -4, 3, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -11, 10, -14, -4, 5],\n [-11, -9, -12, 14, -5, 6],\n [-7, -12, 11, 14, 6, 13],\n [12, -7, 10, -4, 0, -15],\n [-8, -15, 4, 3, -12, -2],\n [7, 13, -2, -7, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -1, -6, 1, -7, -12],\n [0, 13, -2, -13, 13, 9],\n [0, 0, 6, -15, -15, -3],\n [0, 0, 0, -6, -1, -8],\n [0, 0, 0, 0, 7, -3],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2196", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -4, 13, 5, 4, 4],\n [0, -8, 8, -5, -9, -15],\n [0, 0, -12, -15, -5, 14],\n [0, 0, 0, -12, -14, -9],\n [0, 0, 0, 0, -4, 14],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-137", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -6, 2, -2, 4],\n [4, 3, -12, -6, 4, -4],\n [-6, -12, -10, 2, -4, -7],\n [2, -6, 2, -13, -6, 6],\n [-2, 4, -4, -6, -5, -4],\n [4, -4, -7, 6, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, -8, 8, -2, 2, -11],\n [0, 6, 9, 6, 10, 6],\n [0, 0, -1, -10, -7, -6],\n [0, 0, 0, -2, -12, 15],\n [0, 0, 0, 0, -9, 14],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13937", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 13, 13, -15, 9, 10],\n [0, 9, -1, 15, -12, -1],\n [0, 0, -3, -9, 10, 14],\n [0, 0, 0, -5, -2, -10],\n [0, 0, 0, 0, 11, 10],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8523", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 10, -4, 7, 11, -7],\n [-2, -10, -1, -3, -9, -5],\n [-6, -15, -9, 2, 7, -13],\n [-7, 13, -11, 7, 8, -3],\n [0, 0, -4, 2, -5, 1],\n [-9, -1, -10, -10, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 4) of the inverse of matrix 1/180 * A where A =\n[[4, 3, -14, -13, -2, 6],\n [9, -12, 6, 1, 12, -10],\n [12, 3, -7, -12, -9, -12],\n [-5, 6, 14, 7, -14, -6],\n [-10, -8, -1, -3, 13, 15],\n [12, 6, -14, 4, -15, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -2, 8, -4, -5, -2],\n [-2, 11, 0, -4, -2, 7],\n [8, 0, 14, -6, -8, 3],\n [-4, -4, -6, -5, -4, 8],\n [-5, -2, -8, -4, -8, -3],\n [-2, 7, 3, 8, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[15, 6, -8, 8, 3, 4],\n [14, -10, 2, 12, 12, -5],\n [-4, 7, -14, 11, -11, 12],\n [-12, -7, -3, -3, -1, -14],\n [7, -3, -9, 7, 1, -8],\n [2, -1, -1, -11, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-216", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the inverse of matrix 1/180 * A where A =\n[[13, -11, 7, -10, 13, 15],\n [-4, -11, 4, -8, -5, -2],\n [8, 1, -6, -14, -13, -3],\n [1, 11, -13, -6, 12, -8],\n [-12, -3, 13, -9, -9, 0],\n [11, -11, 12, 1, -6, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[11, -12, -10, 15, -8, -3],\n [0, 4, -12, -11, -6, -11],\n [0, 0, 13, 8, -6, 13],\n [0, 0, 0, 4, -4, 7],\n [0, 0, 0, 0, -4, -3],\n [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": "-384", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-11, 15, 13, 11, 14, 2],\n [-2, 2, 13, 4, -15, -9],\n [13, 1, -13, -6, -9, 11],\n [12, -4, 6, 15, -1, 7],\n [5, 0, -8, -10, 12, -12],\n [14, -5, 1, -14, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-12, -13, -9, -9, 0, -14],\n [0, -1, 15, 11, 0, -15],\n [0, 0, -9, 0, -6, -4],\n [0, 0, 0, -1, -2, 3],\n [0, 0, 0, 0, 14, 10],\n [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": "-3740", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, 7, -15, -3],\n [0, -13, 1, 2, 9, -6],\n [0, 0, -3, 4, -4, -12],\n [0, 0, 0, -1, 12, 0],\n [0, 0, 0, 0, -4, 0],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9719", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -12, -4, 2, 2, -3],\n [-12, -12, 2, 6, -10, -2],\n [-4, 2, 11, 6, 12, -6],\n [2, 6, 6, 5, 0, 14],\n [2, -10, 12, 0, -12, 2],\n [-3, -2, -6, 14, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, -11, -7, -15, -12],\n [10, -9, -5, -2, -6, 3],\n [-8, -13, -8, 13, 2, -11],\n [4, -5, -7, 3, -4, 11],\n [-11, 0, 10, 9, -3, -10],\n [0, 2, 1, -4, 11, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-9, -2, 12, 2, 7, -15],\n [0, -6, 15, -1, 13, -5],\n [0, 0, 5, 14, 0, 14],\n [0, 0, 0, 1, 7, -5],\n [0, 0, 0, 0, 11, -1],\n [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": "-1271", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-7, 0, -8, -7, -12, 2],\n [0, -9, -2, 0, 2, -8],\n [-8, -2, 8, -10, 4, -5],\n [-7, 0, -10, -6, 10, 5],\n [-12, 2, 4, 10, 11, -2],\n [2, -8, -5, 5, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[-8, -9, -5, -5, 10, 1],\n [0, -2, -14, 4, 5, -8],\n [0, 0, -14, 5, -1, -11],\n [0, 0, 0, 3, -11, 7],\n [0, 0, 0, 0, -3, 15],\n [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": "578", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, -3, 14, -14, -12, -13],\n [0, -12, 7, 5, -12, 14],\n [0, 0, 7, 12, 14, 11],\n [0, 0, 0, -13, -9, -4],\n [0, 0, 0, 0, -8, 13],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "469", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, -7, 8, 0, 6, 0],\n [-7, 2, -3, -5, 9, -6],\n [13, -6, -10, 0, 9, -4],\n [-12, -11, -14, 3, -15, -12],\n [-4, -14, -4, 15, 0, -14],\n [1, 10, 12, -14, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, 7, -9, 7, -1],\n [4, -4, -11, -2, 0, -5],\n [-4, 3, 1, 14, 8, 10],\n [11, -9, 14, -7, -2, 10],\n [4, -4, -1, -4, 5, 5],\n [13, 7, -3, -7, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, -15, 12, -6, 13, -10],\n [10, -1, -1, -7, -3, 7],\n [-15, -7, -13, 14, -7, 4],\n [15, 9, 13, -1, 8, -9],\n [-12, 9, 4, 1, 6, -12],\n [10, 3, 12, -11, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-213", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, 9, 12, 6, -1, 3],\n [0, 8, -2, 0, 8, -10],\n [0, 0, 5, 1, 0, -14],\n [0, 0, 0, -12, -10, 11],\n [0, 0, 0, 0, -15, 9],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 10, 5, 12, 4, -4],\n [10, -14, 2, -4, 2, -8],\n [5, 2, -3, 8, -7, 0],\n [12, -4, 8, -15, -6, -12],\n [4, 2, -7, -6, -14, -1],\n [-4, -8, 0, -12, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[4, 2, -3, -5, -7, -2],\n [0, 5, -2, 5, 1, 11],\n [0, 0, -2, 10, 11, 8],\n [0, 0, 0, 12, -6, -5],\n [0, 0, 0, 0, -2, 4],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-90", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/180 * A where A =\n[[-3, 4, -2, 8, 2, -8],\n [4, -3, 0, -8, -11, -5],\n [-2, 0, 4, 2, 7, -8],\n [8, -8, 2, -11, 1, -4],\n [2, -11, 7, 1, 14, 12],\n [-8, -5, -8, -4, 12, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-137", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the inverse of matrix 1/180 * A where A =\n[[15, -9, 5, -1, 8, -14],\n [8, 12, 11, -14, -6, -11],\n [11, 13, -12, -1, -3, 1],\n [5, 7, -15, 2, 12, -1],\n [-2, -7, -4, -11, 14, 13],\n [7, -14, 7, 7, -9, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 6) of the inverse. Round your answer to the nearest integer:\n[[-7, 6, -12, -13, 5, 4],\n [6, -15, 10, -2, 0, -6],\n [-12, 10, 12, -5, 2, 10],\n [-13, -2, -5, -5, -10, 1],\n [5, 0, 2, -10, 5, 0],\n [4, -6, 10, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 2, -6, -3, -7, 2],\n [2, -7, -2, 7, 4, -6],\n [-6, -2, -12, -4, -6, -6],\n [-3, 7, -4, -6, 4, 10],\n [-7, 4, -6, 4, -4, 6],\n [2, -6, -6, 10, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-65", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 10, 10, -3, 5, -12],\n [-15, 1, -13, 14, 15, 1],\n [-8, -13, 11, -6, -14, 6],\n [-12, 13, 13, -2, -5, -2],\n [-3, 11, 13, -12, -14, -14],\n [-5, 6, -11, -7, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[15, -5, 3, 3, 0, -9],\n [-5, 12, 4, -4, -8, 6],\n [3, 4, -7, -2, 2, -8],\n [3, -4, -2, -13, 12, 1],\n [0, -8, 2, 12, -1, 3],\n [-9, 6, -8, 1, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "656", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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[[-9, -11, 10, 13, 13, 7],\n [0, 12, 9, -8, 6, -14],\n [0, 0, -2, -12, 8, -1],\n [0, 0, 0, 11, -5, 12],\n [0, 0, 0, 0, 7, 10],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-182", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 7, -15, -7, 5, -3],\n [12, 3, -9, 10, 0, -8],\n [10, 10, 3, -9, 7, -12],\n [-6, 9, -15, 1, 5, -3],\n [3, 10, -3, -7, -11, 7],\n [-15, -14, 15, -5, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-110", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -7, -11, -11, 9, -8],\n [0, -9, 1, 10, 11, -5],\n [0, 0, -13, -3, 2, 4],\n [0, 0, 0, -11, 4, -11],\n [0, 0, 0, 0, 11, 0],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-8, 11, -4, -9, 5, -8],\n [11, -1, -6, 4, 6, 4],\n [-4, -6, -12, -8, 12, -2],\n [-9, 4, -8, 10, 8, -12],\n [5, 6, 12, 8, 15, -2],\n [-8, 4, -2, -12, -2, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 4, 14, 15, -14, -9],\n [9, 0, 6, -12, 5, 11],\n [1, 13, -12, 13, 10, -13],\n [-7, 6, -1, 4, -13, -4],\n [-1, 13, 4, -8, -4, 5],\n [-3, -1, -5, 1, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, 15, -4, 4, 14, 2],\n [0, 15, 0, -13, 14, 11],\n [0, 0, -9, 3, -11, 3],\n [0, 0, 0, -8, 14, -13],\n [0, 0, 0, 0, 10, -3],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-41", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-9, 10, -5, -6, -13, 14],\n [-9, 13, -12, 13, -8, -8],\n [-10, -3, -4, -13, -10, 6],\n [3, -5, -12, -1, -14, -1],\n [1, -14, -9, 10, 0, -11],\n [0, 9, 3, -14, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[-14, 12, 4, 2, 0, 3],\n [12, -11, 3, 12, -2, -3],\n [4, 3, -10, -1, 6, -5],\n [2, 12, -1, 2, -1, 2],\n [0, -2, 6, -1, 3, -6],\n [3, -3, -5, 2, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/180 * A where A =\n[[15, 4, 2, -2, -12, 7],\n [4, -2, 2, -4, -12, -6],\n [2, 2, -11, 12, 6, 6],\n [-2, -4, 12, -7, -4, -10],\n [-12, -12, 6, -4, -5, 8],\n [7, -6, 6, -10, 8, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -15, -3, -5, 13],\n [-12, -12, -1, 11, -13, 8],\n [3, 13, 5, -14, -10, 15],\n [6, 8, -8, 1, -11, -14],\n [10, -4, -11, -6, 12, -7],\n [4, -8, -15, 8, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/180 * A where A =\n[[6, -5, -4, 3, 10, -8],\n [-5, 8, 2, 0, 2, -8],\n [-4, 2, 12, -7, 2, 2],\n [3, 0, -7, 11, 6, 6],\n [10, 2, 2, 6, 10, 11],\n [-8, -8, 2, 6, 11, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "710", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (6, 6) of the inverse. Round your answer to the nearest integer:\n[[-2, -3, 8, -11, -14, 7],\n [7, 3, 14, 1, -5, 0],\n [4, 2, 4, -8, -14, 1],\n [-5, -2, 0, -1, -1, -13],\n [10, -9, 13, -4, 6, 6],\n [7, 8, -13, 3, -6, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-8, 0, 0, -4, 13, 14],\n [13, 7, 10, -11, 4, -10],\n [9, -10, -8, 1, -4, 14],\n [6, 14, -2, -14, 3, -10],\n [2, -12, 6, -11, -10, -1],\n [-10, -8, -7, 5, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, -14, 0, 4, -15, 14],\n [12, 0, -15, -15, -9, 0],\n [1, 0, 0, -10, 2, 6],\n [6, 12, 11, -13, 15, -8],\n [11, -12, 13, 7, -12, 1],\n [6, -11, 9, 15, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, 12, 0, 0, 2, 10],\n [12, 7, 10, -5, 2, 2],\n [0, 10, 10, -4, 8, -7],\n [0, -5, -4, 9, -2, 1],\n [2, 2, 8, -2, -11, -3],\n [10, 2, -7, 1, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/180 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-3, 4, 12, -3, -12, 7],\n [13, 7, -9, 7, -14, 5],\n [10, 2, 5, 12, -10, 0],\n [-13, 6, -1, 5, 4, -6],\n [-7, -5, -2, 8, -4, -9],\n [-5, 15, 1, 9, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/180 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, -3, 0, -13, -11, 7],\n [1, 12, -15, 5, -7, 7],\n [1, 13, -3, -1, 12, 5],\n [15, -8, -8, 12, -14, 7],\n [-6, -11, 0, 9, 3, -15],\n [-3, -12, -9, -15, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/180 * A where A =\n[[-2, -4, 7, -2, 4, -6],\n [-4, -4, 12, -9, 10, -2],\n [7, 12, -14, 0, 8, 6],\n [-2, -9, 0, 2, 8, 3],\n [4, 10, 8, 8, 5, -2],\n [-6, -2, 6, 3, -2, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-113", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-2, 13, 9, 8, 15, -14],\n [-14, 7, 10, -1, -5, 13],\n [15, -6, -13, 1, -7, 14],\n [-1, 14, -2, 3, 1, 6],\n [4, 14, 1, 0, 4, -8],\n [11, -9, 15, -4, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/180 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, 9, -10, 0, 2, 3],\n [7, -13, 13, -13, -11, -13],\n [3, 11, -11, -2, 5, 0],\n [12, 9, -15, 14, 1, -5],\n [14, -7, 5, -12, -14, 12],\n [-7, 6, 15, 9, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "245", "dataset": "MATH"}