{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "400", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "687", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 13, 14, 0, -8, 3],\n [2, -15, -2, 3, -1, 2],\n [-14, 6, 12, 1, 2, 14],\n [-10, 3, 15, -12, -15, -8],\n [13, 7, -9, -13, -6, -6],\n [3, -2, -14, 12, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "836", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(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 to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(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 to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 3, 6, 0, -4, 0],\n [3, -1, 12, 7, 2, -6],\n [6, 12, -4, 6, -4, -3],\n [0, 7, 6, 12, 0, -1],\n [-4, 2, -4, 0, 8, -2],\n [0, -6, -3, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, -3, 7, 12, 3, -8],\n [6, -11, 4, -8, 8, -4],\n [-15, 9, 14, 5, 4, -10],\n [6, 2, -8, -9, -15, 5],\n [0, -4, -10, 4, -14, 13],\n [-2, -12, -15, 7, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 1, -11, -9, 12, 4],\n [13, 4, -12, 12, -10, -9],\n [2, 15, -11, 4, 15, 14],\n [13, -13, -9, 11, 12, 6],\n [-2, -9, -11, 13, 6, -11],\n [14, 7, -14, 14, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[6, -10, -1, 5, -6, 7],\n [0, 8, -9, -11, -15, -3],\n [0, 0, 2, -3, 5, 5],\n [0, 0, 0, -12, 1, -13],\n [0, 0, 0, 0, 5, 4],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\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]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, -12, 10, 11, -2, 6],\n [-5, 11, -6, 3, 2, -10],\n [11, 13, -1, 5, 14, -6],\n [-11, 10, 13, -11, -6, 12],\n [-11, -13, 7, -10, -12, 2],\n [12, -7, 1, 13, -3, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -6, -6, -4, -8, 12],\n [-6, -8, -10, 6, 3, -10],\n [-6, -10, 9, -10, -15, 3],\n [-4, 6, -10, -8, -12, 2],\n [-8, 3, -15, -12, -13, -14],\n [12, -10, 3, 2, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, 2, 2, -9, 8, 10],\n [2, 2, 6, -5, -1, 4],\n [2, 6, -13, 6, -8, 4],\n [-9, -5, 6, -5, -4, -12],\n [8, -1, -8, -4, 2, -6],\n [10, 4, 4, -12, -6, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "996", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "352", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[14, -12, 11, 12, 4, -5],\n [10, 15, -5, 11, 14, -5],\n [-14, 14, 1, -7, 12, 15],\n [12, -14, 13, 8, -1, 0],\n [9, -12, -8, -7, 10, 10],\n [-11, 0, -3, 14, -9, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[0, -6, -7, 10, 8, 0],\n [-6, 11, -9, 0, 8, -2],\n [-7, -9, -5, 0, 7, -6],\n [10, 0, 0, -4, 2, 0],\n [8, 8, 7, 2, 14, -12],\n [0, -2, -6, 0, -12, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "728", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 12, 14, 7, 1],\n [-15, 7, 15, 15, -6, 9],\n [7, -6, 5, 8, -14, -7],\n [6, -3, 9, 0, 2, 3],\n [-4, -8, 1, -1, -6, -1],\n [-1, 15, 7, -9, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "447", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, 5, 14, 13, -15, 4],\n [-10, 13, -1, 10, 10, -2],\n [4, -1, -2, 9, 5, 8],\n [9, 10, -11, -10, 1, -5],\n [0, -4, -1, 7, -12, 11],\n [2, 5, 12, -13, 6, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[15, -5, -1, -4, -13, 1],\n [-13, 3, 4, -12, -13, 10],\n [0, -4, -8, 8, 13, 13],\n [1, -9, -5, 2, -15, -13],\n [-12, -3, -10, 10, -2, -11],\n [0, -1, -1, 14, -12, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "868", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\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]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "848", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 6, 10, 10, 2, 10],\n [6, -6, 0, -5, -3, -4],\n [10, 0, 11, -1, -4, 6],\n [10, -5, -1, 13, -14, -2],\n [2, -3, -4, -14, 4, -11],\n [10, -4, 6, -2, -11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "785", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, 2, -4, -10, -11, 10],\n [0, -4, 11, 15, 10, -5],\n [0, 0, 2, -12, 1, -14],\n [0, 0, 0, -14, -4, 15],\n [0, 0, 0, 0, 9, 5],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -15, -6, -5, 0, -2],\n [0, 8, 1, 9, 2, -4],\n [0, 0, 12, 10, -2, 0],\n [0, 0, 0, 9, 7, -5],\n [0, 0, 0, 0, 9, 2],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "792", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-3, -2, -8, -4, 7, 7],\n [0, 5, 10, -8, 5, 9],\n [0, 0, -10, 7, 3, 7],\n [0, 0, 0, 14, -3, -5],\n [0, 0, 0, 0, 5, 9],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[8, 12, 7, -9, -8, -9],\n [0, 7, 13, -2, 10, 3],\n [0, 0, 15, 9, 15, 2],\n [0, 0, 0, 1, -3, -14],\n [0, 0, 0, 0, 12, -6],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-10, 4, 10, -10, -2, 0],\n [4, 4, 0, -1, 12, 3],\n [10, 0, -7, 10, -6, 2],\n [-10, -1, 10, 3, -9, 2],\n [-2, 12, -6, -9, -15, -2],\n [0, 3, 2, 2, -2, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -15, 7, 7, 10, -3],\n [-9, -1, -4, 11, 10, -15],\n [-1, -12, -3, 7, 11, 9],\n [-11, 13, -14, 7, 10, -15],\n [0, 7, -10, 7, 0, -2],\n [13, 10, -13, -1, -13, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 12, 10, 0, 9, -1],\n [-3, -1, 11, -12, 0, 14],\n [-4, 14, -12, -13, 6, 1],\n [6, 2, 9, 2, 7, 12],\n [1, -4, 7, 5, 8, -12],\n [15, -4, 15, 10, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "878", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "480", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "798", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-4, 2, -7, 5, -10, 0],\n [2, -7, 8, 2, 4, -5],\n [-7, 8, -6, -9, 2, -7],\n [5, 2, -9, -13, 0, 6],\n [-10, 4, 2, 0, -9, -4],\n [0, -5, -7, 6, -4, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "821", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[15, -3, 4, 0, -6, 2],\n [-3, -11, 2, -8, -4, 0],\n [4, 2, 15, 12, -14, -10],\n [0, -8, 12, -10, 8, 1],\n [-6, -4, -14, 8, 9, 13],\n [2, 0, -10, 1, 13, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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": "834", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, 10, -11, 6, -1, -3],\n [0, -15, -5, 7, -15, -5],\n [0, 0, 5, 14, 10, 0],\n [0, 0, 0, 10, 0, -15],\n [0, 0, 0, 0, -10, -2],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -8, 12, -6, 1, 7],\n [0, 13, 10, -10, -2, 6],\n [0, 0, 10, -9, -4, -13],\n [0, 0, 0, 7, 0, -9],\n [0, 0, 0, 0, 5, -7],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -14, 9, -3, -14, 3],\n [0, -14, -13, -10, -13, 15],\n [0, 0, 11, -10, 7, 0],\n [0, 0, 0, 2, -9, -7],\n [0, 0, 0, 0, -5, 9],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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": "224", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-2, 11, 9, -3, 7, 5],\n [-3, 15, -11, 0, 10, -5],\n [6, -11, -3, 12, -5, 9],\n [3, -13, -1, -9, -9, -10],\n [-13, 14, -3, -9, -11, 7],\n [2, 6, 14, -8, 1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, -9, 2, -2, 0, -4],\n [-9, 9, -6, 6, -6, 5],\n [2, -6, -6, 0, -6, -8],\n [-2, 6, 0, 4, -8, 8],\n [0, -6, -6, -8, 15, 0],\n [-4, 5, -8, 8, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\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]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[13, 12, -8, 8, -13, 9],\n [3, -15, -14, -1, 6, 12],\n [-6, 2, 6, -2, 1, 11],\n [-3, -15, -11, 10, -3, 11],\n [9, -2, 8, -13, -1, 3],\n [15, 1, 14, -13, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, 4, -7, 8, -14],\n [-8, 4, -14, -5, 10, -9],\n [-10, 14, -6, -11, -5, -15],\n [-14, 8, -15, 3, -14, 5],\n [4, 13, 7, 5, 8, -12],\n [15, -4, 6, 4, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "923", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[15, -4, 6, 10, 6, 3],\n [-4, 4, 1, 2, 2, -9],\n [6, 1, 8, -2, 6, -6],\n [10, 2, -2, -6, 2, 13],\n [6, 2, 6, 2, -15, -5],\n [3, -9, -6, 13, -5, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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": "98", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[9, 9, 8, 9, 0, 4],\n [0, -10, -11, 5, -12, -14],\n [12, -10, -7, 12, 1, -2],\n [-9, 6, 3, -15, 13, 4],\n [15, 14, 9, -1, 2, -13],\n [2, 14, -14, -6, -5, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "272", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\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]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "830", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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": "736", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\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]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, -15, -4, -14, 11, 12],\n [0, 6, 1, 10, -13, -9],\n [0, 0, 4, -4, -13, 1],\n [0, 0, 0, 6, -10, 9],\n [0, 0, 0, 0, -3, 11],\n [0, 0, 0, 0, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-14, -4, 12, -14, 10, 0],\n [0, -13, -6, 3, -8, -9],\n [0, 0, 13, 12, -11, 0],\n [0, 0, 0, 8, 5, -14],\n [0, 0, 0, 0, -4, -4],\n [0, 0, 0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 0, -2, 1, -2, 1],\n [0, -8, -7, -2, -6, 2],\n [-2, -7, -9, -2, -6, 2],\n [1, -2, -2, -4, 2, -2],\n [-2, -6, -6, 2, -13, -4],\n [1, 2, 2, -2, -4, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix 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 to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 14, 13, 4, -15, -7],\n [-4, -12, 12, 6, -3, -9],\n [-8, 12, -3, -5, -7, 9],\n [8, 0, -6, -5, 15, -4],\n [12, 15, -2, 3, -4, 2],\n [5, 1, -13, -15, 13, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, -2, 1, 9, 3, -15],\n [0, -3, -2, 11, -10, 11],\n [0, 0, 14, -2, -13, 7],\n [0, 0, 0, 3, 12, 7],\n [0, 0, 0, 0, 11, 9],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "792", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -5, -3, 0, 15, 2],\n [15, 1, 1, 13, -5, 4],\n [-6, 13, 0, -14, 1, 6],\n [14, 4, -6, -3, -4, -1],\n [-9, 11, 6, 5, 10, 12],\n [-3, -4, -4, 12, -14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "617", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 9, -14, 7, 10, 14],\n [4, -3, 13, -13, -5, 0],\n [-15, 3, -5, -7, -2, 15],\n [-7, -9, 0, -13, 13, 3],\n [-12, -9, 7, 12, -4, 14],\n [2, 12, 15, -11, 7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 8, 13, 6, -14, -9],\n [0, -7, -11, -1, 2, -12],\n [0, 0, 10, -9, 10, -8],\n [0, 0, 0, 5, 12, 7],\n [0, 0, 0, 0, 1, -11],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, -8, 2, -13, 8, 8],\n [0, -8, -6, -14, -4, 7],\n [0, 0, 5, 7, 8, -13],\n [0, 0, 0, 13, 5, -11],\n [0, 0, 0, 0, -2, 0],\n [0, 0, 0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "880", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 5, 12, -9, 10, -13],\n [0, -10, 5, -7, -6, -12],\n [0, 0, -7, 8, 6, 1],\n [0, 0, 0, -4, 11, -15],\n [0, 0, 0, 0, 3, -10],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\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]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "666", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, 5, 15, -4, 12, -15],\n [0, 1, -7, 7, 3, 9],\n [0, 0, -9, -7, 6, 10],\n [0, 0, 0, -2, -1, -1],\n [0, 0, 0, 0, -8, 15],\n [0, 0, 0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "776", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -7, -10, 4, 10, 14],\n [0, -7, -11, -2, -11, -8],\n [0, 0, -3, -8, -5, 12],\n [0, 0, 0, 3, -10, 6],\n [0, 0, 0, 0, 9, 12],\n [0, 0, 0, 0, 0, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "930", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "24", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, 11, -1, 2, 0],\n [0, 5, 1, -8, -15, 13],\n [0, 0, 11, -13, 0, 12],\n [0, 0, 0, -7, 0, 15],\n [0, 0, 0, 0, -9, 2],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "650", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[14, 9, -3, 0, -9, 0],\n [0, -2, 1, -4, 13, 8],\n [0, 0, -3, 8, 4, -1],\n [0, 0, 0, 6, -14, 12],\n [0, 0, 0, 0, 14, 10],\n [0, 0, 0, 0, 0, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, -12, 4, -10, -2, 1],\n [-12, -13, -4, 8, 3, 3],\n [4, -4, 3, -3, -2, 6],\n [-10, 8, -3, -9, 0, -5],\n [-2, 3, -2, 0, -2, 6],\n [1, 3, 6, -5, 6, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "387", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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": "505", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 4, 3, -4, -2, 0],\n [4, 2, 0, -6, -7, 8],\n [3, 0, -7, 6, -6, -4],\n [-4, -6, 6, -5, -4, 5],\n [-2, -7, -6, -4, 6, -3],\n [0, 8, -4, 5, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "608", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-11, -6, -6, -2, -14, -12],\n [0, 2, -3, 3, -11, 4],\n [0, 0, -5, 14, 14, 10],\n [0, 0, 0, 7, 12, -6],\n [0, 0, 0, 0, -5, 3],\n [0, 0, 0, 0, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(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 to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-12, 12, -1, -2, 5, -5],\n [8, 15, -12, -13, -14, 4],\n [11, -6, 14, -3, 4, 13],\n [10, 5, 13, 7, 9, 2],\n [5, 0, -5, -6, -7, -4],\n [14, 13, 3, -15, 2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "783", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[5, -3, 6, -8, -1, 1],\n [-11, 4, -12, -5, 2, -6],\n [1, 14, -1, -10, 7, 5],\n [0, -1, -8, -7, -5, 11],\n [-14, 11, -3, -12, 11, -7],\n [-11, 3, 6, 15, -13, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "620", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[5, -3, 5, -8, 15, -3],\n [-1, 4, 4, -3, 7, 11],\n [-11, 6, 6, 12, -10, 14],\n [10, -11, -3, 13, -11, 9],\n [-3, 8, 15, 4, 7, -8],\n [12, -7, 5, 3, 15, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 8, 8, 6, -2, -2],\n [8, 9, -1, -6, -8, 2],\n [8, -1, 8, 1, -12, 3],\n [6, -6, 1, -12, -4, -3],\n [-2, -8, -12, -4, 1, 2],\n [-2, 2, 3, -3, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "420", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-8, 0, -11, 2, 4, -2],\n [-14, 7, 7, 14, 15, -13],\n [-2, 13, -9, -1, 1, -15],\n [-7, 6, 13, -2, 0, 12],\n [5, -3, -10, 6, -15, 5],\n [9, -12, -13, 1, 14, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, -1, -9, 3, 4, 6],\n [14, -5, 7, -2, -3, 4],\n [10, 11, 9, -7, -7, 0],\n [-4, -6, -10, 2, -14, 11],\n [4, -7, 3, -10, -14, -1],\n [1, 0, 12, 5, -8, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -8, 8, -9, 5, 2],\n [-2, -1, -6, 10, 5, -4],\n [-9, 12, 12, -9, -5, -3],\n [-1, 2, -9, -10, 7, -5],\n [-8, 4, -15, -8, -8, 3],\n [-13, -11, 14, -13, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\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]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\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": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\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]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\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]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-11, 0, 8, -11, 8, 7],\n [-4, -12, 15, 7, -10, 3],\n [-7, -4, 10, -1, 0, -3],\n [9, 14, 5, 8, -9, 9],\n [7, 4, -12, -5, -8, -10],\n [9, 14, -6, 14, -9, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "828", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -13, 8, -9, -12, -3],\n [0, 1, 11, -9, 1, 10],\n [0, 0, -5, 14, -13, -5],\n [0, 0, 0, -12, -2, -15],\n [0, 0, 0, 0, -1, 15],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\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]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, 8, -10, -4, 5, 1],\n [8, 3, -4, 0, 2, -4],\n [-10, -4, -10, 10, 7, 6],\n [-4, 0, 10, -11, -10, 2],\n [5, 2, 7, -10, -12, -8],\n [1, -4, 6, 2, -8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, 6, 9, -4, 8, -2],\n [6, 3, -12, -7, -10, 4],\n [9, -12, -14, 2, 9, 0],\n [-4, -7, 2, -9, 0, -3],\n [8, -10, 9, 0, -1, -3],\n [-2, 4, 0, -3, -3, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -2, -10, -4, 2, -8],\n [-2, 0, -6, 3, 0, 6],\n [-10, -6, -2, 8, -10, 8],\n [-4, 3, 8, 15, -2, -2],\n [2, 0, -10, -2, 3, 5],\n [-8, 6, 8, -2, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 9, -11, -10, 3, -15],\n [11, 0, 12, 2, 8, -3],\n [-15, -6, -9, -11, -3, 6],\n [0, 8, 4, 6, -2, -5],\n [3, 7, -14, 12, -8, -3],\n [-9, -4, 12, -8, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "746", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, -6, 5, -7, 14, 5],\n [-3, -6, -10, -5, -12, 10],\n [-2, 14, 15, 1, 4, -14],\n [-6, -13, -9, -9, -15, -8],\n [7, -15, -8, -2, -2, -14],\n [-8, 3, -6, -9, -3, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "377", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -1, -2, -15, 1, -15],\n [7, 13, 5, 6, -3, 15],\n [14, -8, 14, -3, 0, -14],\n [-3, 2, -13, -3, 3, -3],\n [3, -12, 3, 2, 9, -10],\n [3, 9, 15, -12, -12, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "951", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, -5, 1, 13, 10],\n [0, -2, 0, 8, -6, 15],\n [0, 0, -6, 10, 4, 13],\n [0, 0, 0, -1, -7, -9],\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": "680", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -5, 7, 5, 4, 3],\n [0, 4, -8, 10, -13, -6],\n [0, 0, -10, -1, 0, -11],\n [0, 0, 0, -14, -10, 11],\n [0, 0, 0, 0, -9, 15],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 2, -9, -15, 12, -15],\n [2, -12, 7, 4, 5, 4],\n [-12, 9, 15, -10, 12, -13],\n [-10, -3, 7, -9, 8, 13],\n [-12, -15, -10, 8, -11, -3],\n [3, -12, 8, -10, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "134", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -10, -10, 2, -10],\n [0, 6, 12, -3, -2, 5],\n [0, 0, -1, -4, 5, 11],\n [0, 0, 0, -13, 2, 10],\n [0, 0, 0, 0, 2, 12],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -14, 14, 13, 5, -4],\n [-11, -4, 7, -15, 12, -14],\n [11, 0, 11, 6, -14, 0],\n [4, 10, 0, -10, -3, -4],\n [7, -6, -11, -8, -10, -11],\n [4, 6, -10, 6, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 0, -6, -4, -3, -7],\n [11, 5, -3, -10, -10, -5],\n [3, 11, -5, -6, 7, -1],\n [-3, 7, -8, -11, -14, 0],\n [15, -3, 3, -7, -1, -10],\n [-8, 8, -2, -11, 1, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, 10, 13, 5, -11, 6],\n [11, -10, -13, -10, -8, 12],\n [-10, 0, 12, 0, 11, 5],\n [-13, 1, 5, -10, 14, -10],\n [14, 6, 3, 15, 4, -1],\n [3, -14, -8, -9, 11, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[11, 8, 0, 0, -8, -13],\n [4, -1, -15, -6, -14, -9],\n [15, -2, 0, 11, 12, -1],\n [-9, -3, 9, -6, -7, -7],\n [-10, 8, 9, -4, 14, 7],\n [4, 14, 4, 6, -2, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\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]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "968", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, -12, -12, -13, -11, 9],\n [15, -5, -8, 10, -14, 12],\n [0, 9, 12, -6, 2, -9],\n [-11, 15, 13, -9, 5, 12],\n [-10, 8, -15, 13, -5, -3],\n [-4, -15, 5, -1, -15, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-14, -13, 13, 8, -8, -5],\n [-4, -12, -7, 8, 1, 8],\n [0, 1, -1, 4, 10, 6],\n [-9, -6, 13, -12, 8, 8],\n [-2, -2, -2, 9, -2, 6],\n [4, 2, -1, 7, 10, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[11, -3, -4, 3, 3, 4],\n [0, 13, 13, 5, -13, -6],\n [0, 0, 13, -9, -7, -14],\n [0, 0, 0, -4, -10, 11],\n [0, 0, 0, 0, -7, 4],\n [0, 0, 0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, -10, 9, 1, 10, 6],\n [-3, -8, 8, -4, -1, 15],\n [3, 13, 5, 10, 4, 12],\n [1, -7, 5, 2, 12, -14],\n [-5, 7, 4, 1, 5, 2],\n [-1, -9, 0, 15, 9, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 10, 0, -10, 0, 0],\n [10, -5, 0, 2, 7, -2],\n [0, 0, 0, -4, -11, 3],\n [-10, 2, -4, -8, 2, 0],\n [0, 7, -11, 2, 13, 2],\n [0, -2, 3, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\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": "296", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-14, -4, 11, 8, 1, 4],\n [0, 14, -6, 4, -8, 2],\n [0, 0, 2, 13, -14, -4],\n [0, 0, 0, -6, -5, -2],\n [0, 0, 0, 0, 7, -6],\n [0, 0, 0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, 0, -4, -8, 6, -2],\n [0, 11, 10, 4, -8, 7],\n [-4, 10, 0, 6, -4, -2],\n [-8, 4, 6, -6, 8, 1],\n [6, -8, -4, 8, -13, 2],\n [-2, 7, -2, 1, 2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, -3, 3, -8, 2, -8],\n [-3, 5, 4, 0, 4, 1],\n [3, 4, -2, 0, 0, 10],\n [-8, 0, 0, 12, -6, -10],\n [2, 4, 0, -6, -2, -2],\n [-8, 1, 10, -10, -2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 10, 5, 15, -7, -3],\n [0, -3, 1, -8, -7, -7],\n [0, 0, 4, 14, 14, -9],\n [0, 0, 0, -11, 1, -8],\n [0, 0, 0, 0, 14, 15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 2, -12, -14, 8, 12],\n [0, -15, 9, -4, -3, -2],\n [0, 0, 12, -13, 12, 11],\n [0, 0, 0, -5, -8, -4],\n [0, 0, 0, 0, 5, 1],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, -11, 8, 8, 13, 2],\n [-3, 15, -11, 10, 8, 3],\n [7, -13, 15, 6, 2, -10],\n [-10, 8, -11, 14, -15, 15],\n [-8, 12, 9, -15, 5, 12],\n [-10, 4, -2, -5, -14, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 1, -2, -2, 3, 13],\n [0, -3, 2, 10, -1, 13],\n [0, 0, -9, 11, 3, 14],\n [0, 0, 0, -11, -14, -1],\n [0, 0, 0, 0, 4, -5],\n [0, 0, 0, 0, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -1, -12, -11, 15, 13],\n [-1, 11, 1, 7, -8, 12],\n [9, 13, 3, 15, -7, -6],\n [-11, -6, 6, -15, 9, 9],\n [6, 8, -12, 5, -11, 7],\n [-9, 7, -11, 4, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "446", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, -7, -11, 13, -10],\n [3, -4, -11, -11, 15, 14],\n [2, 10, -10, -7, -5, 15],\n [7, -2, 8, -14, 11, 13],\n [-2, 9, 3, -6, -11, 14],\n [7, -12, -9, 8, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, 14, -6, -12, 0, -1],\n [0, -5, 3, 5, 8, -13],\n [0, 0, -2, 13, -11, 10],\n [0, 0, 0, -15, 13, 11],\n [0, 0, 0, 0, 5, -2],\n [0, 0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, 8, -14, 4, 8, 7],\n [9, -11, 6, 15, 11, 8],\n [-1, -4, -2, 15, -5, 15],\n [5, 14, -7, 4, -8, -4],\n [14, -13, 5, -1, -8, 15],\n [10, 12, -9, 1, -4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-4, -6, -4, -8, 11, -10],\n [8, 3, -15, -3, 6, 0],\n [2, -4, 15, 9, -11, 5],\n [-3, 10, -8, -10, -13, 9],\n [10, 4, 10, -12, -4, -3],\n [-14, 3, -12, 7, -3, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "539", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -2, -11, 0, -8, -1],\n [-2, -7, -2, -9, -10, 8],\n [-11, -2, 0, 4, 8, 4],\n [0, -9, 4, -4, -5, 6],\n [-8, -10, 8, -5, 0, 10],\n [-1, 8, 4, 6, 10, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-4, 13, 7, 13, 15, -7],\n [-12, -14, 6, 6, -7, 15],\n [4, 8, -3, -2, 13, -13],\n [2, -7, -1, 6, 11, 8],\n [11, -6, 9, 1, -3, -15],\n [-5, -11, -7, -9, -9, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -10, 2, 6, 2, 3],\n [0, 1, 12, -15, -7, -3],\n [0, 0, 10, 14, 15, 7],\n [0, 0, 0, 11, -6, 9],\n [0, 0, 0, 0, -3, -3],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-12, 1, 1, 5, 7, -11],\n [15, -3, -13, 11, 7, 1],\n [-5, -15, 12, 2, 1, -7],\n [4, -9, -11, 14, 0, -9],\n [-3, -3, -1, 7, 1, 1],\n [11, 3, -6, -14, -2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -1, 3, -6, -7, -6],\n [4, 7, -12, 3, -6, 1],\n [14, -4, 9, 13, 11, -15],\n [-5, -3, -15, 15, -15, 14],\n [5, 0, -9, 7, -6, 0],\n [-15, 6, -7, -10, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "658", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 11, 8, 6, -9, 8],\n [-1, 1, -1, -6, 12, -12],\n [6, 1, -12, 6, 7, 13],\n [6, -5, -12, -4, 13, 7],\n [-6, -2, 2, -10, -11, -14],\n [9, -3, 7, -2, -13, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "420", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, 3, 6, -4, 2, -4],\n [3, 9, 12, -6, -1, 5],\n [6, 12, 13, -5, -8, -9],\n [-4, -6, -5, -3, 1, -2],\n [2, -1, -8, 1, 4, 12],\n [-4, 5, -9, -2, 12, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "237", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, 2, -2, 1, -2],\n [1, 5, 6, -14, 1, -10],\n [2, 6, -1, -5, 6, -4],\n [-2, -14, -5, -10, -2, 10],\n [1, 1, 6, -2, -14, 0],\n [-2, -10, -4, 10, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 8, 4, -12, 6, 12],\n [8, -6, -6, 2, 2, -3],\n [4, -6, 11, -6, 2, 1],\n [-12, 2, -6, 8, -10, -8],\n [6, 2, 2, -10, 13, 2],\n [12, -3, 1, -8, 2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "728", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 2, -9, -6, 7, 4],\n [-2, 4, 4, -5, -14, -3],\n [-3, -7, 1, -1, 8, 6],\n [15, 13, 10, 7, 12, 5],\n [6, 6, 13, 0, 9, -6],\n [13, 4, 12, 11, -4, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[9, 7, -5, -3, -15, 3],\n [12, 5, -12, -11, 7, 9],\n [1, -11, 3, -13, -5, -14],\n [6, -2, -10, 3, -15, -9],\n [-14, 8, 3, -15, 10, -7],\n [5, 1, -6, 11, -10, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-13, -13, -14, -9, -8, -8],\n [-13, 1, 6, 1, 2, 0],\n [-14, 6, 11, -4, -3, 4],\n [-9, 1, -4, -9, -5, 3],\n [-8, 2, -3, -5, -3, 2],\n [-8, 0, 4, 3, 2, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-12, 3, -2, -6, -2, 3],\n [3, 14, 4, 5, 7, 10],\n [-2, 4, 4, 2, -10, -6],\n [-6, 5, 2, 4, -2, 0],\n [-2, 7, -10, -2, 15, 6],\n [3, 10, -6, 0, 6, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, 0, 4, -13, 11, -11],\n [0, 11, 12, -14, -14, -12],\n [0, 0, 14, 7, 6, 10],\n [0, 0, 0, 3, -4, 0],\n [0, 0, 0, 0, -6, 9],\n [0, 0, 0, 0, 0, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, -1, 2, -3, 9, -8],\n [0, 4, 2, -3, -2, -1],\n [0, 0, -9, -15, -1, 13],\n [0, 0, 0, 10, 14, -13],\n [0, 0, 0, 0, -10, -12],\n [0, 0, 0, 0, 0, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -14, -11, -2, -8, 13],\n [-4, -9, -10, -3, 6, -4],\n [1, 0, -15, -9, -13, -10],\n [12, 5, -13, 6, -13, -8],\n [-2, 15, 7, -7, -11, 12],\n [-1, 1, 11, -6, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 10, 6, 0, 5, 10],\n [10, 8, 6, 1, 0, -2],\n [6, 6, -6, 0, 4, 4],\n [0, 1, 0, 2, 0, -4],\n [5, 0, 4, 0, -14, 0],\n [10, -2, 4, -4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[6, -2, 10, -2, -6, 12],\n [8, -9, 0, -12, -9, -1],\n [1, -13, 0, -14, -9, 9],\n [0, 5, -7, -4, 13, 8],\n [-15, -2, -5, 2, 6, -11],\n [-1, 11, -9, 9, -2, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, -12, -13, -4, 2, 8],\n [0, -5, 8, -5, -4, 3],\n [0, 0, -10, 5, -8, -1],\n [0, 0, 0, -6, 12, -1],\n [0, 0, 0, 0, -11, -4],\n [0, 0, 0, 0, 0, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-4, 14, -11, -6, 8, -3],\n [13, 3, -9, 14, 0, 13],\n [-10, -6, 11, -6, 10, -5],\n [6, -6, 9, -2, -1, -9],\n [-3, -5, -9, -5, -2, 1],\n [0, -15, -7, -7, 12, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -13, 12, 4, 13, -3],\n [7, 7, 3, 0, -12, -13],\n [-1, -1, 2, 6, -9, 4],\n [-11, -8, 9, 7, -6, 14],\n [-15, -5, 14, -13, 11, 5],\n [-13, -1, 1, 2, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-3, -6, -13, 4, -2, -3],\n [0, -3, 4, 8, 9, 7],\n [0, 0, 9, 0, 7, 7],\n [0, 0, 0, 12, -4, 3],\n [0, 0, 0, 0, 6, 2],\n [0, 0, 0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-11, 10, -14, -15, 0, -11],\n [0, 15, 9, -9, 14, -7],\n [0, 0, 11, 4, -1, -9],\n [0, 0, 0, 5, 13, 9],\n [0, 0, 0, 0, -13, 12],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -6, -8, 4, -1, -15],\n [11, -1, 8, 1, -3, -4],\n [-13, 7, 3, 13, 8, -11],\n [-13, 5, -11, 8, 12, -7],\n [-10, 0, -6, 0, -13, 2],\n [-5, 3, 9, 7, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 9, 13, 15, 6, 8],\n [0, 11, -7, -13, 7, -7],\n [0, 0, 7, 5, 8, 0],\n [0, 0, 0, -3, 15, 10],\n [0, 0, 0, 0, -8, 3],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, -11, -11, -12, 14],\n [4, 5, 10, -7, 14, 11],\n [-4, 0, 6, -8, -7, -4],\n [14, 4, 12, 13, -9, 5],\n [-12, 12, 7, -13, -15, -9],\n [-7, -14, -9, -6, -14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -15, 15, -7, 7, 4],\n [0, -8, -4, -9, 12, 2],\n [0, 0, -9, -2, 10, -15],\n [0, 0, 0, -11, -11, -2],\n [0, 0, 0, 0, 3, -11],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "264", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 14, -2, 8, 8, -13],\n [0, -4, 4, -2, 14, -11],\n [0, 0, 5, 0, -9, -13],\n [0, 0, 0, 11, -12, 4],\n [0, 0, 0, 0, -15, -13],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -4, 7, -2, -2, -2],\n [-4, 10, 4, -2, -2, -4],\n [7, 4, -7, 4, -6, 4],\n [-2, -2, 4, 3, -3, 2],\n [-2, -2, -6, -3, 12, 6],\n [-2, -4, 4, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, 4, 4, -14, -6],\n [0, 12, 4, -11, 4, 14],\n [0, 0, -14, -12, 14, 0],\n [0, 0, 0, 1, -1, -3],\n [0, 0, 0, 0, 4, -15],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[14, 0, 7, 2, 10, 1],\n [0, 4, -3, 8, 13, 6],\n [0, 0, 1, 11, -11, 6],\n [0, 0, 0, -13, -8, -4],\n [0, 0, 0, 0, 12, 9],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 1, -10, -9, -2, 11],\n [14, -8, -4, 12, 2, -2],\n [-15, -12, 1, 2, 3, -12],\n [12, 12, -10, -8, 9, -1],\n [4, -15, 14, -11, 0, 5],\n [9, -10, 5, -6, -6, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "424", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-4, 9, -15, 2, 10, 5],\n [5, 6, 14, 8, 12, 1],\n [-6, 12, -7, 4, -8, 12],\n [-1, -3, 12, 5, 1, 14],\n [-7, 8, 5, 14, 15, -5],\n [14, -12, 8, 9, -9, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, -8, -7, 0, -11, 7],\n [0, -15, 11, 8, 3, 1],\n [0, 0, -3, -8, 11, -13],\n [0, 0, 0, 5, 11, -8],\n [0, 0, 0, 0, 4, 8],\n [0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[9, 6, 15, -2, -12, -8],\n [0, -2, 13, 10, 2, 7],\n [0, 0, -1, 4, 4, 10],\n [0, 0, 0, -1, 7, -1],\n [0, 0, 0, 0, -12, 2],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "272", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 8, -4, 6, -2, -1],\n [8, 2, 4, 4, -1, 4],\n [-4, 4, 2, -2, -9, -3],\n [6, 4, -2, 10, 6, 6],\n [-2, -1, -9, 6, 6, 2],\n [-1, 4, -3, 6, 2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "434", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-14, -1, -4, 0, 10, 0],\n [0, 3, -13, 12, 13, 6],\n [4, -12, -15, 6, -8, 8],\n [-1, 8, 5, 10, 6, -11],\n [4, -4, 4, 4, -12, 14],\n [15, 6, -1, -10, -11, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, -11, 1, -6, 5, 1],\n [-7, -3, -6, 13, 15, -8],\n [-9, -14, -14, 14, -12, -7],\n [14, 9, -2, 8, -5, 15],\n [5, 14, -9, 12, 9, 3],\n [-12, -14, 9, 7, 6, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 0, -5, 10, -4],\n [-2, 9, -3, -6, 6, -2],\n [0, -3, -12, 4, -9, 2],\n [-5, -6, 4, 4, 0, 2],\n [10, 6, -9, 0, -13, 3],\n [-4, -2, 2, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-14, 4, 1, 3, 4, 0],\n [0, 3, 5, 1, 13, -12],\n [0, 0, 5, -13, 14, 6],\n [0, 0, 0, 5, 4, -11],\n [0, 0, 0, 0, 14, 11],\n [0, 0, 0, 0, 0, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, 2, -6, 0, -4, 6],\n [2, 2, 12, -2, 0, 0],\n [-6, 12, 8, 6, -2, 2],\n [0, -2, 6, 13, 8, -4],\n [-4, 0, -2, 8, 0, 0],\n [6, 0, 2, -4, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 11, 13, -5, -9, 13],\n [-7, -2, -11, 2, 14, 8],\n [15, 9, 7, 12, -3, -11],\n [-8, -1, 6, 12, -12, -15],\n [-10, 8, 3, -4, -9, -3],\n [12, -9, -7, -15, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "628", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[7, 5, -6, 7, -4, 0],\n [5, 0, 4, 2, 0, 10],\n [-6, 4, 6, 8, -10, 5],\n [7, 2, 8, 10, -10, -12],\n [-4, 0, -10, -10, -2, -4],\n [0, 10, 5, -12, -4, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "392", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 9, -3, -3, -7, -10],\n [0, 9, 14, -11, 9, 5],\n [0, 0, -12, -14, -14, 15],\n [0, 0, 0, -2, 3, 1],\n [0, 0, 0, 0, 13, -9],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[8, 4, 1, 9, 3, 14],\n [1, 9, 11, 11, -2, 15],\n [-3, 10, -2, 10, 0, 5],\n [12, -1, 14, 9, 3, 6],\n [-5, -4, -5, 12, 7, -11],\n [12, -8, 10, -10, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, -10, -9, 10, 11, -8],\n [11, 15, -13, 8, -1, 6],\n [-10, -5, 14, -13, 0, -10],\n [-5, 13, -8, 13, 7, -6],\n [15, -6, 7, -13, 10, -2],\n [3, 5, 12, 5, -7, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -3, -6, 2, 5, -6],\n [-3, -2, 0, -10, -3, -4],\n [-6, 0, 0, 0, 0, 4],\n [2, -10, 0, -9, 9, 12],\n [5, -3, 0, 9, -11, -8],\n [-6, -4, 4, 12, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 2, -3, -4, -6],\n [0, 15, 4, 2, 0, 4],\n [2, 4, -7, 2, -14, 6],\n [-3, 2, 2, -4, 8, 4],\n [-4, 0, -14, 8, -13, -12],\n [-6, 4, 6, 4, -12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "843", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -13, -15, -1, 2, 4],\n [-13, 13, -1, 11, 6, 12],\n [12, -11, 5, -6, -9, 7],\n [9, -8, -13, 2, 1, 15],\n [0, 10, 6, 13, -3, -12],\n [-13, -5, 11, -14, 2, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "282", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -2, 5, 8, 0, 4],\n [-2, -6, 4, 10, -2, 6],\n [5, 4, -6, -1, 7, 6],\n [8, 10, -1, -3, 0, -8],\n [0, -2, 7, 0, -7, 2],\n [4, 6, 6, -8, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[13, 4, -3, 1, -8, -2],\n [4, 9, 6, 4, 6, 3],\n [-3, 6, 1, 1, -4, -4],\n [1, 4, 1, -1, -6, -5],\n [-8, 6, -4, -6, 14, 2],\n [-2, 3, -4, -5, 2, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-14, 12, -10, 0, 8, -9],\n [0, 3, -4, 2, -6, -9],\n [0, 0, 1, 1, -12, 5],\n [0, 0, 0, 6, 10, 7],\n [0, 0, 0, 0, -12, 13],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[2, -13, 2, 10, -9, 12],\n [0, 9, 2, 4, -8, -5],\n [0, 0, -9, -1, -6, -4],\n [0, 0, 0, -1, 5, 5],\n [0, 0, 0, 0, 9, -7],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 15, 10, -11, 13, -12],\n [-10, -5, 14, 12, -11, 13],\n [6, -2, 14, -6, -5, -13],\n [15, 7, -8, 5, -11, 12],\n [4, 15, 10, 5, 12, -6],\n [11, -8, 5, -7, 13, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "671", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -12, -2, 3, 15, -12],\n [-12, -10, 6, -6, 0, -2],\n [-2, 6, -15, 6, 13, 4],\n [3, -6, 6, -7, 4, -6],\n [15, 0, 13, 4, 2, -4],\n [-12, -2, 4, -6, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[13, -12, 13, -13, -15, 14],\n [-12, -7, -15, 0, 7, -13],\n [8, -10, -3, 1, -1, 10],\n [5, 14, -4, 13, -8, 11],\n [15, 0, -13, 12, 12, -12],\n [-9, -1, -5, 0, 6, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, 12, -8, -2, 13],\n [1, 13, -12, -9, 1, 12],\n [8, 0, -2, 0, 11, -14],\n [8, -1, -5, -3, -12, 8],\n [-15, -1, -4, 5, -7, -9],\n [-13, 0, -12, 10, 7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "442", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, 13, -14, -8, 5, 14],\n [0, 8, -4, -2, 12, -2],\n [0, 0, -14, -2, 7, 9],\n [0, 0, 0, -7, 13, -8],\n [0, 0, 0, 0, -1, 9],\n [0, 0, 0, 0, 0, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-5, 3, -2, 11, -12, 11],\n [14, -5, 0, 7, 10, 14],\n [-14, -14, -7, 6, 11, 15],\n [15, 7, 5, 13, 5, 15],\n [-12, -8, 7, 10, 2, -1],\n [-14, 6, 12, -5, 1, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, 5, 2, -6, -3, -8],\n [5, 12, 2, 4, -5, 0],\n [2, 2, -2, -1, -6, 4],\n [-6, 4, -1, 8, -5, -4],\n [-3, -5, -6, -5, -6, 2],\n [-8, 0, 4, -4, 2, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "769", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[6, -15, -5, 5, -10, -8],\n [-9, -10, 2, -4, -8, 8],\n [11, 5, 3, 12, 11, 8],\n [-11, 3, -7, 9, -4, -1],\n [7, -3, 8, -3, 5, 5],\n [-11, 15, -14, 3, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "521", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[7, -3, 5, -7, 5, -7],\n [6, 6, -5, 15, -10, 7],\n [-4, 11, -12, -12, 9, 15],\n [12, 7, 11, 10, 6, 1],\n [-9, -10, 12, 4, 13, -8],\n [-9, -8, -7, -15, -13, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, 13, -7, 8, 4, 5],\n [0, 1, 14, -10, -13, 11],\n [0, 0, 1, -10, -8, -2],\n [0, 0, 0, -1, -8, -5],\n [0, 0, 0, 0, -3, 15],\n [0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, 0, -1, 2, 10],\n [0, -5, -1, 7, -6, 2],\n [0, -1, -2, -2, -2, -8],\n [-1, 7, -2, -2, 6, 10],\n [2, -6, -2, 6, -3, -2],\n [10, 2, -8, 10, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, 12, -11, 7, 4, -11],\n [-9, 1, 15, -4, -1, -13],\n [1, -2, -1, -1, -1, 3],\n [-5, 2, 5, -6, 5, 10],\n [-7, 8, -13, -15, 5, -5],\n [0, -13, 5, -7, -5, 14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -6, 4, 5, 5],\n [2, -5, -7, 10, -7, -3],\n [-6, -7, -11, 1, 12, 1],\n [4, 10, 1, 1, 1, 0],\n [5, -7, 12, 1, -7, 3],\n [5, -3, 1, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, 2, 6, 11, 12, -5],\n [11, 7, -15, -9, 12, 11],\n [-8, 9, -2, 8, 3, -8],\n [3, 6, -12, 7, 8, -6],\n [6, -6, -12, -8, -9, 10],\n [-1, -8, 13, -6, -9, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 0, 5, 1, -3, 10],\n [-13, 11, 4, 4, 7, -11],\n [-7, 7, 2, 13, -5, -5],\n [0, -8, 11, -14, 7, 5],\n [-6, -10, 11, -12, 5, 12],\n [-11, 7, -5, -4, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "498", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, -2, 1, -7, -4, 11],\n [-6, -5, -14, 15, 12, 0],\n [11, -15, 6, 13, -15, 15],\n [6, -14, -4, 11, 7, 7],\n [12, 4, 2, -4, 11, 7],\n [-15, 12, 11, -5, -14, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "623", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, -14, 1, 9, -10, 0],\n [0, 12, -10, -9, 3, 15],\n [0, 0, 1, -10, -1, 6],\n [0, 0, 0, 5, 7, -11],\n [0, 0, 0, 0, -4, -1],\n [0, 0, 0, 0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -15, -4, 11, -5, -3],\n [0, -12, 9, -10, 6, 9],\n [0, 0, 6, -3, -10, 6],\n [0, 0, 0, 9, 14, -1],\n [0, 0, 0, 0, 1, 10],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 3, -11, -9, -7, -11],\n [-8, -14, 6, 8, 9, 11],\n [4, 4, -9, 13, -12, 5],\n [-1, 15, 2, -14, 11, -2],\n [-6, -11, -4, -6, 10, 13],\n [15, 2, 12, -10, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "700", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -4, 8, 15, 12, -15],\n [0, -4, 15, -9, -7, 4],\n [0, 0, -4, -3, 6, -12],\n [0, 0, 0, -13, 8, 13],\n [0, 0, 0, 0, 14, 12],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 12, -10, 9, -4, -13],\n [0, 4, -7, -6, 14, -3],\n [0, 0, 10, -10, 12, -13],\n [0, 0, 0, -5, -10, -14],\n [0, 0, 0, 0, 3, 2],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, 7, -2, -8, -5, 6],\n [7, 6, 8, -6, 4, 10],\n [-2, 8, -10, 2, 9, 1],\n [-8, -6, 2, 13, -4, 4],\n [-5, 4, 9, -4, 10, 0],\n [6, 10, 1, 4, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 9, 9, -5, -4, 14],\n [0, 3, 13, 14, -5, -3],\n [0, 0, -10, 6, 9, 0],\n [0, 0, 0, 7, 2, 1],\n [0, 0, 0, 0, -1, -14],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -4, -2, 6, 1, -4],\n [-4, -14, -2, 12, 4, 10],\n [-2, -2, 10, -1, 9, 14],\n [6, 12, -1, 7, 4, -14],\n [1, 4, 9, 4, 12, -10],\n [-4, 10, 14, -14, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, 2, 12, -12, 7, 9],\n [9, 11, -13, 12, 7, -12],\n [9, 7, 0, -3, 13, 6],\n [9, 7, -5, 8, -5, -11],\n [4, -15, -2, 8, 6, 4],\n [3, -11, 4, 11, 11, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 10, -2, 8, -7, 8],\n [10, 6, -5, 12, 6, 2],\n [-2, -5, 10, -5, -7, 3],\n [8, 12, -5, 15, -2, 0],\n [-7, 6, -7, -2, 5, 11],\n [8, 2, 3, 0, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, 4, -6, 0, -6],\n [-4, -14, 2, 4, 1, -3],\n [4, 2, -6, -8, 0, 4],\n [-6, 4, -8, 15, -6, 6],\n [0, 1, 0, -6, 14, 12],\n [-6, -3, 4, 6, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "962", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 2, -9, -4, -10, 12],\n [0, 4, 11, -1, 4, -1],\n [0, 0, -10, 3, -1, 9],\n [0, 0, 0, -14, -9, -11],\n [0, 0, 0, 0, 3, -4],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, 9, 9, 8, -15],\n [0, 13, -4, 2, 2, -13],\n [0, 0, -5, -11, 6, 13],\n [0, 0, 0, 2, 13, -9],\n [0, 0, 0, 0, 6, -8],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[14, 14, 2, 8, -10, 4],\n [14, 15, 6, 0, -11, 2],\n [2, 6, 2, 4, -3, 2],\n [8, 0, 4, -5, -2, 2],\n [-10, -11, -3, -2, 7, -2],\n [4, 2, 2, 2, -2, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, 7, 0, 5, 10, 12],\n [7, -7, 1, 8, 3, -10],\n [0, 1, 8, 6, 3, -3],\n [5, 8, 6, -6, -2, 8],\n [10, 3, 3, -2, 4, 5],\n [12, -10, -3, 8, 5, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 4, 11, 1, 0, -15],\n [0, 13, 11, -15, 14, 4],\n [0, 0, 8, -14, -1, 13],\n [0, 0, 0, 3, -15, -3],\n [0, 0, 0, 0, -13, -8],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -5, 1, -8, 4, -14],\n [5, 4, -15, 0, 12, 7],\n [-12, 8, -7, -8, -15, -8],\n [-11, -15, 9, 9, -9, -1],\n [-9, 11, -15, -7, -15, 13],\n [15, -4, -9, 9, -7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 9, 0, 8, 14, 7],\n [-3, -5, -8, 10, 8, 1],\n [-7, -10, -15, -15, -3, -9],\n [-6, 2, -10, -3, -11, 5],\n [10, -1, -4, 6, 14, -5],\n [-8, -11, -8, -11, -6, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -6, 5, -4, 8, -12],\n [-3, 10, -6, 0, 3, -10],\n [10, 14, -7, -2, 8, -6],\n [-8, -13, 1, 3, 14, -13],\n [-2, 12, -10, 13, 3, 2],\n [-4, -1, 9, -10, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "502", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -7, -5, 15, 5, 7],\n [0, 5, 13, 10, 14, 4],\n [0, 0, -14, 3, 8, -13],\n [0, 0, 0, 7, -6, -7],\n [0, 0, 0, 0, -3, -15],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "700", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 11, 2, -2, 4, -10],\n [11, -5, 13, -9, 9, 3],\n [2, 13, -2, 11, -3, -2],\n [-2, -9, 11, 9, -2, 8],\n [4, 9, -3, -2, -10, 8],\n [-10, 3, -2, 8, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, 7, 1, 4, 3],\n [0, -7, 12, 7, -4, -6],\n [7, 12, -8, 4, 6, 14],\n [1, 7, 4, 8, -8, 0],\n [4, -4, 6, -8, 3, -1],\n [3, -6, 14, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, 10, 6, -15, -8],\n [0, -7, 15, 8, 15, -3],\n [0, 0, 6, 9, -7, -9],\n [0, 0, 0, -6, 5, 11],\n [0, 0, 0, 0, -7, -14],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -4, -2, -8, 12, 10],\n [-4, 0, 4, 4, 2, -5],\n [-2, 4, 8, -9, -6, 6],\n [-8, 4, -9, 15, -7, -2],\n [12, 2, -6, -7, -10, 2],\n [10, -5, 6, -2, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 2, 2, 3, 2, 10],\n [2, -11, -6, -8, -10, -6],\n [2, -6, -5, 3, 2, -6],\n [3, -8, 3, 4, 2, 4],\n [2, -10, 2, 2, 9, -4],\n [10, -6, -6, 4, -4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-3, 15, 14, -6, 10, -10],\n [-5, -8, 3, 14, -5, -10],\n [15, -4, 2, -13, -3, -12],\n [-7, 15, 0, -4, 4, -9],\n [-4, -8, 5, -1, -14, 15],\n [-5, 8, 5, -11, 7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, 6, -11, 6, 4, -5],\n [6, 8, -2, 2, 2, 5],\n [-11, -2, -14, -2, -8, -8],\n [6, 2, -2, 8, 4, -6],\n [4, 2, -8, 4, 3, 8],\n [-5, 5, -8, -6, 8, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 13, -3, 1, 15, -8],\n [-5, 1, -7, -14, 11, -6],\n [6, 8, 5, -2, -14, -11],\n [1, 8, -8, 14, 2, 6],\n [11, 8, 10, 13, -8, -4],\n [-2, 15, 14, 7, -13, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 8, 9, -6, 0, 4],\n [-8, -15, -14, 13, -6, -6],\n [-6, -7, 2, 15, -14, 8],\n [-11, 5, -5, -10, -8, -8],\n [9, -6, -5, 3, 9, -2],\n [-5, -13, -15, 12, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "414", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[5, 0, -2, 4, 2, -8],\n [0, 11, 8, 10, -11, 12],\n [-2, 8, -4, 0, -7, 4],\n [4, 10, 0, 14, 3, 0],\n [2, -11, -7, 3, 2, 1],\n [-8, 12, 4, 0, 1, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -8, 0, -8, -2, 12],\n [-8, -2, -8, 11, 6, -2],\n [0, -8, -6, 8, -4, -4],\n [-8, 11, 8, -3, 6, -7],\n [-2, 6, -4, 6, -11, 2],\n [12, -2, -4, -7, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, 0, -6, -1, -3, 4],\n [0, -4, 8, -5, 7, 10],\n [-6, 8, -7, -4, -13, -10],\n [-1, -5, -4, 9, -2, 2],\n [-3, 7, -13, -2, -13, -10],\n [4, 10, -10, 2, -10, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "910", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, -1, 7, 1, 0, 14],\n [0, -1, 10, -3, -14, 1],\n [0, 0, 14, -6, -12, -6],\n [0, 0, 0, -15, 3, -15],\n [0, 0, 0, 0, 11, -2],\n [0, 0, 0, 0, 0, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, -9, -8, 4, 0, 0],\n [-9, 13, 0, -8, -2, -8],\n [-8, 0, 10, -11, 0, 0],\n [4, -8, -11, 7, -5, 1],\n [0, -2, 0, -5, -7, 0],\n [0, -8, 0, 1, 0, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "418", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -8, 1, 1, 0, 2],\n [-8, 14, 8, 6, -6, -6],\n [1, 8, -2, -2, 0, 6],\n [1, 6, -2, -6, 0, 6],\n [0, -6, 0, 0, 6, 5],\n [2, -6, 6, 6, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[13, -12, -1, -9, -1, -12],\n [14, -13, 7, -2, -10, -15],\n [-7, -4, 2, 13, -13, 5],\n [15, 3, -13, 8, -2, -12],\n [-3, -3, 10, -14, 5, -14],\n [-6, -5, 12, 8, -1, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, 7, -12, 5, 8, -6],\n [7, 10, -6, -14, -8, -8],\n [-7, -14, -2, 4, -14, -12],\n [-13, 7, -2, 5, 0, -1],\n [-9, 2, 4, -10, 12, 5],\n [0, -5, -14, 12, 7, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -14, 0, -10, 6, 10],\n [-14, 1, 8, -8, -1, -6],\n [0, 8, 2, -3, -6, 2],\n [-10, -8, -3, 0, -12, 4],\n [6, -1, -6, -12, 12, 4],\n [10, -6, 2, 4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, -2, -4, 7, 12, 6],\n [4, -1, 3, -5, 14, 6],\n [10, -1, 14, 13, 12, 5],\n [14, -4, 3, 0, -12, 2],\n [-7, 0, -9, 12, 14, 10],\n [3, 8, 8, -5, 1, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "491", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[4, 4, -4, 1, -2, -4],\n [4, 0, -6, -1, -10, 13],\n [-4, -6, 3, 2, -2, 0],\n [1, -1, 2, 9, -10, 1],\n [-2, -10, -2, -10, -6, -8],\n [-4, 13, 0, 1, -8, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "710", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, 11, -5, -14, 10, -11],\n [0, 15, -3, 6, -13, 3],\n [0, 0, 3, 0, 15, 0],\n [0, 0, 0, 12, 7, 9],\n [0, 0, 0, 0, -2, 12],\n [0, 0, 0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-14, -10, 4, 5, 2, -1],\n [-10, 8, 10, 1, 10, 1],\n [4, 10, -7, 6, -6, 0],\n [5, 1, 6, 4, -11, 1],\n [2, 10, -6, -11, -10, -1],\n [-1, 1, 0, 1, -1, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -14, -5, -8, -10, 2],\n [0, 13, -5, 8, -10, -7],\n [0, 0, 3, 9, 10, 15],\n [0, 0, 0, 3, -6, -2],\n [0, 0, 0, 0, -14, -1],\n [0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, -2, -2, 0, 2, 6],\n [-2, 14, -2, 11, 0, 2],\n [-2, -2, -2, 2, -4, -2],\n [0, 11, 2, 3, -6, -4],\n [2, 0, -4, -6, -12, -5],\n [6, 2, -2, -4, -5, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-10, -5, -1, 5, 1, 15],\n [-14, -3, 7, 9, -15, -12],\n [14, 15, -1, 0, -5, -13],\n [-4, -4, -5, 0, 13, 5],\n [5, -3, -4, -6, 10, -5],\n [2, -11, 4, -3, 1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "845", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, 8, 11, -12, 13, 8],\n [1, 12, 8, 10, 2, 6],\n [-10, 3, 13, -11, -14, -5],\n [8, 8, -3, -11, 7, -8],\n [-5, -12, 2, 14, -1, -11],\n [7, 15, -4, -12, -12, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "976", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -7, -2, 11, 10, 8],\n [11, -8, 7, -15, 8, -5],\n [11, -12, 13, 1, 1, 3],\n [-3, 3, 10, 1, 8, 4],\n [-4, 4, -2, 6, -7, 9],\n [-4, 8, 15, 1, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 10, -14, -13, 11, -11],\n [0, 5, -3, 10, 8, 2],\n [0, 0, -15, -7, 2, 12],\n [0, 0, 0, -4, -8, -8],\n [0, 0, 0, 0, -15, 8],\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": "What is the determinant of the matrix:\n[[3, 0, -1, 0, 1, 0],\n [0, 12, 6, -6, -6, 11],\n [-1, 6, -6, 6, -9, 2],\n [0, -6, 6, 0, -4, 2],\n [1, -6, -9, -4, -3, -2],\n [0, 11, 2, 2, -2, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, -15, -14, 4, -6, 11],\n [0, 7, -12, -8, 0, -9],\n [-11, 7, -8, -13, -13, 2],\n [-12, 11, -12, -1, 14, -1],\n [13, -12, -14, 7, 10, -13],\n [12, 15, -6, -15, 2, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, 4, -10, 3, -7, 2],\n [0, -1, -1, 11, -2, 14],\n [0, 0, 3, -5, 12, 12],\n [0, 0, 0, -6, 4, -5],\n [0, 0, 0, 0, -7, 9],\n [0, 0, 0, 0, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "938", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 11, -1, -8, 2, 13],\n [0, 3, -12, -13, 6, -7],\n [0, 0, 4, -14, 10, -15],\n [0, 0, 0, -11, 2, -2],\n [0, 0, 0, 0, 3, 13],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[12, 2, 9, -5, 6, -15],\n [0, 8, -6, 6, -12, -10],\n [0, 0, -4, 6, 8, 13],\n [0, 0, 0, 13, -10, 1],\n [0, 0, 0, 0, -13, -8],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, 3, 10, -6, -13, 6],\n [0, -3, 0, -4, 6, 5],\n [0, 0, -14, 0, -5, -15],\n [0, 0, 0, 12, 13, -11],\n [0, 0, 0, 0, 2, -4],\n [0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, 15, -12, 8, -5, -13],\n [0, -1, 0, -4, 2, 14],\n [0, 0, -1, -14, 7, -4],\n [0, 0, 0, -8, -1, 3],\n [0, 0, 0, 0, -2, -1],\n [0, 0, 0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-8, 6, 2, -4, 0, 6],\n [6, -4, 1, 0, -3, -2],\n [2, 1, -5, -12, -8, 6],\n [-4, 0, -12, 5, 4, -8],\n [0, -3, -8, 4, -11, -6],\n [6, -2, 6, -8, -6, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, 14, 3, -14, -11, -15],\n [0, -2, 7, -7, 1, -4],\n [0, 0, 7, 10, 4, 14],\n [0, 0, 0, 14, 7, 2],\n [0, 0, 0, 0, -5, -1],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 13, -6, -10, -10, 1],\n [0, -3, -1, -12, 13, 12],\n [0, 0, 7, 15, -2, -5],\n [0, 0, 0, 1, 9, -6],\n [0, 0, 0, 0, -12, 15],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, 5, -15, -2, -7, 10],\n [14, -1, 5, 6, 7, -2],\n [-7, -5, -11, -4, 0, 4],\n [12, -13, -11, 14, 10, 10],\n [13, 3, -11, 8, 2, 13],\n [-12, 8, -1, 14, -11, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 11, 9, -8, 9, 5],\n [0, 9, 13, 3, -9, -13],\n [0, 0, 2, -1, 8, 1],\n [0, 0, 0, 1, 6, 10],\n [0, 0, 0, 0, -7, 7],\n [0, 0, 0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 15, 15, -2, 6, -14],\n [0, -1, -15, 6, -15, -4],\n [0, 0, 10, 2, -1, -9],\n [0, 0, 0, -14, -10, 4],\n [0, 0, 0, 0, -6, -13],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, 9, 8, -13, 2, 15],\n [0, -10, 11, 12, 10, 4],\n [0, 0, -6, -6, 13, 9],\n [0, 0, 0, -5, 11, -3],\n [0, 0, 0, 0, 2, -12],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, 4, -12, 10, 0, 5],\n [4, 2, 6, 0, 0, -7],\n [-12, 6, 10, -4, 6, -10],\n [10, 0, -4, 14, -4, -5],\n [0, 0, 6, -4, -3, -10],\n [5, -7, -10, -5, -10, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -3, -6, 2, -12, 6],\n [0, 11, -8, 8, 4, 6],\n [0, 0, 13, -8, 8, 2],\n [0, 0, 0, 2, -15, -5],\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": "314", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, -4, 1, 4, 1, 4],\n [-4, -1, 10, -2, 5, -2],\n [1, 10, 7, 1, -6, -7],\n [4, -2, 1, 12, -7, 5],\n [1, 5, -6, -7, -3, 0],\n [4, -2, -7, 5, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "857", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, 10, 14, -4, 0, -5],\n [6, 1, -6, 7, 0, 0],\n [-1, 10, -1, 7, 4, -12],\n [11, 6, -13, -2, 14, 15],\n [-6, -10, 11, -5, -12, -6],\n [0, 8, 5, 13, -8, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-12, 1, -6, 7, -3, 7],\n [0, 5, 1, 15, 3, 1],\n [0, 0, 12, -12, 14, 7],\n [0, 0, 0, -7, -10, -6],\n [0, 0, 0, 0, -3, 0],\n [0, 0, 0, 0, 0, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 13, 10, 14, -8, -1],\n [0, 13, -3, 11, 7, -14],\n [0, 0, 7, 10, -4, 10],\n [0, 0, 0, 10, 11, 4],\n [0, 0, 0, 0, 1, 10],\n [0, 0, 0, 0, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, 2, 0, -4, -4, 2],\n [2, -14, 0, 7, 0, 8],\n [0, 0, 2, 2, 6, -11],\n [-4, 7, 2, -5, 5, -2],\n [-4, 0, 6, 5, -8, -5],\n [2, 8, -11, -2, -5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "580", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 12, 1, -1, -12, -6],\n [12, 8, -9, -2, 3, 0],\n [1, -9, -4, -3, 6, -3],\n [-1, -2, -3, -6, 4, -6],\n [-12, 3, 6, 4, 15, 3],\n [-6, 0, -3, -6, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 2, -15, 5, 7, 9],\n [0, 11, -5, 0, -15, 3],\n [0, 0, 7, 0, 10, -13],\n [0, 0, 0, -6, 14, 6],\n [0, 0, 0, 0, -11, -11],\n [0, 0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "656", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -11, 15, -1, 1, 1],\n [0, 2, 10, -6, 7, -9],\n [0, 0, -7, 1, -14, 14],\n [0, 0, 0, 4, 8, -6],\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": "432", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -13, -4, 0, -12, -12],\n [0, -7, 8, -2, -4, -6],\n [0, 0, -4, -14, 3, -3],\n [0, 0, 0, -15, -15, 12],\n [0, 0, 0, 0, -3, 9],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[7, 4, 2, 0, -6, 2],\n [4, 2, -3, 1, -2, 0],\n [2, -3, -7, -8, 2, 14],\n [0, 1, -8, 11, -5, 3],\n [-6, -2, 2, -5, 9, -7],\n [2, 0, 14, 3, -7, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, 12, 5, -7, -3, -5],\n [0, -8, 13, 12, 10, -9],\n [0, 0, 12, 6, 9, 15],\n [0, 0, 0, -1, -1, 5],\n [0, 0, 0, 0, -3, 0],\n [0, 0, 0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 4, -8, -2, 13, 5],\n [4, 15, 2, 0, -2, 2],\n [-8, 2, -14, -6, -4, -3],\n [-2, 0, -6, -8, 5, -6],\n [13, -2, -4, 5, 15, 8],\n [5, 2, -3, -6, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[7, 9, -6, 15, -6, -15],\n [-9, 4, -7, -5, 4, -14],\n [-15, 7, -4, -9, 3, -11],\n [10, -4, -2, 12, -9, -8],\n [-2, -4, -7, -6, -6, -15],\n [9, 6, -10, -2, 7, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -3, -7, -2, -15, 14],\n [-7, -10, -6, -5, -9, 4],\n [9, 12, 6, -4, 6, -4],\n [-2, -6, 0, 6, -12, 13],\n [7, -2, -14, -14, 13, -5],\n [-5, -10, 9, -13, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 2, -13, -11, -14, -7],\n [8, -11, 11, 1, 5, 4],\n [-1, 14, -3, -7, -14, 7],\n [-14, 13, 13, -5, 12, -13],\n [14, -13, -6, 8, -14, -15],\n [-10, -10, -5, 0, 15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 9, 10, 11, -6, 5],\n [12, 7, -10, -5, 10, 0],\n [4, -3, -4, 2, 10, -3],\n [-11, 12, 12, 14, 14, 10],\n [-3, 9, -3, 3, 3, -3],\n [12, -5, 0, 7, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "710", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, -7, 6, -2, 0, 1],\n [-7, 11, -12, 0, 2, -2],\n [6, -12, 11, 0, 2, -3],\n [-2, 0, 0, -6, -1, 0],\n [0, 2, 2, -1, 6, 0],\n [1, -2, -3, 0, 0, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, 6, -9, 8, 0, 2],\n [11, -8, 11, 10, 14, 15],\n [2, -14, -7, 7, 8, 0],\n [1, -6, 6, -15, 5, 2],\n [-1, -7, -13, 0, 10, 7],\n [-1, -14, -6, -12, 10, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[15, 0, -3, 2, -4, 4],\n [0, -11, -8, 8, -4, 2],\n [-3, -8, 0, 6, 8, -4],\n [2, 8, 6, 8, 7, -2],\n [-4, -4, 8, 7, 14, 7],\n [4, 2, -4, -2, 7, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[14, 12, -13, -15, 3, 8],\n [14, -8, 0, 12, -1, -9],\n [-14, -3, -11, -6, -8, -3],\n [3, -10, 2, -8, -7, 1],\n [-12, 6, 14, 2, -10, -5],\n [7, 6, -6, 10, -5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "568", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-14, -6, 13, 2, 7, 2],\n [-6, 0, 12, -14, 6, 4],\n [13, 12, -12, 0, 3, 0],\n [2, -14, 0, -4, 2, 11],\n [7, 6, 3, 2, 5, 7],\n [2, 4, 0, 11, 7, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -6, -7, 9, -3, 13],\n [13, -8, 6, -3, 12, 11],\n [6, 12, 15, 2, 7, -7],\n [15, -7, -14, 9, -9, -11],\n [5, -10, -3, 8, 2, -13],\n [-6, 7, -13, -15, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, -6, -1, -8, -2],\n [0, 3, -13, -3, 14, 12],\n [0, 0, 9, -11, 5, 3],\n [0, 0, 0, -8, -10, -13],\n [0, 0, 0, 0, 4, 15],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "976", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 7, -14, -4, -5, 0],\n [-5, -13, 7, -6, 13, -11],\n [12, 15, -3, 9, 8, -10],\n [12, 4, -13, 6, -7, 5],\n [12, -9, 7, 14, -9, 9],\n [-14, -8, 2, 15, 11, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -14, 15, 11, 6, -1],\n [8, 12, -8, -3, -13, -12],\n [10, -12, -12, 15, -14, -3],\n [6, -8, -7, 13, -15, -15],\n [-7, -5, 0, 13, -12, -1],\n [11, -9, -14, -6, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[11, 5, 3, 6, 10, -13],\n [0, -8, -12, 5, -13, -11],\n [0, 0, 7, 3, 3, 1],\n [0, 0, 0, -7, -13, -6],\n [0, 0, 0, 0, 6, -9],\n [0, 0, 0, 0, 0, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -9, -2, -1, 0, 5],\n [-9, -14, -2, 2, -14, -6],\n [-2, -2, -7, -1, -5, 6],\n [-1, 2, -1, -1, 2, 0],\n [0, -14, -5, 2, -12, 5],\n [5, -6, 6, 0, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 11, -7, -6, 11, 9],\n [0, 3, -12, 12, 0, -4],\n [0, 0, 15, 1, 0, -9],\n [0, 0, 0, -4, 15, -3],\n [0, 0, 0, 0, 5, 0],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-2, 12, -5, 15, 12, -3],\n [4, 2, -3, 5, 11, 3],\n [-12, -4, -13, 0, -15, -12],\n [-7, 7, -3, 6, 14, -6],\n [-7, 4, -10, 15, 3, -13],\n [-6, -6, 8, 5, 15, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, -8, 7, -14, 4, -11],\n [9, -6, 14, 2, -4, 12],\n [7, 5, -14, -6, -4, 3],\n [-11, -6, -15, -9, -15, 6],\n [12, 6, 1, -4, 15, -9],\n [-8, -13, -1, -4, 10, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[9, 13, 3, 12, 3, -15],\n [0, 3, -14, 13, -2, 3],\n [0, 0, 1, -14, 15, 1],\n [0, 0, 0, -10, 10, 13],\n [0, 0, 0, 0, -9, 8],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, -12, -11, 0, -14, 15],\n [0, 8, 8, -3, 12, -12],\n [0, 0, 11, -4, -1, -11],\n [0, 0, 0, -7, -1, 14],\n [0, 0, 0, 0, 11, -15],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, -10, -4, -4, 8, 6],\n [-10, 4, 3, -3, -12, 4],\n [-4, 3, 2, -1, -6, 2],\n [-4, -3, -1, 10, -2, 6],\n [8, -12, -6, -2, 13, 8],\n [6, 4, 2, 6, 8, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, 0, 1, 2, 15, 13],\n [0, -5, 3, -5, -6, 14],\n [0, 0, -6, 5, 7, -12],\n [0, 0, 0, 6, 13, -5],\n [0, 0, 0, 0, 11, -10],\n [0, 0, 0, 0, 0, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[3, 0, -8, 4, 0, 8],\n [0, -11, 0, 5, 6, 2],\n [-8, 0, -13, 13, 10, -10],\n [4, 5, 13, -15, 8, 0],\n [0, 6, 10, 8, -14, 0],\n [8, 2, -10, 0, 0, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 4, 7, 6, 1, 3],\n [4, 9, 5, -9, 6, 0],\n [7, 5, 12, 0, 8, 2],\n [6, -9, 0, 1, -4, -8],\n [1, 6, 8, -4, -4, 0],\n [3, 0, 2, -8, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, -3, 0, 10, 3, -7],\n [0, 3, -12, 12, -1, -7],\n [0, 0, 8, -10, -8, -15],\n [0, 0, 0, 11, 0, -12],\n [0, 0, 0, 0, -6, 9],\n [0, 0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, -2, -5, 4, 5, -6],\n [-2, 12, -4, 8, 2, -2],\n [-5, -4, 6, -4, 2, 2],\n [4, 8, -4, 5, 4, -2],\n [5, 2, 2, 4, 5, -2],\n [-6, -2, 2, -2, -2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 8, -5, -9, -10, -13],\n [-7, -1, -14, -12, -14, -10],\n [-4, -9, -7, -10, 6, -11],\n [10, 11, 12, 10, -12, -6],\n [11, 4, -12, -11, 1, 2],\n [-13, 7, -3, 13, -15, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 7, 6, -14, -12, 0],\n [0, 1, 12, 5, -4, -14],\n [0, 0, -6, -10, -4, -4],\n [0, 0, 0, -12, -13, 9],\n [0, 0, 0, 0, 6, 14],\n [0, 0, 0, 0, 0, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -3, 4, -7, -7, -12],\n [0, -2, 2, -15, 3, -14],\n [0, 0, 6, -2, -7, 4],\n [0, 0, 0, -15, 14, 3],\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": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[10, 0, 4, -4, 11, 12],\n [0, -9, 10, -9, 2, 1],\n [4, 10, -4, 1, 6, 12],\n [-4, -9, 1, -6, 6, 7],\n [11, 2, 6, 6, 7, 0],\n [12, 1, 12, 7, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, -9, -12, 4, -11, -8],\n [-2, 4, 9, -13, 9, 2],\n [6, -1, 5, -11, 15, -1],\n [11, 15, -10, -6, 7, 4],\n [-1, 4, 12, -7, -12, -8],\n [10, -3, 1, -12, -14, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[4, -12, 3, -2, -12, -8],\n [3, 10, 3, 6, -15, 10],\n [6, -1, -5, -7, -13, 2],\n [3, 0, 0, 12, -13, 2],\n [-3, 11, 4, -8, -9, 10],\n [9, 8, 13, 7, 6, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "934", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, -14, 7, -9, 5, 5],\n [-14, -5, -6, -10, 2, 6],\n [7, -6, 14, -2, 0, -5],\n [-9, -10, -2, -11, 4, -2],\n [5, 2, 0, 4, 3, -2],\n [5, 6, -5, -2, -2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 5, -12, -4, -12, -11],\n [0, 15, 7, 3, -6, -2],\n [0, 0, -2, 0, -8, -7],\n [0, 0, 0, -2, 2, 15],\n [0, 0, 0, 0, 5, 11],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 12, 6, 12, -4, 14],\n [10, -1, 13, -8, -8, 6],\n [2, -2, 9, -6, -12, 0],\n [0, 13, 5, 1, -7, -5],\n [11, 11, 10, -3, -15, -9],\n [-5, 9, -13, -14, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[14, 12, 11, 2, -4, 0],\n [-13, -4, 10, 3, 4, 2],\n [-8, 15, 8, 14, -3, 12],\n [-8, -6, -2, -1, 5, -1],\n [10, -10, -2, -10, 7, -15],\n [-6, 3, -5, -13, 11, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 6, 1, -4, -11, -14],\n [0, -1, -5, -1, 15, -3],\n [0, 0, 15, -1, -4, 7],\n [0, 0, 0, -12, -5, 6],\n [0, 0, 0, 0, 14, -11],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 12, 2, -8, 7, 0],\n [0, 12, -7, -10, -9, 10],\n [0, 0, -7, -9, -7, 8],\n [0, 0, 0, 7, 1, 4],\n [0, 0, 0, 0, -11, 2],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, 13, -14, -5, -8, -2],\n [-4, 4, 8, 12, -9, 2],\n [9, -11, -10, -3, 14, 15],\n [-14, 3, 10, 12, -8, -5],\n [5, 0, 10, -15, 9, 15],\n [13, 11, 0, -4, 1, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[5, -6, -10, -10, -4, 5],\n [-6, 9, -2, -15, -12, 8],\n [-10, -2, -10, 0, 6, 4],\n [-10, -15, 0, 11, -8, 0],\n [-4, -12, 6, -8, -11, 1],\n [5, 8, 4, 0, 1, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[9, -8, 1, 14, -2, 1],\n [0, 2, -15, 8, -9, -10],\n [0, 0, -5, 9, 13, 1],\n [0, 0, 0, -6, -2, -4],\n [0, 0, 0, 0, 8, -4],\n [0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 4, -3, -8, 0, 3],\n [4, 0, -4, 0, -4, 0],\n [-3, -4, 0, 0, -13, 10],\n [-8, 0, 0, 11, -10, 0],\n [0, -4, -13, -10, -13, 2],\n [3, 0, 10, 0, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[9, 1, 12, -14, -15, 2],\n [-13, 13, -2, -3, -14, 6],\n [-12, -1, -11, -6, -7, 2],\n [-13, -2, -6, 1, -1, 2],\n [1, 14, 9, -13, 0, 3],\n [-3, 7, 1, 9, 7, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "491", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[8, -2, 6, -6, 0, 4],\n [-2, 2, -4, -2, -8, -6],\n [6, -4, 7, 2, 1, 2],\n [-6, -2, 2, -6, -6, -4],\n [0, -8, 1, -6, 10, 0],\n [4, -6, 2, -4, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, 12, 9, 12, -1],\n [0, 8, 3, 12, -2, -4],\n [0, 0, -10, 3, -14, -10],\n [0, 0, 0, -5, -15, 12],\n [0, 0, 0, 0, -1, 12],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-2, 9, 15, -15, -4, 5],\n [0, 4, 15, 3, 2, -2],\n [0, 0, 1, -3, -15, 13],\n [0, 0, 0, -14, 3, -1],\n [0, 0, 0, 0, -6, 2],\n [0, 0, 0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -10, 13, 0, -4, 2],\n [-10, 12, -6, 4, -3, 3],\n [13, -6, -3, -6, 2, -10],\n [0, 4, -6, 9, 0, 0],\n [-4, -3, 2, 0, -9, -8],\n [2, 3, -10, 0, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[6, -12, 3, -5, 10, -4],\n [-12, -13, 0, -2, -6, 10],\n [3, 0, 3, 2, -14, 4],\n [-5, -2, 2, 0, 2, 6],\n [10, -6, -14, 2, 15, 0],\n [-4, 10, 4, 6, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, 2, 11, 4, -6, 12],\n [2, 2, 2, 0, 2, 0],\n [11, 2, 9, -10, 6, 8],\n [4, 0, -10, 10, -2, -5],\n [-6, 2, 6, -2, 6, -6],\n [12, 0, 8, -5, -6, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -13, -13, 0, 9, 4],\n [0, -10, -15, -5, 2, 11],\n [0, 0, 2, 14, -5, 10],\n [0, 0, 0, 14, 5, -4],\n [0, 0, 0, 0, 9, -1],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 10, 11, 3, 5, -13],\n [0, -9, 0, 5, 5, -15],\n [0, 0, -1, -14, 0, -9],\n [0, 0, 0, 8, 14, 8],\n [0, 0, 0, 0, -7, 14],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 6, -8, 0, -2, -7],\n [6, -11, 2, -2, -8, -8],\n [-8, 2, 13, -2, -10, 4],\n [0, -2, -2, -10, 8, -6],\n [-2, -8, -10, 8, -12, -6],\n [-7, -8, 4, -6, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-4, 0, 8, 0, -11, -4],\n [0, -12, -10, 4, -6, 6],\n [8, -10, 2, 8, -8, 2],\n [0, 4, 8, -4, 2, 2],\n [-11, -6, -8, 2, -9, 0],\n [-4, 6, 2, 2, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "608", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, 0, 2, 10, -4],\n [2, 7, -2, 2, 0, 0],\n [0, -2, -13, 1, 6, 2],\n [2, 2, 1, 2, -5, 1],\n [10, 0, 6, -5, -12, 0],\n [-4, 0, 2, 1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, -2, 4, -8, -5, -6],\n [-2, 5, -9, -5, 2, -2],\n [4, -9, 14, 6, -2, 0],\n [-8, -5, 6, -8, 0, -4],\n [-5, 2, -2, 0, 14, -14],\n [-6, -2, 0, -4, -14, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "982", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[12, 14, -9, 4, -6, 8],\n [0, -15, 2, 10, -2, 3],\n [0, 0, -3, -9, -14, -9],\n [0, 0, 0, 1, 14, 14],\n [0, 0, 0, 0, 4, 6],\n [0, 0, 0, 0, 0, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, -6, -5, -10, 5, -6],\n [0, -5, 4, 8, 11, 3],\n [0, 0, 5, -4, 5, -10],\n [0, 0, 0, -3, 1, 15],\n [0, 0, 0, 0, 1, 3],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "750", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -12, -8, -6, 4, 2],\n [-12, -1, -6, -8, 8, -6],\n [-8, -6, -6, -4, 6, 10],\n [-6, -8, -4, -9, 8, 1],\n [4, 8, 6, 8, 14, -4],\n [2, -6, 10, 1, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[8, -14, -7, -1, 6, -2],\n [0, 1, 15, 1, -3, -8],\n [0, 0, -3, -9, -13, 8],\n [0, 0, 0, -9, 14, -11],\n [0, 0, 0, 0, -9, -9],\n [0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-15, 14, -5, -13, 6, -6],\n [-4, -10, 8, -9, 1, 1],\n [-12, -15, -15, 15, 10, 1],\n [-5, -13, 13, -6, -14, 0],\n [0, 11, 10, -8, -9, -6],\n [13, 8, -12, 14, -7, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-9, -12, -15, 11, -4, 0],\n [0, -8, 9, -3, -7, -6],\n [0, 0, -15, -13, -11, -9],\n [0, 0, 0, -15, 5, -13],\n [0, 0, 0, 0, 1, 11],\n [0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, -15, -1, 6, -13, -12],\n [0, -4, 8, 5, -4, -2],\n [0, 0, 9, -2, 11, 11],\n [0, 0, 0, 2, -8, -14],\n [0, 0, 0, 0, 4, -12],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, 13, 15, 5, 10, 15],\n [15, 4, 6, 9, 9, -8],\n [10, 1, 9, -11, 11, -13],\n [8, 8, 9, 2, -6, -12],\n [-6, 2, 13, -3, 6, 1],\n [-2, 10, 3, 2, 7, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "798", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-7, -12, -3, -14, 7, 9],\n [2, 8, 6, 9, -11, 1],\n [5, -6, 7, 11, 14, 7],\n [-12, 10, -10, 6, 11, 10],\n [-6, 1, -11, -9, -11, -8],\n [-15, 9, -14, 0, -8, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 2, -14, 7, 5, -3],\n [12, -2, -13, 0, 9, -2],\n [-1, 9, -13, -14, -13, -7],\n [13, -8, 3, 4, 5, 4],\n [12, -1, 11, -4, -2, 2],\n [11, 9, -14, 5, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "861", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[13, -2, -8, 5, -3, 8],\n [-2, 7, -10, 0, -12, 2],\n [-8, -10, 10, -1, 2, -3],\n [5, 0, -1, 3, 0, -2],\n [-3, -12, 2, 0, 4, 10],\n [8, 2, -3, -2, 10, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -9, -4, 10, -2, -1],\n [-9, 8, 0, -8, -1, 4],\n [-4, 0, -2, 5, 1, -6],\n [10, -8, 5, 1, -11, -4],\n [-2, -1, 1, -11, 4, -4],\n [-1, 4, -6, -4, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[11, -11, 0, -1, 0, -3],\n [-11, -2, -2, 8, -6, 1],\n [0, -2, 3, 4, -4, 2],\n [-1, 8, 4, 12, 3, 3],\n [0, -6, -4, 3, -15, -7],\n [-3, 1, 2, 3, -7, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-3, 9, 6, -7, 0, 0],\n [9, -2, 2, -14, 2, -3],\n [6, 2, -5, 4, -12, 12],\n [-7, -14, 4, -12, 14, 8],\n [0, 2, -12, 14, -14, 0],\n [0, -3, 12, 8, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, 2, -8, -8, 0, -2],\n [2, 12, -4, -2, 4, 4],\n [-8, -4, 5, 4, -10, 0],\n [-8, -2, 4, -11, -4, -2],\n [0, 4, -10, -4, 14, 0],\n [-2, 4, 0, -2, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -6, 9, -1, -12, 4],\n [-6, 10, -3, -2, 8, -2],\n [9, -3, -2, -14, 2, 0],\n [-1, -2, -14, -7, 4, -1],\n [-12, 8, 2, 4, -9, -4],\n [4, -2, 0, -1, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "803", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 0, 6, 0, 9, 0],\n [0, -10, 5, -3, 10, 2],\n [6, 5, 7, -2, 3, 9],\n [0, -3, -2, 6, 8, 0],\n [9, 10, 3, 8, -9, 0],\n [0, 2, 9, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "193", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, -15, -8, 0, 5, 9],\n [0, -11, -2, -4, -4, 14],\n [0, 0, -4, -5, -1, -9],\n [0, 0, 0, -1, -14, 6],\n [0, 0, 0, 0, 15, -15],\n [0, 0, 0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, 12, 5, 7, -13, -1],\n [-6, 5, 12, 3, -4, -13],\n [12, -2, 1, 11, -13, -9],\n [11, 9, 1, -1, 4, -6],\n [-9, 6, 4, 11, -13, 6],\n [-1, 4, -11, -14, -7, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -3, 13, -6, -7, -9],\n [-4, 15, -15, 8, 0, -12],\n [14, -2, 14, 12, 7, 13],\n [6, 7, 10, 10, 1, -4],\n [-1, 6, -4, -13, -6, 4],\n [1, -2, -3, 14, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "454", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -2, -14, 3, 7, -14],\n [0, 4, -4, 7, 12, 3],\n [0, 0, -8, -14, -6, 0],\n [0, 0, 0, 4, 6, 11],\n [0, 0, 0, 0, -12, -15],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, 14, -2, -3, -11],\n [-4, -8, -10, 2, -9, 3],\n [-1, -6, -7, 4, 0, 11],\n [4, -12, -6, -6, -8, -15],\n [-13, 8, -4, -9, 6, 7],\n [-15, 8, 4, 15, -15, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, -2, 6, -8, 14],\n [13, 13, 3, -2, 10, -2],\n [10, 6, 4, -8, -7, 9],\n [-2, -4, -3, -10, 15, -2],\n [15, -1, -14, 2, 14, -6],\n [9, 5, -9, 6, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "272", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, -3, -9, 9, 2],\n [0, -4, 8, 10, 1, -6],\n [0, 0, 5, -11, 7, -1],\n [0, 0, 0, -6, -2, 4],\n [0, 0, 0, 0, -15, 15],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 15, 12, 9, 1, -10],\n [8, -9, -10, -13, 9, 5],\n [-1, 12, 0, 1, -7, 10],\n [-7, 1, 13, -9, 9, -14],\n [10, -10, -6, 1, -2, -13],\n [11, 0, 0, -11, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "621", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 0, 0, 9, -6, 0],\n [0, -9, 8, 10, -3, 1],\n [0, 8, -5, 4, 2, 7],\n [9, 10, 4, 0, 3, 9],\n [-6, -3, 2, 3, 8, -2],\n [0, 1, 7, 9, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -9, 15, 3, -15, -15],\n [0, -5, 11, 12, 7, 2],\n [0, 0, 6, 14, 14, -1],\n [0, 0, 0, 5, -7, 3],\n [0, 0, 0, 0, -2, -3],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, 1, -4, -2, 6, 1],\n [1, 8, -6, 2, -8, 3],\n [-4, -6, -11, 0, 6, -14],\n [-2, 2, 0, -12, -1, 7],\n [6, -8, 6, -1, 5, -6],\n [1, 3, -14, 7, -6, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "581", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -9, 2, -6, 2, 2],\n [-9, -15, -11, -8, -6, -1],\n [2, -11, -7, -4, -5, -4],\n [-6, -8, -4, -9, 2, -5],\n [2, -6, -5, 2, 2, -12],\n [2, -1, -4, -5, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "687", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, -2, 1, -13, 9, -13],\n [0, -3, 5, 4, -6, 13],\n [0, 0, -4, 11, -7, 10],\n [0, 0, 0, 3, -10, -1],\n [0, 0, 0, 0, -11, 5],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 1, -12, 10, -4, 3],\n [0, 3, 3, 10, 13, -9],\n [0, 0, -14, 11, -8, -10],\n [0, 0, 0, 14, -7, -8],\n [0, 0, 0, 0, -1, 5],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "608", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, 1, 2, -1, -6, 4],\n [0, -9, 13, 15, 13, 1],\n [-11, 2, -2, 15, 2, 2],\n [-1, 9, -5, 10, -11, 0],\n [15, -8, -3, 10, 6, 11],\n [1, 10, -7, -1, -9, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "923", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, 6, -11, 4, 7, -8],\n [-2, 6, 1, 7, 4, -14],\n [3, 10, -12, -2, -9, 9],\n [0, -6, -5, 6, 10, -11],\n [9, -4, 8, 8, 8, -1],\n [8, 8, -6, 10, 7, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[13, 0, 9, 15, 13, 7],\n [-4, 13, -10, 0, 15, 3],\n [-5, -4, -12, -3, -14, 3],\n [-5, -15, -7, -6, -13, -8],\n [0, -12, -5, -8, -9, 4],\n [-1, 7, 12, -8, -6, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, -10, 10, 7, 2, -3],\n [0, -8, -7, -3, 14, 1],\n [0, 0, -6, -5, -6, 5],\n [0, 0, 0, -9, 9, -4],\n [0, 0, 0, 0, 12, 8],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "968", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -12, 4, 5, -8, -11],\n [-12, 4, 6, -2, 8, -8],\n [4, 6, -6, 10, -1, -3],\n [5, -2, 10, -14, 2, 6],\n [-8, 8, -1, 2, 13, 0],\n [-11, -8, -3, 6, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "776", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, -8, -7, 2, -14, 2],\n [-8, -14, 6, 0, -11, -6],\n [-7, -14, 0, 0, 1, -14],\n [10, -11, 15, -8, 8, -14],\n [-4, -3, 0, -11, -4, -1],\n [14, 15, 13, -14, -4, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "435", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -9, -10, -11, 3, -2],\n [0, 8, -5, 14, 7, 15],\n [0, 0, 5, -2, 5, 2],\n [0, 0, 0, 1, 9, -9],\n [0, 0, 0, 0, -14, 6],\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": "Compute |A| for the matrix A =\n[[-13, 3, -10, 7, -8, -9],\n [-1, -4, -1, -7, -14, 10],\n [4, -1, 2, -3, 0, -1],\n [-5, -13, 13, -6, 1, 14],\n [-8, -11, 5, -8, -1, 15],\n [-5, -7, 9, 10, 9, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "934", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, -11, -2, 8, -14, 11],\n [0, 4, -3, 0, 15, 14],\n [0, 0, -11, 6, 9, 5],\n [0, 0, 0, -11, -13, 6],\n [0, 0, 0, 0, 11, 11],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[15, 6, 13, 0, -3, 2],\n [2, 11, -7, 12, 15, -15],\n [12, -14, -8, 15, -3, -10],\n [3, 15, 3, 14, 11, 9],\n [-14, 15, -6, -11, 7, 6],\n [14, -15, -3, -4, -6, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[0, -12, 2, 12, -6, -10],\n [-5, -6, -15, 0, -11, -7],\n [15, 1, -12, -14, 11, 15],\n [-14, -11, -14, -3, -11, -15],\n [5, 13, 14, -1, 15, 3],\n [-2, -4, -14, 11, 4, -15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-2, -15, -11, -10, -7, 4],\n [0, -15, 14, 6, 9, -10],\n [0, 0, -12, 13, 2, 13],\n [0, 0, 0, 1, -14, -9],\n [0, 0, 0, 0, 11, 15],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, 15, -7, -7, 1, 10],\n [0, -14, -4, 6, 0, -14],\n [0, 0, 7, 14, 6, 12],\n [0, 0, 0, 1, -12, 3],\n [0, 0, 0, 0, -15, 11],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-15, 3, -4, 9, -9, -14],\n [5, -1, 4, -3, -9, -2],\n [15, 4, 0, 14, -7, 3],\n [6, -11, -6, -8, 13, -2],\n [-5, 14, -15, -6, -14, -9],\n [1, -11, 8, -6, -11, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "412", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, -5, -1, 11, -11, 15],\n [0, 3, -2, 5, 8, 10],\n [0, 0, 4, 12, -12, -13],\n [0, 0, 0, -6, 2, 3],\n [0, 0, 0, 0, -14, 0],\n [0, 0, 0, 0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-2, -1, 4, -9, 2, -5],\n [-6, -2, 14, -13, 2, -4],\n [5, -15, 14, -3, -14, -1],\n [15, -5, -10, -10, 12, 8],\n [9, 9, 7, -4, 0, 0],\n [-6, 1, 4, 7, -14, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "868", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 4, 0, 1, -3, 8],\n [4, 12, 4, -11, 0, 2],\n [0, 4, -11, 7, -4, 0],\n [1, -11, 7, 8, -10, -8],\n [-3, 0, -4, -10, -3, 10],\n [8, 2, 0, -8, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "894", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-5, 10, 2, 0, 8, -4],\n [10, -13, -7, 8, -6, 0],\n [2, -7, -13, 6, -3, 7],\n [0, 8, 6, 4, 6, -10],\n [8, -6, -3, 6, -2, 6],\n [-4, 0, 7, -10, 6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, -7, -13, 3, -5, -12],\n [0, 10, 11, -4, -12, -1],\n [0, 0, 6, -11, -6, 4],\n [0, 0, 0, 15, -4, -8],\n [0, 0, 0, 0, -7, -12],\n [0, 0, 0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 9, 7, -15, 14, -7],\n [0, 9, 2, -5, -9, 8],\n [0, 0, 7, 14, 7, -13],\n [0, 0, 0, -1, -1, -11],\n [0, 0, 0, 0, -2, 5],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -2, -1, -10, 2, 3],\n [-2, 11, -2, 3, 4, -3],\n [-1, -2, 3, 6, 3, -1],\n [-10, 3, 6, -6, 11, -4],\n [2, 4, 3, 11, -2, 11],\n [3, -3, -1, -4, 11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[2, -12, 4, -15, -3, 13],\n [0, -6, 12, -1, 8, 8],\n [0, 0, 2, -12, -15, -6],\n [0, 0, 0, -13, -12, -4],\n [0, 0, 0, 0, 12, -5],\n [0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[12, 8, -4, 2, 6, 10],\n [0, -1, -11, 8, -15, -7],\n [0, 0, -5, 12, 7, 8],\n [0, 0, 0, 15, -11, -2],\n [0, 0, 0, 0, 14, -1],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[11, -14, 1, -5, 7, 2],\n [0, 7, -15, 11, -4, 9],\n [0, 0, 1, 1, -14, 12],\n [0, 0, 0, -15, 13, 4],\n [0, 0, 0, 0, -8, -9],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, 6, -4, 2, -2, -5],\n [6, 6, 3, -10, -7, 6],\n [-4, 3, 11, 0, -2, 0],\n [2, -10, 0, 6, 8, 5],\n [-2, -7, -2, 8, 12, -4],\n [-5, 6, 0, 5, -4, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "919", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 2, -1, -8, 0, 6],\n [2, 7, 12, -2, 5, 0],\n [-1, 12, -2, 7, 0, -6],\n [-8, -2, 7, -15, 0, 7],\n [0, 5, 0, 0, 7, 0],\n [6, 0, -6, 7, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, -9, -9, 4, 2, 14],\n [-9, 5, 1, -6, -5, -8],\n [-9, 1, -8, 12, 0, 7],\n [4, -6, 12, 12, -12, -10],\n [2, -5, 0, -12, 4, -8],\n [14, -8, 7, -10, -8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 8, -2, 7, -10, 9],\n [12, -4, 14, 4, 10, -4],\n [14, -15, 14, -4, 10, -10],\n [-12, 1, -6, 3, -5, -15],\n [-11, 8, 12, -2, -3, -14],\n [12, -2, -10, -10, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 3, 0, 4, -4, -2],\n [3, 11, -2, -1, -7, 12],\n [0, -2, -2, 0, 4, -7],\n [4, -1, 0, -4, -4, 4],\n [-4, -7, 4, -4, -15, -6],\n [-2, 12, -7, 4, -6, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, -3, 14, -3, -1, 3],\n [-1, 12, -1, -11, -11, -14],\n [2, -10, 2, 14, 6, 12],\n [12, -9, 13, 4, 10, 4],\n [13, -13, 1, 4, 3, -8],\n [5, 7, 3, 3, 11, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, 10, -8, 7, 9, -7],\n [0, 12, -13, 14, 12, 11],\n [0, 0, 3, -15, -3, -4],\n [0, 0, 0, 13, -8, 14],\n [0, 0, 0, 0, 7, -2],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "620", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, -7, 11, 12, 12, -11],\n [0, 15, -9, -6, 15, -7],\n [0, 0, -1, 13, 12, -5],\n [0, 0, 0, 13, -1, 1],\n [0, 0, 0, 0, 10, 15],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 2, -2, 10, -4, -10],\n [2, -15, 0, 6, 5, 2],\n [-2, 0, 2, -6, 6, -4],\n [10, 6, -6, 9, 12, 4],\n [-4, 5, 6, 12, -13, 6],\n [-10, 2, -4, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[15, -4, -12, 0, -8, 6],\n [-4, 12, 5, -2, -10, -8],\n [-12, 5, 14, -9, 2, 0],\n [0, -2, -9, -13, 1, 9],\n [-8, -10, 2, 1, 0, -6],\n [6, -8, 0, 9, -6, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, 2, -12, 7, 12, 2],\n [-5, -4, -6, 12, 8, -13],\n [-1, 2, 0, -9, -5, 12],\n [-6, -7, 4, 2, 9, 10],\n [5, -3, 10, 7, -6, 5],\n [-4, -3, 5, 6, -11, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-11, -7, -7, 2, 8, -11],\n [14, 0, -14, 9, -12, 5],\n [7, 2, -11, -8, -4, -2],\n [11, 1, -4, 11, 8, -14],\n [-12, -5, -4, 3, -14, -6],\n [-6, -14, 10, 6, 3, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[12, -4, 14, -9, 0, 8],\n [-4, -3, -8, 4, -5, -1],\n [14, -8, 7, -2, -2, -13],\n [-9, 4, -2, -12, -1, -5],\n [0, -5, -2, -1, 5, -8],\n [8, -1, -13, -5, -8, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "911", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, -6, -8, -2, 3, -2],\n [-6, -1, 6, -8, -13, -1],\n [-8, 6, -4, -9, -2, -6],\n [-2, -8, -9, -13, -6, 0],\n [3, -13, -2, -6, -15, 2],\n [-2, -1, -6, 0, 2, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, -2, -11, 13, 3, -14],\n [0, 15, -10, -5, -4, 8],\n [0, 0, 13, -6, -2, -12],\n [0, 0, 0, -1, -7, 10],\n [0, 0, 0, 0, -4, -2],\n [0, 0, 0, 0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 15, 15, 15, -8, -8],\n [0, 3, -11, 15, -9, 14],\n [0, 0, -2, 9, 5, -1],\n [0, 0, 0, 15, 4, 15],\n [0, 0, 0, 0, 13, 1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "830", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 14, -11, -2, 10, 4],\n [0, 7, -2, 6, -14, 5],\n [0, 0, 2, -10, -7, -7],\n [0, 0, 0, -4, 9, 5],\n [0, 0, 0, 0, 6, 4],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 0, -1, 13, -5, 4],\n [7, 1, 14, 12, 3, 6],\n [10, 1, -1, -3, 7, 2],\n [7, 0, 14, 4, 9, 5],\n [-15, 12, 11, 4, 11, -3],\n [-12, -4, -1, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 10, -1, 5, -11, -5],\n [0, -6, 12, 10, -3, 9],\n [0, 0, 4, -1, 2, -8],\n [0, 0, 0, -5, 11, -11],\n [0, 0, 0, 0, 10, -10],\n [0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -1, -1, -3, 0, 8],\n [-1, -3, -6, 6, 6, 2],\n [-1, -6, -9, 2, -10, 3],\n [-3, 6, 2, -5, -5, 2],\n [0, 6, -10, -5, 0, -4],\n [8, 2, 3, 2, -4, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, -5, 2, 6, 9, -11],\n [-11, 4, 1, -12, -7, -2],\n [-7, 7, -3, 0, 4, -3],\n [-7, 5, -4, -4, -6, 13],\n [-14, 9, 6, -11, -5, 10],\n [12, 8, -14, 5, -6, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, -6, 10, -5, -7, -9],\n [0, -9, 0, 9, 3, 0],\n [0, 0, -2, -3, 13, -13],\n [0, 0, 0, -9, -14, -6],\n [0, 0, 0, 0, -10, 13],\n [0, 0, 0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -11, -2, 2, -4, 6],\n [-11, 2, -4, -4, 2, 0],\n [-2, -4, -5, -6, 2, 2],\n [2, -4, -6, 14, 0, -3],\n [-4, 2, 2, 0, -9, 4],\n [6, 0, 2, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "761", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[10, -13, 11, 2, -13, 13],\n [-4, -14, 14, -8, 15, 12],\n [5, -2, 3, -5, 0, -2],\n [-8, 14, 8, 11, 4, -2],\n [9, -4, 1, 7, -4, 5],\n [-4, -4, -9, -6, 14, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "751", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 2, 11, 15, -13, -13],\n [-9, 6, 1, 12, 13, -10],\n [0, 12, -11, 6, 8, 1],\n [13, -5, 6, -4, -4, -12],\n [-7, -2, -4, -6, -8, 7],\n [-13, 11, -3, 0, 9, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "824", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 3, 6, 14, 2, -8],\n [0, 1, 8, -7, -6, -7],\n [0, 0, -6, 13, -8, -12],\n [0, 0, 0, -9, 9, -6],\n [0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-12, 0, 4, -6, -2, -14],\n [0, -12, -4, -1, 6, -2],\n [4, -4, -6, -7, -4, 3],\n [-6, -1, -7, 15, 0, 3],\n [-2, 6, -4, 0, -10, 4],\n [-14, -2, 3, 3, 4, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "924", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-12, 8, 0, 9, 0, 4],\n [8, -5, 2, -2, 4, -4],\n [0, 2, 13, 2, 4, 3],\n [9, -2, 2, 12, -8, -2],\n [0, 4, 4, -8, 0, 4],\n [4, -4, 3, -2, 4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, 8, 13, 10, -7, 3],\n [0, -4, -5, 10, -15, -5],\n [0, 0, 11, -8, 9, 4],\n [0, 0, 0, -5, 13, 3],\n [0, 0, 0, 0, -10, 12],\n [0, 0, 0, 0, 0, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-7, 9, -6, 6, -4, 2],\n [9, -14, -6, 2, 10, 2],\n [-6, -6, 14, -2, 0, 2],\n [6, 2, -2, -12, 10, -8],\n [-4, 10, 0, 10, 10, 6],\n [2, 2, 2, -8, 6, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[8, 1, 10, 9, 4, -10],\n [0, 3, -15, -10, 10, -11],\n [0, 0, -3, 4, 1, 10],\n [0, 0, 0, -3, 7, -15],\n [0, 0, 0, 0, 11, 8],\n [0, 0, 0, 0, 0, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "504", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, 4, -4, 2, 0, 6],\n [4, -2, -6, 0, -9, -4],\n [-4, -6, -11, -3, -7, -7],\n [2, 0, -3, 11, -14, -7],\n [0, -9, -7, -14, 10, -2],\n [6, -4, -7, -7, -2, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, 8, -11, -5, 6, 1],\n [0, 3, 4, 11, 7, 11],\n [0, 0, -11, 1, 3, -5],\n [0, 0, 0, -13, -1, 2],\n [0, 0, 0, 0, -11, -7],\n [0, 0, 0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, 10, 4, 10, -6, -10],\n [10, 15, 10, -6, -2, 2],\n [4, 10, 13, -5, 3, 5],\n [10, -6, -5, -8, 5, 6],\n [-6, -2, 3, 5, 14, -4],\n [-10, 2, 5, 6, -4, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -4, -5, 0, -10, 6],\n [-4, 12, 10, 4, -6, 0],\n [-5, 10, -8, 10, 7, -4],\n [0, 4, 10, -11, 8, 8],\n [-10, -6, 7, 8, 5, 11],\n [6, 0, -4, 8, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "848", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 12, 0, -10, 4, 8],\n [-6, -12, -10, 14, -4, -13],\n [12, -4, 7, 0, -4, -1],\n [6, 7, 15, 5, 5, 2],\n [0, -10, 1, 7, -13, 2],\n [-5, 7, 9, 1, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, 3, -1, 0, -1],\n [-4, 10, 4, 6, -8, 9],\n [3, 4, 5, -2, -9, 2],\n [-1, 6, -2, 10, 2, -1],\n [0, -8, -9, 2, -1, -12],\n [-1, 9, 2, -1, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[2, -10, -2, 2, -5, 4],\n [0, 5, -3, 0, 11, 8],\n [0, 0, 7, -2, 6, -13],\n [0, 0, 0, -6, -15, 2],\n [0, 0, 0, 0, -11, 10],\n [0, 0, 0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, 9, 11, 6, -3],\n [0, 14, 6, -10, -15, -15],\n [0, 0, 2, 11, -4, -15],\n [0, 0, 0, 13, -3, -2],\n [0, 0, 0, 0, -12, -7],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "472", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 10, -9, 12, -9, 4],\n [-15, -8, 10, -15, -4, 14],\n [1, 9, 13, 10, 15, -6],\n [12, 3, -7, -6, -5, -6],\n [14, 12, 14, 1, -9, -11],\n [12, 12, 4, 11, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "765", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[14, -15, -6, -9, 11, -4],\n [0, 14, 12, -7, -11, -11],\n [0, 0, 3, 10, 2, -8],\n [0, 0, 0, -13, 12, -2],\n [0, 0, 0, 0, -4, -5],\n [0, 0, 0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[5, 6, 4, 2, 2, -1],\n [6, 4, 2, -4, 8, -5],\n [4, 2, 3, 0, 4, 1],\n [2, -4, 0, 3, -10, 2],\n [2, 8, 4, -10, 0, 5],\n [-1, -5, 1, 2, 5, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "444", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, 3, -6, -8, 4, -11],\n [0, 5, 11, -14, -15, 15],\n [0, 0, 12, -11, 2, 7],\n [0, 0, 0, -7, 0, 4],\n [0, 0, 0, 0, -15, 9],\n [0, 0, 0, 0, 0, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -2, 10, 0, 4, -3],\n [-2, 6, 4, -12, 4, -8],\n [10, 4, -8, -8, 8, -10],\n [0, -12, -8, 4, 4, -8],\n [4, 4, 8, 4, 3, 6],\n [-3, -8, -10, -8, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -8, 11, 1, 3, -1],\n [14, -15, 14, 2, -9, -9],\n [13, 0, -5, -11, 5, -2],\n [7, 10, 11, 15, 12, -6],\n [-11, 14, 8, 3, 2, 10],\n [-12, 15, 7, -7, 3, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, 2, 0, 7, 10, 3],\n [8, -7, -5, -5, -2, -6],\n [-7, -11, 10, 11, -5, 12],\n [-7, -3, 13, 3, -8, 7],\n [-12, -4, 9, 15, -9, 8],\n [11, -8, 3, 7, -8, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[14, -13, -15, 6, -6, 1],\n [-15, 0, 7, -15, 11, 13],\n [-13, -11, 3, 15, 6, 15],\n [-2, -2, 9, 2, -9, 4],\n [13, -5, 6, -6, -4, -6],\n [-10, 15, -8, -9, -3, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-10, 14, -11, 0, -5, 7],\n [9, -15, -6, 13, 1, 15],\n [5, 8, 7, -9, -13, 9],\n [-11, 11, 14, -4, -6, -13],\n [0, -10, 0, 8, -8, 4],\n [13, 15, 4, -7, 14, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-5, -10, 6, 13, 12, -14],\n [-15, 7, -12, -7, -5, 8],\n [-10, 0, -6, -13, 8, 12],\n [-6, -4, 15, -15, 11, 9],\n [-6, 13, 9, -6, 8, 10],\n [-12, -7, 11, -7, -4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0, -8, 2, -7],\n [-12, -2, 8, 4, 6, 8],\n [5, 6, 2, 4, -11, -15],\n [7, -10, 4, -12, 3, 12],\n [1, -10, -11, -10, 15, 10],\n [-15, 2, 15, -1, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-13, -15, -4, -9, -5, -3],\n [0, 6, -4, -10, -10, -9],\n [0, 0, -7, 5, 14, 12],\n [0, 0, 0, -1, -15, -2],\n [0, 0, 0, 0, -3, 5],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 10, -12, 5, 14, 12],\n [0, -4, -3, 14, 2, -3],\n [0, 0, 11, 12, 2, -11],\n [0, 0, 0, 7, -6, -2],\n [0, 0, 0, 0, -5, 14],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, 2, 0, -7, 2, -6],\n [0, -11, 11, -14, -7, 2],\n [0, 0, 11, -15, 15, -2],\n [0, 0, 0, 6, 11, 2],\n [0, 0, 0, 0, 11, -13],\n [0, 0, 0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, 0, -13, 13, -14],\n [5, 9, -2, -1, 12, 8],\n [-8, -15, 9, 8, -2, 11],\n [14, -2, 13, 3, -8, -7],\n [-1, -4, 2, 15, -15, -1],\n [15, -15, -15, 5, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -14, -9, 15, 9, 6],\n [0, -6, -3, -11, 10, 11],\n [0, 0, 13, -2, 2, 6],\n [0, 0, 0, 10, 4, 5],\n [0, 0, 0, 0, -14, -2],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-13, 0, -4, -2, 8, 2],\n [0, 2, 8, 0, -10, 5],\n [-4, 8, -7, 4, -4, -7],\n [-2, 0, 4, -14, 12, 4],\n [8, -10, -4, 12, -2, 0],\n [2, 5, -7, 4, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "588", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -1, 1, 14, -12, 0],\n [-1, 8, -4, 10, -4, 10],\n [1, -4, 2, -2, 2, -10],\n [14, 10, -2, 1, 4, -2],\n [-12, -4, 2, 4, -15, 11],\n [0, 10, -10, -2, 11, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "386", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 3, 14, 3, -7, 5],\n [-13, 11, 5, 12, -7, 3],\n [0, 14, 5, -14, -8, -2],\n [-10, -4, 8, -15, 2, 7],\n [-9, 12, 11, 9, -4, -4],\n [-10, 12, 7, 4, -14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, 2, -5, -8, 12, -6],\n [2, 11, -2, -4, 2, -4],\n [-5, -2, -9, 2, 2, 4],\n [-8, -4, 2, 8, -3, 3],\n [12, 2, 2, -3, 15, -8],\n [-6, -4, 4, 3, -8, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -6, 7, 7, 7, -12],\n [-4, -11, -12, 14, -7, 4],\n [-15, 0, -8, -3, 6, 2],\n [-15, 10, 14, 14, -9, -2],\n [-8, 0, -2, -6, -7, 11],\n [4, -9, -11, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-8, 1, 0, -10, -6, -14],\n [1, 7, -10, -8, -3, -6],\n [0, -10, 15, 5, 9, 4],\n [-10, -8, 5, 10, 5, 0],\n [-6, -3, 9, 5, 11, -7],\n [-14, -6, 4, 0, -7, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[15, -8, 11, 13, 12, -2],\n [7, -12, 4, -14, -7, -10],\n [13, 11, 3, 15, -13, 13],\n [-3, 11, -5, 12, -2, 1],\n [2, -11, 9, -13, -9, -10],\n [11, -13, 11, 4, -3, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 11, -5, -11, -15, 13],\n [0, 4, 9, 2, 10, -2],\n [0, 0, 6, -11, -6, -6],\n [0, 0, 0, 13, 8, -10],\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": "560", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -14, -13, -7, 3, 1],\n [9, -14, 10, -10, -5, 13],\n [12, 14, -5, 7, -7, 12],\n [12, 0, 8, 6, 4, 14],\n [4, 14, -2, 4, -5, -6],\n [-14, -9, -15, -11, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[4, 2, -7, 12, -15, 4],\n [0, 4, 10, -6, -12, 2],\n [0, 0, -4, 10, 9, -7],\n [0, 0, 0, -2, 8, -7],\n [0, 0, 0, 0, 2, -7],\n [0, 0, 0, 0, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 12, 7, 4, 7, -11],\n [-15, 0, -5, -12, -11, 0],\n [11, 13, -4, 14, -4, -12],\n [7, 1, -7, -10, 12, -8],\n [-8, 9, 5, -8, -8, 13],\n [-1, -2, -10, -6, 11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, 2, 15, -9, -15, -9],\n [-15, -2, -3, 5, -3, 1],\n [-8, 1, 14, -3, 6, 15],\n [1, -1, -14, -3, 4, 13],\n [12, -8, -13, 15, 8, -9],\n [12, 6, 10, 1, 15, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, 2, 8, 0, -8, 0],\n [2, -1, -6, 5, 8, -2],\n [8, -6, -3, -4, 0, 2],\n [0, 5, -4, 0, 0, 4],\n [-8, 8, 0, 0, -4, -2],\n [0, -2, 2, 4, -2, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "472", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[2, 1, 4, -3, 8, 0],\n [0, -10, 14, -3, 10, -4],\n [0, 0, -12, 8, -4, 4],\n [0, 0, 0, 11, -2, 5],\n [0, 0, 0, 0, -6, 13],\n [0, 0, 0, 0, 0, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-15, 4, 1, 10, 11, -15],\n [-11, 8, 1, -11, -5, 8],\n [-13, 13, 6, 7, -6, 14],\n [15, 8, -2, 3, 13, -5],\n [-15, -4, 10, 8, 4, -14],\n [-15, -1, -3, 6, -3, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, -6, -3, 10, 14, 0],\n [-6, -8, -1, 10, -6, 6],\n [-3, -1, -4, 3, -4, -7],\n [10, 10, 3, 4, 4, 4],\n [14, -6, -4, 4, 0, 4],\n [0, 6, -7, 4, 4, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, -9, -2, -2, -2, 0],\n [-9, 13, 0, 6, -2, 2],\n [-2, 0, -11, 6, -1, 0],\n [-2, 6, 6, 9, 14, -8],\n [-2, -2, -1, 14, 5, -4],\n [0, 2, 0, -8, -4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "580", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-7, 3, 1, 13, 3, 7],\n [0, 1, -2, -2, 4, 7],\n [0, 0, 14, 12, 3, -9],\n [0, 0, 0, 7, -7, 10],\n [0, 0, 0, 0, 4, -4],\n [0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[13, 6, -6, -8, -5, 0],\n [6, 1, 4, -8, -6, -2],\n [-6, 4, 1, -7, -10, 6],\n [-8, -8, -7, 0, -12, -8],\n [-5, -6, -10, -12, 10, 6],\n [0, -2, 6, -8, 6, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 9, 4, -1, 4, 6],\n [0, -2, -13, -13, 9, 7],\n [0, 0, -14, -12, -8, -7],\n [0, 0, 0, 8, -13, -5],\n [0, 0, 0, 0, -7, 13],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -8, 8, -1, -6, 7],\n [0, -10, 13, 15, 0, -6],\n [0, 0, -3, -8, 15, -12],\n [0, 0, 0, -5, -15, -5],\n [0, 0, 0, 0, 13, 8],\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 determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 3, -14, -15, -2, -4],\n [-1, 3, 6, 10, 1, 14],\n [2, -7, -15, -15, -7, 3],\n [-10, 12, 3, 2, 11, -13],\n [10, -12, -5, 1, -13, 7],\n [-14, 7, -12, 7, -5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "802", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 5, 0, 0, 4, 4],\n [5, -13, -8, 8, -11, 6],\n [0, -8, 10, -7, 4, 6],\n [0, 8, -7, 3, 0, 0],\n [4, -11, 4, 0, -8, 3],\n [4, 6, 6, 0, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, -11, 8, 1, -5],\n [-12, 10, 10, 13, -1, -9],\n [-11, -2, -15, -9, -3, -3],\n [-15, -1, -14, -8, 9, -8],\n [8, -2, 6, 7, -12, 12],\n [-3, -11, -2, 2, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[14, 3, -15, 6, 8, 15],\n [0, -8, 0, 11, -12, 6],\n [-1, -2, -15, 6, 12, -15],\n [-12, -1, 15, 9, -10, -12],\n [10, 4, -12, -6, -9, 11],\n [9, -10, 7, 15, -12, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 15, -15, 13, -11, -5],\n [-5, -5, -1, -15, -5, -10],\n [12, 1, 2, -5, -7, 11],\n [13, -4, -3, 15, -13, 9],\n [14, -12, 5, 0, 7, -12],\n [12, 11, -4, -6, 10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "974", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[12, 11, -15, 6, -6, 12],\n [0, -3, -10, -3, -4, 7],\n [10, 10, -11, 13, -9, -14],\n [2, -6, 8, 6, 5, 3],\n [4, 8, -6, -9, -3, 9],\n [-3, -5, 3, 6, -9, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "806", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[0, 0, 0, -4, -8, -8],\n [0, -15, 6, 2, 11, 10],\n [0, 6, 8, 14, -6, -7],\n [-4, 2, 14, 10, -10, -12],\n [-8, 11, -6, -10, -12, 6],\n [-8, 10, -7, -12, 6, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "968", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 3, 1, 0, 6, 0],\n [3, 7, 0, -8, -2, 4],\n [1, 0, 0, 6, -1, -2],\n [0, -8, 6, -5, -2, -8],\n [6, -2, -1, -2, -9, -7],\n [0, 4, -2, -8, -7, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 3, 5, 8, -15, -5],\n [-15, 7, 1, 3, -8, -7],\n [5, -1, 6, 13, -8, -13],\n [1, 9, 2, 12, -5, 14],\n [9, -5, -14, 8, 0, -13],\n [-3, 9, 10, -3, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "823", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-3, -1, -6, 10, -8, 5],\n [-1, 14, 4, -4, 10, 8],\n [-6, 4, -8, 10, -6, 6],\n [10, -4, 10, -7, 5, 0],\n [-8, 10, -6, 5, -7, 12],\n [5, 8, 6, 0, 12, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, 5, -4, -11, 8, 3],\n [0, 1, -15, 3, 1, 11],\n [0, 0, 3, 11, -7, 5],\n [0, 0, 0, -14, 6, -2],\n [0, 0, 0, 0, 10, 4],\n [0, 0, 0, 0, 0, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -11, -3, -6, -13, -5],\n [-11, 6, 9, 9, -12, 10],\n [-11, -8, 14, -7, -1, -15],\n [3, -4, -3, -12, 0, 9],\n [-4, -1, -15, -2, 11, 14],\n [10, -1, -8, 13, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, -8, 4, 4, 2, 3],\n [-8, 6, 1, -3, 11, 8],\n [4, 1, -12, 0, 4, -6],\n [4, -3, 0, 0, -12, 2],\n [2, 11, 4, -12, 2, 6],\n [3, 8, -6, 2, 6, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -8, -15, 10, 15, 5],\n [0, 15, 13, 13, -10, -11],\n [0, 0, -1, 6, 3, 14],\n [0, 0, 0, 10, 1, 5],\n [0, 0, 0, 0, 3, 6],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 0, -7, -3, -3, 7],\n [0, 3, -14, -11, 2, 2],\n [-7, -14, 4, 2, 7, 6],\n [-3, -11, 2, 6, 6, -2],\n [-3, 2, 7, 6, 13, 9],\n [7, 2, 6, -2, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 7, 3, 8, 5],\n [0, -9, -9, -10, 3, -5],\n [0, 0, -3, 9, 2, -14],\n [0, 0, 0, -14, -15, -4],\n [0, 0, 0, 0, 6, -11],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "472", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -2, 4, -7, -5, -5],\n [0, 9, 4, -14, -1, 2],\n [0, 0, 6, 6, 7, 13],\n [0, 0, 0, 13, 15, -4],\n [0, 0, 0, 0, -7, 11],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 2, -2, 0, -1, 2],\n [2, -4, 0, 2, 2, -2],\n [-2, 0, 4, 5, -3, -2],\n [0, 2, 5, 12, -2, -10],\n [-1, 2, -3, -2, -15, 4],\n [2, -2, -2, -10, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "420", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, -4, 4, 6, -2],\n [7, 0, -3, 10, -3, -1],\n [-5, 12, 7, -8, -7, -11],\n [-14, -6, 12, -3, -1, 5],\n [-2, -5, -2, -9, 13, -2],\n [-13, -6, 5, -10, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[7, 15, 15, -1, 4, 10],\n [-2, -10, -15, -8, 15, 12],\n [-12, -3, -13, 13, 9, -14],\n [8, -5, -10, 13, -3, 6],\n [10, 6, -14, -2, -5, 12],\n [7, -8, 8, -6, -1, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "596", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, 7, -13, 14, -4, 5],\n [0, -1, -5, -13, 3, -5],\n [0, 0, -14, -14, -4, -8],\n [0, 0, 0, -5, 0, -5],\n [0, 0, 0, 0, -5, 6],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "650", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, -5, -5, 2, 2, 4],\n [-5, 13, -1, -12, -12, 10],\n [-5, -1, -1, -6, 4, 2],\n [2, -12, -6, 4, 10, -8],\n [2, -12, 4, 10, 12, 0],\n [4, 10, 2, -8, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-4, -5, 8, -5, -3, -7],\n [0, 0, -15, 3, 7, 12],\n [3, 14, 5, -12, -11, -13],\n [3, -3, 12, 12, 10, -3],\n [8, 3, -3, 8, -11, 1],\n [2, -4, 7, 1, 2, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, 9, -2, -15, 4, 12],\n [0, -10, -14, 10, -7, 0],\n [0, 0, -5, 4, -10, 15],\n [0, 0, 0, -4, -1, 9],\n [0, 0, 0, 0, 7, 4],\n [0, 0, 0, 0, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, -3, -11, -1, -4, -7],\n [0, -4, -1, -4, 8, 6],\n [0, 0, 11, 3, -1, 9],\n [0, 0, 0, -4, -4, 2],\n [0, 0, 0, 0, 3, 7],\n [0, 0, 0, 0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, -8, 3, -6, -3, 8],\n [-8, -8, -8, 0, -8, 6],\n [3, -8, -12, -2, 4, 6],\n [-6, 0, -2, 4, 7, 0],\n [-3, -8, 4, 7, -13, -7],\n [8, 6, 6, 0, -7, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, 4, -11, 14, 5, 0],\n [0, -12, 11, 1, -3, -13],\n [0, 0, 8, -5, -12, 9],\n [0, 0, 0, 8, -12, -14],\n [0, 0, 0, 0, 14, 1],\n [0, 0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 6, -5, -4, -3, -4],\n [6, 4, 10, -4, -6, 14],\n [-5, 10, -4, -4, 6, -8],\n [-4, -4, -4, 1, 2, 10],\n [-3, -6, 6, 2, 13, -6],\n [-4, 14, -8, 10, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -14, -6, -13, 10, -14],\n [0, -14, 10, -14, -10, 15],\n [0, 0, 4, -6, 4, -15],\n [0, 0, 0, 12, -14, -2],\n [0, 0, 0, 0, -7, -5],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[11, 0, -10, -8, -4, -2],\n [0, -10, -4, -8, -2, 2],\n [-10, -4, 8, 2, 1, -2],\n [-8, -8, 2, -14, 3, -2],\n [-4, -2, 1, 3, -7, -2],\n [-2, 2, -2, -2, -2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -14, -6, -9, -13, -15],\n [0, 15, -12, -13, -11, 1],\n [0, 0, 11, -15, -3, -9],\n [0, 0, 0, 5, 2, 9],\n [0, 0, 0, 0, -15, -14],\n [0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -12, -8, 12, -15, -2],\n [-7, 2, 8, 7, 10, -4],\n [-14, 10, 10, -10, -11, 7],\n [2, -2, -1, 10, -3, 15],\n [-7, 12, 3, -15, -8, 0],\n [7, -9, 0, -3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[15, -8, 10, 4, -13, -4],\n [-8, -1, -5, -3, 10, 7],\n [-8, -3, 0, 2, 0, -3],\n [-2, -8, 13, 4, -14, 4],\n [-8, 13, 12, 11, -10, -3],\n [-13, -9, -10, -11, 11, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 6, -13, -11, -13, -1],\n [0, -1, 11, -3, 14, -14],\n [0, 0, -12, -14, 14, 4],\n [0, 0, 0, -2, -13, 15],\n [0, 0, 0, 0, 13, 7],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 14, -3, 0, 4, -11],\n [0, -5, 1, 6, 14, -6],\n [0, 0, 9, -5, -8, 3],\n [0, 0, 0, -15, 9, 10],\n [0, 0, 0, 0, 6, -6],\n [0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, -15, 10, -5, -11],\n [0, 13, -12, -15, 15, -12],\n [0, 0, 9, 7, 6, 15],\n [0, 0, 0, 3, -14, 7],\n [0, 0, 0, 0, -12, -15],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[12, 2, 3, 3, -10, -4],\n [10, -10, -2, 1, 10, 12],\n [-4, -14, -3, -11, 9, 6],\n [15, -10, 15, -15, -8, -7],\n [12, -4, 5, -6, -13, -6],\n [-2, -11, -11, -3, 13, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, 9, -6, -14, -1, 14],\n [0, -11, 11, 1, 7, 7],\n [0, 0, 10, -6, -1, -14],\n [0, 0, 0, 13, -11, -10],\n [0, 0, 0, 0, -3, -2],\n [0, 0, 0, 0, 0, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, -5, 6, 3, -3],\n [-2, 9, -4, 10, -1, -4],\n [-5, -4, -4, 1, -2, 1],\n [6, 10, 1, 6, 5, -1],\n [3, -1, -2, 5, 3, -2],\n [-3, -4, 1, -1, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "930", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[11, 11, 15, 14, 1, -13],\n [0, 10, 13, 15, 8, 5],\n [0, 0, 2, -1, -6, -1],\n [0, 0, 0, -10, -2, 10],\n [0, 0, 0, 0, -5, 9],\n [0, 0, 0, 0, 0, 14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 9, 5, 0, -13, -9],\n [0, -6, 3, -10, 10, -7],\n [0, 0, -11, 10, -11, -10],\n [0, 0, 0, -5, 14, 0],\n [0, 0, 0, 0, -12, -11],\n [0, 0, 0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, 15, -13, 10, -12, 5],\n [-12, 3, -7, 11, 15, -1],\n [13, -7, -4, -11, 1, 1],\n [12, -2, -9, 3, -8, 6],\n [15, -10, -10, -10, 3, 6],\n [3, 5, 1, -14, -14, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "852", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-7, -2, 0, 6, -3, 6],\n [-2, -10, 0, 2, -4, 11],\n [0, 0, 1, 2, 4, 4],\n [6, 2, 2, -10, 0, -2],\n [-3, -4, 4, 0, 11, 2],\n [6, 11, 4, -2, 2, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "808", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, -4, 5, 4, 8, 3],\n [-4, 12, -7, -4, 8, 8],\n [5, -7, 3, -6, 0, 0],\n [4, -4, -6, -11, -10, -2],\n [8, 8, 0, -10, -10, -3],\n [3, 8, 0, -2, -3, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 7, 15, 5, 4, -12],\n [0, -15, -8, 11, 1, 6],\n [0, 0, -5, -9, -5, -5],\n [0, 0, 0, -1, 12, -10],\n [0, 0, 0, 0, -3, 0],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[4, -1, -14, 14, 5, 14],\n [-4, -9, -5, 6, 9, -1],\n [15, -9, 6, -8, 7, 7],\n [8, -4, -10, 10, -2, 12],\n [-11, -12, 8, 9, 14, 9],\n [11, 12, -12, 13, -7, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 0, -11, 4, -3, -6],\n [0, 14, 12, 14, 6, -6],\n [-11, 12, 5, -9, -1, 10],\n [4, 14, -9, -13, 8, 0],\n [-3, 6, -1, 8, 5, -10],\n [-6, -6, 10, 0, -10, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, -5, 4, 4, -8, 4],\n [-5, -9, 8, 0, -11, 0],\n [4, 8, -10, 4, -14, -4],\n [4, 0, 4, 7, 6, 6],\n [-8, -11, -14, 6, -7, -6],\n [4, 0, -4, 6, -6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "572", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -7, 4, 1, 10, -7],\n [0, -1, -6, -6, 14, -12],\n [0, 0, -7, -11, -6, -7],\n [0, 0, 0, 9, 3, 9],\n [0, 0, 0, 0, 7, 11],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "869", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -2, 0, -12, -10, -2],\n [-2, 7, -6, -6, 8, 4],\n [0, -6, 9, 2, -2, -4],\n [-12, -6, 2, -6, -2, 3],\n [-10, 8, -2, -2, 6, -2],\n [-2, 4, -4, 3, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, 4, 6, 0, 8, 6],\n [4, 10, 9, 8, 4, -8],\n [6, 9, 13, -4, 11, 6],\n [0, 8, -4, 12, 2, -2],\n [8, 4, 11, 2, 3, -6],\n [6, -8, 6, -2, -6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "608", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 7, -4, -1, 0, -1],\n [7, -15, 4, -7, 0, 8],\n [-4, 4, -3, 6, 3, 14],\n [-1, -7, 6, -7, 2, 3],\n [0, 0, 3, 2, 11, 2],\n [-1, 8, 14, 3, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, -6, -11, 2, 6, 0],\n [-6, -2, 2, 0, 2, -3],\n [-11, 2, 13, 2, -4, 3],\n [2, 0, 2, 9, 2, 4],\n [6, 2, -4, 2, 9, 6],\n [0, -3, 3, 4, 6, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "460", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[9, 4, -7, 1, -12, -2],\n [-10, 7, -15, -5, -5, 1],\n [9, 12, -9, -7, 0, 5],\n [11, -7, -11, -10, -8, -7],\n [10, -3, -13, 11, 2, -11],\n [6, 13, 8, 4, -15, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "853", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 4, 12, 5, -8, 0],\n [4, 13, 6, 4, 2, 10],\n [12, 6, 11, 0, -8, 2],\n [5, 4, 0, -1, 0, 6],\n [-8, 2, -8, 0, 13, 5],\n [0, 10, 2, 6, 5, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 3, -6, -15, 12, -15],\n [-9, 11, 2, -5, -3, 13],\n [-7, 12, 12, 7, 10, 1],\n [-5, -15, 4, 0, 3, 6],\n [-5, -2, -4, -8, 14, -1],\n [10, 7, -15, -10, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, 2, -8, 11, 15, 4],\n [0, 7, -11, 15, 6, 4],\n [0, 0, 3, -11, -14, -12],\n [0, 0, 0, 5, 6, 11],\n [0, 0, 0, 0, -5, -2],\n [0, 0, 0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "725", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-3, 10, -12, 13, -1, 7],\n [0, 13, -15, 0, -8, -9],\n [0, 0, 4, -14, 13, 6],\n [0, 0, 0, 15, 10, -2],\n [0, 0, 0, 0, 5, -11],\n [0, 0, 0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 15, 13, 13, 2, 0],\n [0, 13, -4, -5, 14, 14],\n [0, 0, 12, 10, 7, -6],\n [0, 0, 0, -4, -10, 13],\n [0, 0, 0, 0, 15, 2],\n [0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -8, -12, -15, -3, -6],\n [-4, 4, 11, -14, -10, 8],\n [-6, -6, -13, -10, 12, -1],\n [-4, 15, -7, -12, -10, 2],\n [11, 14, -10, 14, -15, -4],\n [7, -13, 13, -4, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, 2, 8, -13, 4, -8],\n [2, -1, -2, -11, -4, 2],\n [8, -2, -2, 2, 3, 6],\n [-13, -11, 2, 3, -7, -13],\n [4, -4, 3, -7, 4, -1],\n [-8, 2, 6, -13, -1, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[4, -3, 13, 1, 6, -11],\n [-12, 11, 13, -3, -4, -13],\n [-12, 1, 5, 2, -1, -9],\n [-7, -2, 6, 6, -6, 12],\n [-6, 3, 8, -3, -13, 0],\n [-5, -12, -13, -14, 14, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[5, -2, -8, 4, 8, -8],\n [-2, -4, 3, -2, -7, -2],\n [-8, 3, 14, 8, -6, 2],\n [4, -2, 8, 9, -3, -6],\n [8, -7, -6, -3, 1, 0],\n [-8, -2, 2, -6, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, -12, -6, -6, -14, 2],\n [-13, -5, 6, 7, -11, -1],\n [8, 1, -14, -11, 1, -5],\n [-6, 7, 3, -10, -6, -5],\n [-9, 0, 5, -3, 7, -5],\n [-13, -8, 7, -12, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "398", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, 15, -5, -11, 10, -11],\n [0, -1, -9, -12, -9, -9],\n [0, 0, -12, 2, 6, -10],\n [0, 0, 0, 7, -13, -9],\n [0, 0, 0, 0, 9, -11],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 9, 13, -3, -5, -14],\n [-12, -5, 15, 15, 11, -7],\n [9, 8, -4, 5, 1, -14],\n [12, -2, 4, -7, -12, -11],\n [1, -3, 5, -2, 2, -7],\n [10, -6, -4, 11, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, -6, 8, 11, -2, -2],\n [-6, 5, 5, -4, -2, 3],\n [8, 5, -13, 0, 4, 1],\n [11, -4, 0, -3, 2, -6],\n [-2, -2, 4, 2, 1, -4],\n [-2, 3, 1, -6, -4, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "976", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[9, -4, 11, -2, 13, -5],\n [7, -15, -14, 0, -14, 11],\n [-15, -15, -6, 2, 6, 5],\n [5, 15, -14, 7, -13, -2],\n [-4, 9, 8, 9, -7, -3],\n [-6, 14, -10, -11, 2, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "274", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -8, -4, 10, -6, 2],\n [-8, 3, -1, 0, -5, -4],\n [-4, -1, -13, -10, -7, -4],\n [10, 0, -10, 12, 0, 0],\n [-6, -5, -7, 0, 14, -2],\n [2, -4, -4, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -7, -14, 1, 5, 2],\n [-10, 2, 11, 6, -10, 14],\n [10, -14, -14, -10, -7, 14],\n [14, -12, -6, 4, 14, -14],\n [-3, -12, -5, -6, -3, -9],\n [-12, 6, -11, -9, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, 8, 0, -6, -2],\n [-6, -10, 1, 2, 10, -10],\n [8, 1, 7, -6, -3, 4],\n [0, 2, -6, 4, 0, -3],\n [-6, 10, -3, 0, 7, -3],\n [-2, -10, 4, -3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 15, 8, -9, 3, 5],\n [0, -8, 2, -12, -11, 0],\n [0, 0, 7, 8, -4, 4],\n [0, 0, 0, -3, 6, -3],\n [0, 0, 0, 0, 14, -7],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[4, -7, -7, 0, -1, 4],\n [-7, 2, 4, -2, -10, -2],\n [-7, 4, -4, -6, -8, 4],\n [0, -2, -6, 4, 6, 6],\n [-1, -10, -8, 6, 6, 8],\n [4, -2, 4, 6, 8, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "504", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, 6, -8, -9, 15, 5],\n [0, 3, 12, 7, -7, 11],\n [0, 0, -15, 10, -3, 15],\n [0, 0, 0, 7, 10, 13],\n [0, 0, 0, 0, -4, -4],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-12, 1, 2, -2, -8, 6],\n [1, -4, 5, 10, 4, 4],\n [2, 5, -8, 12, -2, 0],\n [-2, 10, 12, -13, -4, 3],\n [-8, 4, -2, -4, -9, 1],\n [6, 4, 0, 3, 1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, 2, -2, -3, 2],\n [2, -13, -12, 0, 3, 0],\n [2, -12, 0, -5, -4, -2],\n [-2, 0, -5, 7, 2, -2],\n [-3, 3, -4, 2, 0, 4],\n [2, 0, -2, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "972", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, -1, 6, 13, -8, 10],\n [-1, -1, -1, 0, -3, -4],\n [6, -1, -10, 2, 10, -2],\n [13, 0, 2, -6, -6, 2],\n [-8, -3, 10, -6, 10, 4],\n [10, -4, -2, 2, 4, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, -11, -7, -9, 7, 14],\n [-4, 15, -11, -13, -8, 4],\n [-13, -12, -4, 14, 14, -15],\n [-8, -7, -13, 10, -10, 4],\n [-7, -14, -13, -2, -3, -2],\n [-2, 1, -1, -4, -9, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "865", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 11, -11, -11, 12, 6],\n [-9, -4, -3, -12, -7, -8],\n [-2, -10, -15, -10, 0, 1],\n [-11, -3, 6, 2, 3, 12],\n [7, 5, 10, 15, -5, 9],\n [-4, -8, -3, 10, -1, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -10, 2, 0, 11, -10],\n [0, -2, -6, -12, -7, -14],\n [0, 0, -3, 11, 3, -12],\n [0, 0, 0, -3, -15, -7],\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": "560", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[11, 7, 12, 7, -6, 1],\n [6, 14, -1, -2, -5, 7],\n [13, 2, 10, -1, 3, 9],\n [-8, -5, -15, -13, 3, -5],\n [12, 3, 2, 5, -2, -2],\n [-3, 3, -4, 3, -5, -15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, 14, -2, 5, 7, -3],\n [14, -4, 6, 10, -2, 7],\n [-2, 6, -12, 5, -7, -3],\n [5, 10, 5, 14, -2, 6],\n [7, -2, -7, -2, 7, -6],\n [-3, 7, -3, 6, -6, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "679", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-4, 6, 1, -7, -4, -10],\n [0, -13, 6, -12, 13, -7],\n [0, 0, -14, -13, -1, 8],\n [0, 0, 0, -8, 5, -1],\n [0, 0, 0, 0, -2, 15],\n [0, 0, 0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[12, -1, 8, 13, 10, 6],\n [-12, -15, 9, -11, 12, 15],\n [1, -13, -6, 13, -2, 8],\n [14, -7, 15, 0, 6, 2],\n [-5, 6, -11, 7, 13, 9],\n [-3, 10, -4, -6, -5, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-10, 5, -13, -13, 5, 4],\n [0, -5, -14, -13, -3, -3],\n [0, 0, -11, 5, -11, 2],\n [0, 0, 0, 1, -12, -8],\n [0, 0, 0, 0, 11, 10],\n [0, 0, 0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[14, -5, 5, -15, 15, 12],\n [0, 9, 8, 10, 1, 15],\n [0, 0, 15, 2, -12, -2],\n [0, 0, 0, 3, 0, 6],\n [0, 0, 0, 0, -2, -1],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, -11, 7, -4, 10, -2],\n [0, 14, 0, -8, -4, 15],\n [0, 0, -9, 8, 5, -8],\n [0, 0, 0, -2, 7, 14],\n [0, 0, 0, 0, 3, 9],\n [0, 0, 0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[13, 12, 11, -5, -3, -8],\n [8, 1, 5, -5, -12, 4],\n [9, -4, 11, -4, 3, 8],\n [12, 9, 8, 4, 2, -6],\n [-9, 3, -10, 3, 4, 2],\n [-4, -5, -1, -11, -6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, 1, 15, 2, 4, 10],\n [0, 14, -11, 11, -9, 7],\n [0, 0, -2, -13, 5, -3],\n [0, 0, 0, -15, -3, -8],\n [0, 0, 0, 0, -4, 12],\n [0, 0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-11, 1, 5, -6, 5, -4],\n [1, -1, -7, 0, -10, 0],\n [5, -7, 11, 6, -5, -4],\n [-6, 0, 6, 3, -1, -6],\n [5, -10, -5, -1, -3, 2],\n [-4, 0, -4, -6, 2, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "430", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, -12, 4, 15, 13, 14],\n [0, -11, 13, 4, -7, 5],\n [0, 0, 8, 7, -4, 2],\n [0, 0, 0, 10, 13, -10],\n [0, 0, 0, 0, -6, -6],\n [0, 0, 0, 0, 0, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, -2, 2, 8, -11, 10],\n [-2, 2, 2, -1, -8, 1],\n [2, 2, -14, -14, -8, 8],\n [8, -1, -14, 10, 8, -10],\n [-11, -8, -8, 8, 3, 4],\n [10, 1, 8, -10, 4, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -8, 6, 3, -1, 9],\n [-8, -15, 2, 4, 6, 4],\n [6, 2, -5, 2, 4, -2],\n [3, 4, 2, 13, -5, 0],\n [-1, 6, 4, -5, -11, -4],\n [9, 4, -2, 0, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -11, -9, 13, -6, 0],\n [0, 4, 8, 11, -5, 15],\n [0, 0, 2, 11, 4, -3],\n [0, 0, 0, -1, -10, 11],\n [0, 0, 0, 0, -12, -8],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, 12, -12, -9, -8, -1],\n [0, 13, -9, -7, 4, -15],\n [0, 0, 14, -1, -6, 11],\n [0, 0, 0, 9, -4, -8],\n [0, 0, 0, 0, -4, 3],\n [0, 0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, -8, -9, 1, -10, -6],\n [-4, 5, -14, -3, -3, 13],\n [-11, 6, 10, 13, -10, 0],\n [2, 1, 4, -1, 12, -1],\n [-1, -12, -7, -4, -2, -15],\n [11, -6, -1, -5, -15, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, 11, -11, 10, -12, -5],\n [6, -6, 8, 7, -13, 2],\n [-1, 10, -4, 5, 9, 0],\n [11, 10, -11, -6, -5, -15],\n [12, 9, 0, -4, -14, 13],\n [-4, -14, 6, -5, -13, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "711", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, -11, 11, 3, -4, -8],\n [0, -13, 6, 15, 12, 10],\n [0, 0, -5, 11, -5, -9],\n [0, 0, 0, -1, 0, 11],\n [0, 0, 0, 0, -10, -4],\n [0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "700", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-4, -8, 15, 7, -15, -13],\n [0, -8, 2, -8, -14, -4],\n [0, 0, 11, -7, 12, 15],\n [0, 0, 0, -1, 3, -1],\n [0, 0, 0, 0, 2, 0],\n [0, 0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 0, 4, 0, -1, -2],\n [0, -2, 14, 0, 1, -12],\n [4, 14, 13, 7, 3, 8],\n [0, 0, 7, 0, 2, -2],\n [-1, 1, 3, 2, 11, -8],\n [-2, -12, 8, -2, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 2, -7, 0, -11, -4],\n [2, 4, 0, 6, 2, 0],\n [-7, 0, -11, 4, -4, 0],\n [0, 6, 4, 4, -1, 5],\n [-11, 2, -4, -1, -11, -8],\n [-4, 0, 0, 5, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, 11, -9, -13, -14, 11],\n [-8, -13, 2, 7, 14, 0],\n [15, 13, 9, -10, 14, 2],\n [-14, -15, -7, -12, -4, -12],\n [-3, 10, 4, -3, 1, -4],\n [-6, -2, -5, 13, 14, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -10, 7, -8, -12, -15],\n [0, -1, -15, 3, 9, -2],\n [0, 0, 14, -9, -14, -5],\n [0, 0, 0, -7, -12, -3],\n [0, 0, 0, 0, 8, 6],\n [0, 0, 0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-12, 5, 6, 7, 14, -9],\n [-9, 5, -4, -2, -6, -9],\n [-11, -11, 3, 9, -4, -7],\n [-15, 4, -5, 13, -5, 3],\n [-1, -12, 2, 15, 6, 6],\n [14, -9, 0, 13, 14, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[8, 4, -2, -11, -6, 15],\n [-8, -8, 12, 5, 13, 0],\n [6, -7, -14, -3, -13, 11],\n [15, 9, 14, 13, -13, -11],\n [3, 15, 10, -12, -13, -6],\n [4, 1, 12, 8, -6, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, 8, -6, -1, 3],\n [0, 8, -12, -5, -6, -9],\n [8, -12, -3, 9, 2, 2],\n [-6, -5, 9, -1, 14, 8],\n [-1, -6, 2, 14, -2, 7],\n [3, -9, 2, 8, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -3, 6, -11, -4, -3],\n [0, 13, -4, 11, -13, 0],\n [0, 0, 1, -6, -3, 12],\n [0, 0, 0, 13, 12, 7],\n [0, 0, 0, 0, -14, 0],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -1, 2, 6, 4, -10],\n [-1, -12, -12, 8, 4, -12],\n [2, -12, -2, 8, 9, -5],\n [6, 8, 8, -4, 7, 0],\n [4, 4, 9, 7, 5, 0],\n [-10, -12, -5, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, 7, -14, 5, 10, -2],\n [2, 8, -13, -15, 6, -1],\n [-5, 0, 13, -2, 8, -9],\n [-10, 5, 8, 10, -1, -2],\n [4, -9, 2, -7, 8, -4],\n [12, 4, 13, -9, 1, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 1, -6, 0, -11, -10],\n [1, 1, 2, -10, -2, -7],\n [-6, 2, 6, -12, -1, -10],\n [0, -10, -12, -15, -2, 8],\n [-11, -2, -1, -2, -2, 5],\n [-10, -7, -10, 8, 5, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[6, -9, -2, 1, -5, 12],\n [0, 6, -8, -8, 13, -7],\n [0, 0, 6, -7, -8, -12],\n [0, 0, 0, -7, 1, 10],\n [0, 0, 0, 0, 7, 6],\n [0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 12, 4, -13, -7, -3],\n [0, -2, -6, 1, -4, 14],\n [0, 0, 8, 4, 13, -7],\n [0, 0, 0, -5, -7, -3],\n [0, 0, 0, 0, -4, -7],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[2, -4, -6, 2, 10, -6],\n [-4, 1, -5, 0, 0, 2],\n [-6, -5, -14, -12, 4, -7],\n [2, 0, -12, 11, -6, 1],\n [10, 0, 4, -6, 14, -9],\n [-6, 2, -7, 1, -9, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, 1, 12, 3, 8, 8],\n [1, -5, 6, 5, 2, 2],\n [12, 6, -3, -4, 4, 4],\n [3, 5, -4, -1, 4, 2],\n [8, 2, 4, 4, 7, 6],\n [8, 2, 4, 2, 6, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "504", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, 3, -12, 10, 3, 2],\n [0, 4, -5, 14, 15, 5],\n [0, 0, -5, 11, -10, -10],\n [0, 0, 0, -12, -8, 8],\n [0, 0, 0, 0, 8, 5],\n [0, 0, 0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 0, -1, 7, 11, 14],\n [0, -3, -6, 1, -8, -2],\n [0, 0, -2, -6, -1, -2],\n [0, 0, 0, 2, -4, 0],\n [0, 0, 0, 0, -12, -9],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -8, 3, 5, 9, 12],\n [0, 9, 13, 4, -15, 0],\n [0, 0, 13, -13, -5, 0],\n [0, 0, 0, -2, -6, 1],\n [0, 0, 0, 0, 7, -14],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, -8, -13, -10, -1, 4],\n [-1, -8, 15, 3, -11, -3],\n [-14, -4, 0, -9, -7, 5],\n [-4, 9, -1, -3, -14, -8],\n [3, -6, -11, 3, 5, 5],\n [-15, 12, -8, -2, 7, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -2, 4, -15, -15, 1],\n [-8, 1, 5, -6, 15, -10],\n [-9, 11, 5, 0, 9, 1],\n [14, -9, -10, 9, -5, -10],\n [14, 2, -7, -12, -7, -13],\n [11, -13, -2, 11, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 6, 0, -6, 1, -4],\n [6, 1, -5, -4, 6, 0],\n [0, -5, -5, -2, 11, 2],\n [-6, -4, -2, -1, 8, -8],\n [1, 6, 11, 8, -6, -3],\n [-4, 0, 2, -8, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "898", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 7, -5, -8, -8, -4],\n [0, 3, 3, 2, -15, -1],\n [0, 0, 13, 6, 5, 1],\n [0, 0, 0, -8, 15, 8],\n [0, 0, 0, 0, -14, 2],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, 0, -10, 4, -4],\n [2, 3, -3, 10, 2, -5],\n [0, -3, -3, -13, -6, 2],\n [-10, 10, -13, -13, -9, -5],\n [4, 2, -6, -9, 1, -10],\n [-4, -5, 2, -5, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, -6, -14, 7, -7, 15],\n [0, 10, 10, 2, -12, 1],\n [0, 0, -11, -10, -14, 5],\n [0, 0, 0, 8, 10, 7],\n [0, 0, 0, 0, 2, -8],\n [0, 0, 0, 0, 0, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 11, 12, 10, 10, -1],\n [-2, -8, -10, 12, 10, -8],\n [2, -10, 12, 2, -10, -10],\n [-6, -3, -9, -2, -15, 1],\n [1, -11, -15, 3, -15, 7],\n [8, 4, -7, -8, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "216", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 6, 4, -2, 5, 2],\n [6, -14, 0, -2, 2, -4],\n [4, 0, -5, -11, -10, 2],\n [-2, -2, -11, -2, 2, -2],\n [5, 2, -10, 2, 0, 4],\n [2, -4, 2, -2, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "588", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, -9, -5, 0, -4, 9],\n [-9, -12, 2, -6, 2, 2],\n [-5, 2, -9, 4, 6, 1],\n [0, -6, 4, -14, 15, -1],\n [-4, 2, 6, 15, 3, -2],\n [9, 2, 1, -1, -2, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[0, -4, 2, 0, 0, -4],\n [-4, -13, -1, -2, 0, 0],\n [2, -1, -11, 8, -6, 2],\n [0, -2, 8, 6, -2, 5],\n [0, 0, -6, -2, 11, -8],\n [-4, 0, 2, 5, -8, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -1, 0, -1, -11, 7],\n [-11, 15, 8, 10, 15, -14],\n [6, -6, 13, 6, -12, -15],\n [14, 6, 9, 15, -4, -15],\n [6, 12, 4, -7, -7, 0],\n [7, -15, 3, -15, -11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "386", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-11, -2, 8, 15, -6, -11],\n [0, 6, -4, 2, -5, -15],\n [0, 0, -14, -3, -7, 7],\n [0, 0, 0, -7, 8, 10],\n [0, 0, 0, 0, 5, -3],\n [0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -11, -3, 3, -13, -8],\n [0, -1, -8, 13, 12, -8],\n [0, 0, 7, 11, -11, -3],\n [0, 0, 0, 6, -5, -1],\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": "490", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, 3, -4, -7, -14],\n [11, 12, 14, 13, 14, -11],\n [-6, -13, 3, 11, 5, 2],\n [-11, -13, 2, 5, -2, -13],\n [-8, 2, 7, -8, -9, 2],\n [9, -6, 6, -7, -13, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, 15, 8, 1, -6, -1],\n [-8, 2, -2, 14, 0, -9],\n [1, 13, -2, -13, 7, -6],\n [-15, -5, -7, -12, -11, 3],\n [9, -5, -10, 12, 7, 8],\n [-4, -3, 1, -15, 6, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, 11, 6, 0, 0, 2],\n [11, 2, -1, 4, 6, -2],\n [6, -1, -1, 3, 2, 0],\n [0, 4, 3, -12, 4, 10],\n [0, 6, 2, 4, -6, -4],\n [2, -2, 0, 10, -4, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 13, -5, 13, 10, -7],\n [0, -1, 4, 14, -3, -1],\n [0, 0, 7, 3, 15, -10],\n [0, 0, 0, -4, -4, -5],\n [0, 0, 0, 0, -9, 7],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, -2, -1, -10, -2, -2],\n [-2, -1, 0, -1, 8, 8],\n [-1, 0, -4, 5, 2, 4],\n [-10, -1, 5, 14, -6, -1],\n [-2, 8, 2, -6, -5, -6],\n [-2, 8, 4, -1, -6, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "725", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, 11, 14, -1, 13, 9],\n [12, 10, -10, 4, 11, -12],\n [-12, -4, 9, -5, -6, -11],\n [2, 12, -12, 5, -13, 12],\n [1, 15, 14, 9, -14, -1],\n [1, 8, -14, 7, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -14, -7, -8, -4, -10],\n [-14, -9, 5, 2, 6, -3],\n [-7, 5, 11, 0, 13, -8],\n [-8, 2, 0, 1, 7, 2],\n [-4, 6, 13, 7, -10, -8],\n [-10, -3, -8, 2, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, -6, 0, -6, 6, 2],\n [-6, 0, 5, 8, 10, 0],\n [0, 5, -15, -2, -6, -2],\n [-6, 8, -2, 6, 6, -6],\n [6, 10, -6, 6, 4, 10],\n [2, 0, -2, -6, 10, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "584", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, -13, 2, 6, 7],\n [0, 12, 2, 13, 3, -12],\n [0, 0, -12, 4, -2, 3],\n [0, 0, 0, 4, 14, -3],\n [0, 0, 0, 0, -12, -12],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, 7, 14, -2, -6, -2],\n [7, -5, -6, -8, -2, 10],\n [14, -6, -11, 14, 5, 1],\n [-2, -8, 14, 2, -12, 0],\n [-6, -2, 5, -12, 4, 1],\n [-2, 10, 1, 0, 1, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[14, 12, 6, -5, 5, 4],\n [0, 12, 1, 11, -4, -3],\n [0, 0, 4, 6, -10, -9],\n [0, 0, 0, 9, 5, 3],\n [0, 0, 0, 0, 2, 2],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, 14, 11, -4, -3],\n [-10, 3, 11, 4, -2, 7],\n [-3, 14, 8, 14, 0, 12],\n [13, -1, -6, -2, -7, -6],\n [-8, 2, 2, -4, 5, 2],\n [1, 10, -5, -5, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[0, 15, 1, -7, -1, 3],\n [15, 5, -7, -8, -11, -4],\n [1, -7, 4, 2, 0, 4],\n [-7, -8, 2, 1, -2, -9],\n [-1, -11, 0, -2, -6, -10],\n [3, -4, 4, -9, -10, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-11, -7, -13, 9, -1, 0],\n [0, -8, -6, -5, 9, 2],\n [0, 0, 6, -8, 11, 7],\n [0, 0, 0, 5, -12, -4],\n [0, 0, 0, 0, 5, 0],\n [0, 0, 0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, 15, 11, -15, -8, 2],\n [0, 11, -5, -6, -12, -5],\n [0, 0, -1, -13, 1, -8],\n [0, 0, 0, -13, -7, -3],\n [0, 0, 0, 0, -4, 11],\n [0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-14, 9, 13, 3, 0, -6],\n [0, -2, 9, -9, -14, 15],\n [0, 0, 1, 0, -9, 2],\n [0, 0, 0, 14, -2, -10],\n [0, 0, 0, 0, -14, -2],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -4, 9, -4, -6, -10],\n [-4, 15, 2, -10, 4, 3],\n [9, 2, -5, -2, -2, 2],\n [-4, -10, -2, 7, 4, 2],\n [-6, 4, -2, 4, 11, 4],\n [-10, 3, 2, 2, 4, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, -12, 1, 11, 14, -4],\n [6, 4, 9, 1, -2, 7],\n [8, 1, 11, 4, -2, 1],\n [6, -2, 11, -1, 3, 15],\n [-11, 1, -15, -9, -10, 9],\n [-1, 5, 1, 8, -15, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 8, -3, 7, 5, 6],\n [8, 14, 3, 8, -2, -8],\n [-3, 3, -3, 10, 2, -2],\n [7, 8, 10, -1, 0, -4],\n [5, -2, 2, 0, -5, -9],\n [6, -8, -2, -4, -9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 4, -3, -13, 9, 6],\n [-10, 6, 9, 15, -7, -7],\n [-3, -12, 6, -7, -1, -1],\n [-10, -8, 8, -11, 0, 3],\n [-10, 5, -2, 0, -13, 6],\n [-12, 6, 14, 7, -15, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "623", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[15, 0, 8, -6, -2, -13],\n [0, 13, -9, 13, -6, -12],\n [0, 0, -8, 0, -3, -14],\n [0, 0, 0, 2, 0, -6],\n [0, 0, 0, 0, -2, -4],\n [0, 0, 0, 0, 0, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, 3, 8, -13, -12, 0],\n [0, -2, -2, 10, -8, -2],\n [0, 0, 13, -11, 14, -4],\n [0, 0, 0, 1, 15, -5],\n [0, 0, 0, 0, 4, 11],\n [0, 0, 0, 0, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[10, -15, -8, -4, 1, 14],\n [0, -1, -5, -13, -5, -5],\n [0, 0, 1, -13, 14, -11],\n [0, 0, 0, 10, -10, 5],\n [0, 0, 0, 0, 15, 8],\n [0, 0, 0, 0, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[0, 2, -14, 12, 5, 2],\n [-3, -15, 11, 10, 5, -14],\n [2, 1, -6, 3, 2, 7],\n [8, 9, -4, 8, 6, 8],\n [-15, -7, 13, -3, 8, 12],\n [-13, 2, -7, -4, 0, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 0, -2, -2, 4, -6],\n [0, -12, -2, 8, -8, 8],\n [-2, -2, 3, 7, -4, 10],\n [-2, 8, 7, -10, -5, 5],\n [4, -8, -4, -5, -6, -14],\n [-6, 8, 10, 5, -14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -13, 3, -10, -10, 9],\n [0, -7, 11, -15, -5, -4],\n [0, 0, -4, -15, 15, -12],\n [0, 0, 0, 11, -5, 14],\n [0, 0, 0, 0, 6, 9],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, -10, 10, -2, -15, -7],\n [0, -13, 10, 4, -15, 2],\n [0, 0, 5, -1, -14, 7],\n [0, 0, 0, 1, -1, 14],\n [0, 0, 0, 0, -3, 11],\n [0, 0, 0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -6, 6, 0, 4, 1],\n [-6, -2, 6, 0, 10, -2],\n [6, 6, -11, 0, -9, 4],\n [0, 0, 0, 5, 8, 4],\n [4, 10, -9, 8, 3, 2],\n [1, -2, 4, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, 5, 8, 4, 15, 4],\n [0, -4, -5, -3, -11, -5],\n [0, 0, 3, -8, -12, 0],\n [0, 0, 0, 15, -10, 13],\n [0, 0, 0, 0, -4, -8],\n [0, 0, 0, 0, 0, -15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 12, -8, 1, -15, -10],\n [9, -15, 14, 14, -11, -7],\n [-8, 8, 9, 7, -7, -8],\n [-10, 5, 3, -13, -9, 0],\n [-15, -6, -10, -11, 1, 5],\n [13, 14, 15, -13, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, 13, -5, -10, -15, 11],\n [0, 5, -13, 9, -8, -13],\n [0, 0, 1, 5, 14, 12],\n [0, 0, 0, 3, -7, -2],\n [0, 0, 0, 0, 6, -9],\n [0, 0, 0, 0, 0, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -9, -14, 6, 10, 3],\n [0, 8, -2, 0, -5, 14],\n [0, 0, -9, -2, -3, -13],\n [0, 0, 0, 14, 11, 15],\n [0, 0, 0, 0, 1, 6],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 15, -11, 2, 3, -10],\n [0, 7, -5, -1, -14, -4],\n [0, 0, 9, 12, 0, -4],\n [0, 0, 0, -2, -9, -8],\n [0, 0, 0, 0, 5, -13],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 14, -4, -12, -11, -2],\n [0, -1, -8, -9, 12, -8],\n [0, 0, -15, -4, -5, 9],\n [0, 0, 0, 9, -12, 14],\n [0, 0, 0, 0, -10, 2],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-9, 1, -5, -3, -2, 1],\n [1, 3, -12, 2, 1, 7],\n [-5, -12, 15, 14, -1, -4],\n [-3, 2, 14, -9, 0, 6],\n [-2, 1, -1, 0, -9, -6],\n [1, 7, -4, 6, -6, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "442", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, 6, -9, 7, 5, -14],\n [-10, -3, 5, -10, -4, 15],\n [-4, -1, -4, -13, -15, -4],\n [9, -6, -15, 10, 9, -6],\n [4, 15, 15, -4, -1, -8],\n [-10, 0, 12, -8, 8, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "806", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, 6, -6, -4, 3, 6],\n [6, 3, 1, 2, 0, 0],\n [-6, 1, -12, 0, -8, 4],\n [-4, 2, 0, 4, -9, 2],\n [3, 0, -8, -9, -3, 2],\n [6, 0, 4, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "686", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[14, 8, 3, 0, -5, 5],\n [12, -7, -5, 2, -4, -5],\n [-9, 7, 2, -10, -8, -3],\n [-13, 9, 8, 12, 14, -13],\n [7, -1, -8, -1, -15, -13],\n [10, -4, -7, -9, -15, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-11, -3, -4, 3, 1, -4],\n [-3, 8, -6, 6, -6, -8],\n [-4, -6, -5, -1, 0, 3],\n [3, 6, -1, -6, -12, -8],\n [1, -6, 0, -12, -13, 8],\n [-4, -8, 3, -8, 8, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 15, -3, 8, 14, 10],\n [-2, -5, -13, 6, -3, 3],\n [6, 1, 7, 6, 15, -9],\n [5, 8, -7, -1, 9, 6],\n [8, -4, -9, 12, 14, 5],\n [7, -15, -11, -12, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, -4, 15, 4, -6, 6],\n [-1, 9, -4, 4, -1, 13],\n [10, -9, 2, -13, 13, 0],\n [-8, 3, 11, -7, 4, 10],\n [3, 0, 14, 13, -14, 12],\n [-14, 1, -12, 7, 4, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[0, 2, 6, -4, -2, 4],\n [2, -5, -3, -6, 1, 3],\n [6, -3, -14, -6, -4, 0],\n [-4, -6, -6, 9, 2, -5],\n [-2, 1, -4, 2, -2, 2],\n [4, 3, 0, -5, 2, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-10, -2, -7, -13, -12, 7],\n [0, -14, -10, -8, -13, 0],\n [0, 0, 4, -13, -10, 5],\n [0, 0, 0, -2, 0, 10],\n [0, 0, 0, 0, 6, -15],\n [0, 0, 0, 0, 0, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-14, 10, 9, -10, 1, -12],\n [-5, -11, 2, -9, -12, 5],\n [-8, -9, -4, 3, -11, -8],\n [-6, -12, -9, 12, -7, -5],\n [12, 2, -11, -15, 6, 13],\n [7, 6, 6, 6, -1, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-3, 0, 2, 7, -3, -4],\n [0, -14, 12, -4, -4, 3],\n [2, 12, 14, -10, 10, -8],\n [7, -4, -10, -12, 1, 10],\n [-3, -4, 10, 1, 0, -6],\n [-4, 3, -8, 10, -6, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -2, 9, -1, 15, -6],\n [0, 11, -9, -6, -10, -2],\n [0, 0, 15, -7, 5, 0],\n [0, 0, 0, -5, -14, -8],\n [0, 0, 0, 0, -4, 4],\n [0, 0, 0, 0, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, -11, 5, -7, 5, 1],\n [-2, -11, -5, -9, -4, -12],\n [7, 10, 0, 12, 13, -14],\n [0, -14, -5, 7, 3, 7],\n [3, 6, -3, 7, 5, 14],\n [-9, -3, 4, 0, 1, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -15, 8, -14, -5, -11],\n [14, -1, 9, -7, -15, 13],\n [-7, -5, 6, -4, -15, 0],\n [0, -9, -13, -11, -12, 14],\n [13, 12, -13, -13, 4, 15],\n [-13, 6, 2, -4, 1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "700", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-2, -4, -5, 1, -11, -7],\n [6, -6, 10, 4, 5, 1],\n [-3, 14, -12, 4, -7, -11],\n [3, 10, -8, -6, 10, 14],\n [7, 8, 15, -12, 7, 11],\n [-12, 9, 13, 15, 5, 14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "738", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, -13, 4, -3, -4, 3],\n [0, -13, -11, -11, 8, -3],\n [0, 0, 12, 9, -1, -4],\n [0, 0, 0, 12, -12, -3],\n [0, 0, 0, 0, 14, 9],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, 13, -11, -8, 2, 5],\n [-1, -3, -4, -15, -1, -9],\n [-8, 8, -9, 9, 1, -11],\n [-2, 1, 14, 15, 15, -6],\n [7, -5, 2, 2, 8, -8],\n [-15, -7, -6, 0, 10, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, -11, -7, -15, 14, -4],\n [-9, 12, -4, 4, -6, 14],\n [4, 12, -13, 12, 15, -8],\n [-9, 15, -14, 15, 2, -6],\n [0, -8, 5, 5, -5, -2],\n [5, 15, 11, 13, -2, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -10, -10, 15, 1, 11],\n [0, 9, 9, 13, 8, -7],\n [0, 0, -3, -11, -7, 14],\n [0, 0, 0, 8, -9, 3],\n [0, 0, 0, 0, 4, -2],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 0, 0, -7, 3, 6],\n [0, 8, 4, 6, -6, 13],\n [0, 4, -1, 5, -6, -5],\n [-7, 6, 5, -1, 4, 2],\n [3, -6, -6, 4, 3, 1],\n [6, 13, -5, 2, 1, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "493", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[14, 3, 5, 14, 0, 11],\n [0, 6, -13, 14, 0, 7],\n [0, 0, -4, -13, -11, -9],\n [0, 0, 0, -10, 6, 1],\n [0, 0, 0, 0, -3, 4],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, -5, 7, -5, -10, -9],\n [0, -14, -3, 0, 10, 8],\n [0, 0, -7, 6, -14, 5],\n [0, 0, 0, 5, -8, -6],\n [0, 0, 0, 0, -5, 15],\n [0, 0, 0, 0, 0, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -14, 8, 5, -5, -6],\n [0, -11, -5, 8, -9, 10],\n [0, 0, -7, -4, -6, 4],\n [0, 0, 0, 5, 6, -14],\n [0, 0, 0, 0, -5, 11],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 7, 2, -13, -3, -3],\n [-14, 12, -14, -15, -3, 0],\n [-15, 8, 15, -4, 12, 11],\n [10, 2, -2, 10, 8, -7],\n [0, 14, -8, -12, -2, 12],\n [-2, 9, 10, -6, -15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -4, 5, 1, 10, -1],\n [-4, -13, -4, 8, 2, -11],\n [5, -4, -11, 10, -11, -4],\n [1, 8, 10, 8, 5, -6],\n [10, 2, -11, 5, 3, -2],\n [-1, -11, -4, -6, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-14, 8, 0, -13, 8, -8],\n [0, -1, -8, 13, 14, -14],\n [0, 0, 15, 6, 12, 1],\n [0, 0, 0, -5, 7, 13],\n [0, 0, 0, 0, 13, -11],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[12, 1, 5, 2, 2, 14],\n [1, -15, 2, 6, 2, 1],\n [5, 2, 5, 2, -10, 0],\n [2, 6, 2, -7, -10, 0],\n [2, 2, -10, -10, -5, 0],\n [14, 1, 0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, -7, 11, 14, -11, -12],\n [3, -11, 0, 5, 6, 0],\n [5, 8, 12, -14, -11, 0],\n [-14, -3, 3, -2, 5, 12],\n [-12, -6, -6, -2, 0, 7],\n [9, -5, 14, -15, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 4, -5, 12, 14, -14],\n [0, -5, 10, -9, -1, 4],\n [0, 0, -11, 5, -1, -10],\n [0, 0, 0, 3, -6, 15],\n [0, 0, 0, 0, -11, -7],\n [0, 0, 0, 0, 0, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, 11, -3, -12, 0, -11],\n [0, -2, -3, 1, -1, -9],\n [0, 0, 6, 7, -11, -12],\n [0, 0, 0, -3, -13, 10],\n [0, 0, 0, 0, -15, -5],\n [0, 0, 0, 0, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-9, -8, 10, 1, 14, 13],\n [0, -4, -10, 13, -2, -15],\n [0, 0, -10, -15, -1, 0],\n [0, 0, 0, 1, -11, -15],\n [0, 0, 0, 0, -15, -6],\n [0, 0, 0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 12, 9, -11, -13, -12],\n [-5, -8, 11, -15, 13, 6],\n [-1, 13, -4, 15, 8, -9],\n [8, -2, 14, -3, -6, -15],\n [3, -11, -14, -3, 15, -1],\n [-5, 5, -8, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 0, 0, -3, 11, -12],\n [-5, 6, -15, -2, -4, 7],\n [-2, 10, -8, -7, -5, 13],\n [-2, -11, -15, 3, -3, -2],\n [-7, 6, 5, 9, -7, -13],\n [5, -2, -2, 15, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, 10, -1, -6, 2, 0],\n [10, 5, 8, 4, -14, -6],\n [-1, 8, -4, -4, 10, 10],\n [-6, 4, -4, -10, 6, 4],\n [2, -14, 10, 6, 0, 3],\n [0, -6, 10, 4, 3, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "994", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 7, -9, 7, -12, 10],\n [-9, -7, 4, 9, 1, 3],\n [1, 3, 0, 5, 11, 5],\n [-3, -11, 11, 1, 4, 6],\n [-11, 4, 1, 13, 13, 5],\n [-3, -5, -5, 2, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 2, 11, -14, -11, 3],\n [-11, -14, -12, 9, -2, -9],\n [-7, 15, 14, -3, 14, -15],\n [13, 10, -5, -4, 13, 7],\n [11, 11, -1, -3, 4, -12],\n [-5, 1, -8, 7, 11, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[12, -3, 1, 14, -9, 10],\n [-4, 8, -12, -13, -2, 15],\n [1, 11, 15, -8, 10, 9],\n [-5, 10, 10, -4, 14, 14],\n [1, -6, 11, -7, 10, -12],\n [-11, -11, 6, 0, -3, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "573", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, 0, 1, 6, 4, -1],\n [0, -5, 2, 4, 8, 8],\n [1, 2, 3, 6, 9, -4],\n [6, 4, 6, -4, -4, 2],\n [4, 8, 9, -4, 1, 0],\n [-1, 8, -4, 2, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[7, -2, 1, 5, 1, 4],\n [0, -6, 2, 6, 14, 8],\n [0, 0, 3, 3, 3, -3],\n [0, 0, 0, -12, -9, -14],\n [0, 0, 0, 0, 12, 5],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "848", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[7, 5, -2, -8, -4, 0],\n [5, -2, 8, -2, -8, -2],\n [-2, 8, 1, -6, 6, -2],\n [-8, -2, -6, 4, 6, 0],\n [-4, -8, 6, 6, -7, -6],\n [0, -2, -2, 0, -6, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 7, -2, 9, -12, 7],\n [0, -1, 13, -8, -11, -6],\n [0, 0, 2, -3, -3, 3],\n [0, 0, 0, 7, -1, 1],\n [0, 0, 0, 0, 15, 9],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -12, -8, -1, 0, 5],\n [-12, -9, -9, -2, -2, -2],\n [-8, -9, -3, -5, 0, 9],\n [-1, -2, -5, -3, 2, -2],\n [0, -2, 0, 2, -14, 5],\n [5, -2, 9, -2, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "669", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, 1, -12, 6, -8, -12],\n [1, 1, -2, 6, 2, 1],\n [-12, -2, 0, -8, 3, 8],\n [6, 6, -8, 6, -3, 0],\n [-8, 2, 3, -3, 5, 2],\n [-12, 1, 8, 0, 2, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[12, 8, -3, 8, -6, -8],\n [8, 10, 2, -2, -4, -7],\n [-3, 2, -10, -7, 6, 6],\n [8, -2, -7, 2, -5, -7],\n [-6, -4, 6, -5, -3, -4],\n [-8, -7, 6, -7, -4, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 9, -7, 8, 6, 7],\n [-12, 8, -15, 8, -3, 2],\n [-9, -8, -12, 4, -2, 12],\n [-6, -9, -9, -2, -5, 12],\n [9, 3, -4, -8, 15, 4],\n [13, -11, 13, 14, 12, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, -9, 14, 11, 10, -3],\n [5, 4, 0, 9, 8, -7],\n [8, -3, -14, -12, 3, 10],\n [-6, -15, -12, 0, -9, 5],\n [-11, -3, 0, -10, 10, 3],\n [2, 13, -5, -1, 7, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 7, -9, 5, -4, -4],\n [7, -15, 2, -4, 10, -2],\n [-9, 2, 1, -3, -12, -8],\n [5, -4, -3, 10, -3, -2],\n [-4, 10, -12, -3, 6, 2],\n [-4, -2, -8, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "356", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, -3, -1, -6, -12],\n [7, -3, -5, 2, -1, 2],\n [-3, -5, -5, 0, 4, -4],\n [-1, 2, 0, -1, -7, -10],\n [-6, -1, 4, -7, 13, 10],\n [-12, 2, -4, -10, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[10, -6, 3, -5, 14, 2],\n [0, 14, -1, -12, -15, 6],\n [0, 0, 14, -4, 8, -9],\n [0, 0, 0, -11, -2, 1],\n [0, 0, 0, 0, 8, 5],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 9, -4, 15, 1, -6],\n [0, -4, -13, -6, 5, 4],\n [0, 0, 7, 8, 0, -13],\n [0, 0, 0, 10, -1, -14],\n [0, 0, 0, 0, -10, -9],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, -10, 2, -10, 15, 12],\n [-12, -3, 8, 0, -6, 8],\n [-10, -3, -4, -13, 2, 7],\n [6, 0, 14, 14, -1, 9],\n [-15, 3, -10, -1, 13, -11],\n [-3, -14, 5, 8, -1, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, 0, -2, 2, 0],\n [-9, -14, 0, 12, 3, -2],\n [0, 0, -15, -12, 4, -1],\n [-2, 12, -12, -14, 10, 3],\n [2, 3, 4, 10, 6, -8],\n [0, -2, -1, 3, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "793", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-13, -9, 4, -10, 6, 8],\n [14, 9, -1, 7, 6, 14],\n [13, -15, -12, -14, -10, -14],\n [-1, -11, 7, 6, 4, 5],\n [-2, 15, -3, -3, 6, -8],\n [10, 11, -1, 15, 4, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -7, 6, -5, 0, -2],\n [-3, -4, -15, -13, 1, -12],\n [-7, 11, 4, -9, -8, 10],\n [8, 9, -4, 1, -4, 7],\n [5, -7, -11, -3, 2, -1],\n [-11, 0, -7, -15, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[13, 14, -6, -12, 4, -4],\n [0, 10, 2, -13, -13, 12],\n [0, 0, 10, -3, 11, 13],\n [0, 0, 0, -7, -14, 10],\n [0, 0, 0, 0, -1, 4],\n [0, 0, 0, 0, 0, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, -13, 11, -12, 13],\n [-10, 0, 11, 8, -13, -6],\n [9, -11, 8, -11, 8, 2],\n [7, -4, -14, -9, 12, 15],\n [-7, -6, -11, -1, -13, 9],\n [2, -10, -10, -11, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -10, 3, 4, -6, 2],\n [-10, 2, -2, 6, 2, 2],\n [3, -2, 2, -2, 2, -2],\n [4, 6, -2, -5, -12, 3],\n [-6, 2, 2, -12, -8, 8],\n [2, 2, -2, 3, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "420", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -6, 9, 9, -6, 12],\n [-1, -11, -4, 3, -13, 8],\n [8, 10, -7, 2, -15, -2],\n [-13, 8, -10, 0, -13, 1],\n [-11, 14, 6, 0, 7, -3],\n [-5, -4, -6, -6, 4, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 9, -8, -3, -14, -12],\n [-4, 14, -4, 6, 14, 0],\n [-3, 1, 0, -13, 12, -15],\n [9, 15, -1, 11, -5, -3],\n [11, 11, 7, -12, -8, 9],\n [3, 2, 7, -3, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "724", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -5, -11, -4, 0, -4],\n [0, 11, -8, -1, -15, -10],\n [0, 0, -15, -9, -2, -14],\n [0, 0, 0, 10, -12, -14],\n [0, 0, 0, 0, -4, -9],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, 15, 8, -13, -3, -14],\n [0, 13, 3, -10, 8, -13],\n [0, 0, 2, -8, -5, -3],\n [0, 0, 0, -3, 8, -4],\n [0, 0, 0, 0, 6, 1],\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": "Compute |A| for the matrix A =\n[[0, -9, 15, -8, -14, -13],\n [1, 3, 4, 2, -2, -9],\n [11, 11, -13, -10, -1, -14],\n [2, 6, 4, 15, -5, -14],\n [12, 8, -9, 7, -9, 4],\n [8, 3, 4, -1, 5, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, -14, 1, -2, 2, -6],\n [-10, 15, 5, 7, 1, -9],\n [15, 2, -14, -9, -10, -15],\n [2, -13, -5, -1, -13, -15],\n [-13, 2, -1, 11, -2, -11],\n [6, 1, 12, 3, 0, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 4, 3, -10, -13, -6],\n [-4, 12, 15, -7, 7, -2],\n [-13, 10, -12, -14, -15, 2],\n [-14, 6, -12, 14, -12, 4],\n [-11, -7, 15, 7, 12, 5],\n [-15, -9, -2, 9, 11, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 7, 2, 8, -3, 14],\n [-8, -3, 7, -7, -8, -1],\n [3, 3, -6, -13, -6, -4],\n [-8, -4, -4, 10, 8, -9],\n [6, -2, -14, -12, 4, 0],\n [-1, 3, -5, -14, -7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, 2, 4, -13, 8, -15],\n [0, 6, 6, -8, 5, 12],\n [0, 0, -13, -13, 9, 2],\n [0, 0, 0, 9, 13, -1],\n [0, 0, 0, 0, -7, 3],\n [0, 0, 0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "860", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 1, 10, 6, 13, -2],\n [-12, 14, -4, 2, 7, 0],\n [9, -5, 3, -6, -5, 14],\n [9, 15, 11, 1, 10, -10],\n [-5, -15, -3, 0, -5, 6],\n [-12, -13, 11, 0, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -8, 14, -11, -11, 5],\n [0, 15, -6, -13, 0, 15],\n [0, 0, 1, -3, -15, 8],\n [0, 0, 0, 4, 13, 5],\n [0, 0, 0, 0, 3, -15],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -15, -3, -1, -9, -13],\n [2, -12, -8, -11, -3, -7],\n [-7, -5, 3, 12, 2, -12],\n [7, 13, 3, 7, -2, -12],\n [12, 1, -12, -6, -4, 10],\n [-14, -2, -9, -11, 4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -4, 1, -5, 2, -6],\n [-4, 9, -2, -2, -2, 3],\n [1, -2, -13, -1, 8, -10],\n [-5, -2, -1, -5, 4, 6],\n [2, -2, 8, 4, -1, 4],\n [-6, 3, -10, 6, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-12, -9, -11, 5, 15, -2],\n [0, -4, -2, 15, 3, 11],\n [0, 0, 2, 8, 7, -14],\n [0, 0, 0, -11, 4, -9],\n [0, 0, 0, 0, 11, -15],\n [0, 0, 0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -4, 10, 3, 8, -13],\n [6, -14, 8, -8, -11, -15],\n [13, -11, -2, -12, -8, 9],\n [0, 15, -11, -5, -3, -8],\n [-5, -13, -15, -12, 3, -2],\n [6, 10, 12, -14, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "691", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 1, 10, 2, 8],\n [0, 12, -6, 6, -4, 1],\n [1, -6, -4, -1, 6, -4],\n [10, 6, -1, -3, 0, -5],\n [2, -4, 6, 0, -5, -1],\n [8, 1, -4, -5, -1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, -4, 11, -8, 8, -11],\n [-5, 0, 9, -8, -3, -13],\n [-7, -8, -6, -1, -2, 3],\n [12, 2, 2, -8, -7, -8],\n [-8, 11, -12, 5, -3, -13],\n [8, 0, 3, 7, 6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 15, -3, -4, 12, 12],\n [0, -7, 4, -1, -12, 8],\n [0, 0, -10, 8, 7, -8],\n [0, 0, 0, 11, 11, -14],\n [0, 0, 0, 0, -7, -8],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "710", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 14, -7, 10, -5, -2],\n [0, 3, 13, -7, -11, 12],\n [0, 0, 4, 6, 8, -13],\n [0, 0, 0, 10, -1, 13],\n [0, 0, 0, 0, -6, -14],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[3, 6, -1, -2, -2, -4],\n [6, -1, -10, -2, 14, -2],\n [-1, -10, -11, 7, 2, 4],\n [-2, -2, 7, 0, -4, 2],\n [-2, 14, 2, -4, 2, -4],\n [-4, -2, 4, 2, -4, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "502", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 4, -1, -6, -8, -1],\n [4, 5, -2, -5, -1, 8],\n [-1, -2, 8, -5, 4, 0],\n [-6, -5, -5, 10, -8, -12],\n [-8, -1, 4, -8, 11, -10],\n [-1, 8, 0, -12, -10, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, 12, -15, -14, -5],\n [0, -11, 12, 14, 15, 0],\n [0, 0, -15, -7, -15, 7],\n [0, 0, 0, -6, 11, -1],\n [0, 0, 0, 0, -15, -7],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[9, 2, -2, -12, 2, -5],\n [2, 4, 0, -2, -2, 1],\n [-2, 0, 9, -5, -10, -4],\n [-12, -2, -5, 15, -6, 8],\n [2, -2, -10, -6, -2, 0],\n [-5, 1, -4, 8, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, -5, 0, 6, 14, -9],\n [11, 2, 8, 7, 1, 11],\n [8, -4, -4, -5, -3, -4],\n [7, 10, -6, -14, -13, 6],\n [-5, -10, 4, 8, 10, -14],\n [-3, -13, -9, -12, -4, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-13, -6, -8, 7, 4, 2],\n [-14, 2, -14, -3, 8, -2],\n [12, 5, 14, -3, -1, 11],\n [10, -4, -4, -4, 7, -4],\n [7, 2, 8, -1, 11, -10],\n [-8, -3, -13, 3, 14, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[0, 7, -2, 8, 0, 1],\n [7, -10, 6, -10, -4, 3],\n [-2, 6, -7, 4, -3, -2],\n [8, -10, 4, 6, -3, -4],\n [0, -4, -3, -3, -10, -4],\n [1, 3, -2, -4, -4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "689", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 12, 3, -9, 8, 7],\n [0, -8, -8, -11, -1, 7],\n [0, 0, -8, -7, -11, 11],\n [0, 0, 0, 4, 5, -2],\n [0, 0, 0, 0, -3, 2],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-13, -11, -7, 9, 4, -9],\n [12, 9, 8, 10, 12, 6],\n [-10, -3, 14, -9, -8, -13],\n [0, 0, 4, 7, -6, -10],\n [3, -10, 10, 2, 11, 4],\n [-2, -10, 1, 14, 3, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "824", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, 4, 0, 10, -4, 0],\n [4, -7, -10, 12, -4, -3],\n [0, -10, 0, -4, 6, 8],\n [10, 12, -4, -1, 6, -2],\n [-4, -4, 6, 6, 12, 2],\n [0, -3, 8, -2, 2, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "504", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -12, -1, -3, 1, 6],\n [0, 2, 4, 13, 15, 12],\n [0, 0, 14, -12, 15, -2],\n [0, 0, 0, -1, 0, -13],\n [0, 0, 0, 0, 7, 0],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-15, -1, -3, 0, 13, -4],\n [-1, -11, -1, -2, 2, 4],\n [-3, -1, -7, -8, 10, -2],\n [0, -2, -8, -3, 6, -2],\n [13, 2, 10, 6, -5, -5],\n [-4, 4, -2, -2, -5, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 8, 6, -9, 13, -14],\n [13, 5, -12, 2, -2, 5],\n [1, 3, 12, -10, -12, 0],\n [-6, -5, -4, -12, 0, 15],\n [-1, -7, -12, -12, 3, -14],\n [8, -5, -13, 12, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "413", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, 0, -8, 0, -6, -14],\n [0, -7, -2, -11, 2, 6],\n [-8, -2, -13, 0, -4, -5],\n [0, -11, 0, -11, 10, 10],\n [-6, 2, -4, 10, 9, -4],\n [-14, 6, -5, 10, -4, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "328", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -13, 4, -4, 2, -13],\n [5, -12, -8, -9, -11, -4],\n [10, -5, 9, 2, 1, 13],\n [-11, -2, 2, -3, 4, -13],\n [2, -2, -3, 6, -3, 6],\n [-11, -2, 5, 9, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "638", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 12, 15, 11, 15, 6],\n [1, 12, 1, 3, -11, 7],\n [0, 0, 10, 7, 14, -1],\n [1, 15, 2, -15, 1, -12],\n [-1, 11, 1, -12, -5, -13],\n [7, 15, 15, -7, -5, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-5, 15, 5, 3, -3, 14],\n [0, 6, -8, -1, 2, -13],\n [0, 0, -9, 15, -13, -13],\n [0, 0, 0, -1, -14, -10],\n [0, 0, 0, 0, 7, 0],\n [0, 0, 0, 0, 0, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, -12, -12, 4, -2, 4],\n [0, -15, -10, 0, -2, 7],\n [0, 0, 8, 15, -5, -14],\n [0, 0, 0, -14, -8, 15],\n [0, 0, 0, 0, -9, 2],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, 6, 0, 12, -1, 1],\n [6, -5, -5, 0, 4, 11],\n [0, -5, -3, -8, -2, -1],\n [12, 0, -8, -2, 8, 2],\n [-1, 4, -2, 8, -5, -5],\n [1, 11, -1, 2, -5, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -4, -9, 1, -2, -4],\n [0, -9, -8, -7, 2, -12],\n [0, 0, -4, 14, -9, 11],\n [0, 0, 0, -1, -14, -6],\n [0, 0, 0, 0, 6, -2],\n [0, 0, 0, 0, 0, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "808", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[2, -8, 2, 1, 0, 4],\n [-8, -15, -7, 2, -12, -2],\n [2, -7, 3, -2, -4, -4],\n [1, 2, -2, 6, 4, -3],\n [0, -12, -4, 4, 4, -2],\n [4, -2, -4, -3, -2, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "728", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[11, -3, 12, -15, -8, -10],\n [0, 6, -3, 10, -10, 7],\n [0, 0, 13, 5, 7, -5],\n [0, 0, 0, 2, 9, 1],\n [0, 0, 0, 0, -15, -10],\n [0, 0, 0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 6, -10, -1, 12, 2],\n [-5, -6, -9, 15, 4, 13],\n [-12, -2, -4, 11, 1, -10],\n [5, 0, 3, -12, -11, 7],\n [6, 7, 9, 6, 13, 4],\n [-3, 4, -3, 5, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-11, -4, 7, -11, -6, -2],\n [0, 6, 12, 9, -5, 7],\n [0, 0, -12, -5, -9, 7],\n [0, 0, 0, -2, -15, 4],\n [0, 0, 0, 0, -9, -10],\n [0, 0, 0, 0, 0, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -3, -13, 0, 6, -15],\n [0, 7, -9, -13, -1, -11],\n [0, 0, -11, -8, 0, 1],\n [0, 0, 0, -3, 7, -12],\n [0, 0, 0, 0, 13, 15],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "991", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-13, 14, 1, -12, 4, 4],\n [14, -4, -7, 6, 0, 0],\n [1, -7, 11, 1, 6, -3],\n [-12, 6, 1, -11, 6, -1],\n [4, 0, 6, 6, 0, -6],\n [4, 0, -3, -1, -6, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "524", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-9, -2, 3, 7, 11, 9],\n [-11, 5, -5, -12, -7, -8],\n [-5, 9, 8, 0, 8, 8],\n [-5, -4, -2, 8, 1, -6],\n [12, -11, 10, -8, -7, 2],\n [9, 4, -8, -9, 0, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, 4, 2, 2, -4, 1],\n [4, -6, -2, 8, 0, -2],\n [2, -2, -13, 10, 1, -2],\n [2, 8, 10, 5, -5, 6],\n [-4, 0, 1, -5, -7, -4],\n [1, -2, -2, 6, -4, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, 5, 7, 12, -8, -6],\n [5, 12, 2, 0, 4, 0],\n [7, 2, -2, -6, -2, -9],\n [12, 0, -6, 4, -10, 10],\n [-8, 4, -2, -10, 6, -4],\n [-6, 0, -9, 10, -4, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, -2, -3, 9, 15],\n [0, -10, -4, -3, -9, -15],\n [0, 0, 1, 14, 14, 14],\n [0, 0, 0, -3, -1, 7],\n [0, 0, 0, 0, 12, -13],\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": "What is the determinant of the matrix:\n[[8, -4, -2, -6, 4, -6],\n [-4, 13, 0, 2, -2, 7],\n [-2, 0, -1, 8, 0, -1],\n [-6, 2, 8, 0, 6, 8],\n [4, -2, 0, 6, -12, 0],\n [-6, 7, -1, 8, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, -1, 4, -12, 1, 6],\n [-1, -15, -14, 12, 1, -4],\n [4, -14, 8, 7, 0, 0],\n [-12, 12, 7, -4, 2, 2],\n [1, 1, 0, 2, -8, -2],\n [6, -4, 0, 2, -2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "658", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 0, -6, -6, -4, -1],\n [0, 13, 8, -8, 10, 10],\n [-6, 8, -12, -8, -3, 6],\n [-6, -8, -8, -7, -10, -3],\n [-4, 10, -3, -10, 7, 8],\n [-1, 10, 6, -3, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, -1, -15, -9, -15, 13],\n [0, 1, -11, 15, 9, -3],\n [0, 0, 10, 13, -7, 11],\n [0, 0, 0, -5, 6, 8],\n [0, 0, 0, 0, -1, -9],\n [0, 0, 0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -1, -9, 0, -13, -1],\n [6, -6, 3, 15, -15, -12],\n [11, -9, -7, -9, -13, -14],\n [-4, -12, -5, 13, 2, -14],\n [10, 5, -3, 2, -4, 1],\n [3, 0, 3, -3, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, 9, 1, -11, -9],\n [-9, 2, 12, 0, 12, -7],\n [1, 9, 1, 15, -1, -13],\n [14, -1, -6, -15, -10, -10],\n [-14, 0, 12, 10, -13, -9],\n [8, -9, 8, -12, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 2, -7, 5, 2, -5],\n [2, -10, -9, -2, 0, 5],\n [-7, -9, 3, 2, -1, -1],\n [5, -2, 2, -8, 0, 0],\n [2, 0, -1, 0, 14, -1],\n [-5, 5, -1, 0, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, -9, -6, 0, -5, 7],\n [0, -6, 0, 2, -9, 4],\n [0, 0, 2, -3, -6, -2],\n [0, 0, 0, -7, -14, 9],\n [0, 0, 0, 0, -13, -6],\n [0, 0, 0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-11, 13, -15, 11, 6, 6],\n [10, 2, -11, -8, -7, -4],\n [3, -5, -14, 0, 2, -14],\n [13, -4, -4, 10, 13, 14],\n [-7, -2, 14, 15, -11, 6],\n [-5, -5, 10, -4, 4, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-14, -2, 1, 2, 14, 11],\n [15, 12, -8, 14, -11, 12],\n [5, -1, 11, 0, 7, 0],\n [-15, 1, 13, 14, -8, -6],\n [6, 3, 3, 11, 4, 12],\n [-5, 3, -4, -3, 6, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, 6, 2, 3, 8, -3],\n [0, -12, -11, 9, 8, -12],\n [0, 0, 10, 9, -3, -13],\n [0, 0, 0, -12, -8, -13],\n [0, 0, 0, 0, -12, 1],\n [0, 0, 0, 0, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, -2, 2, 8, -12],\n [-6, -7, 5, -6, 9, -2],\n [-2, 5, -5, -1, -4, 9],\n [2, -6, -1, 3, 3, 4],\n [8, 9, -4, 3, -8, -6],\n [-12, -2, 9, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "864", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[7, 0, -6, 5, 6, 3],\n [0, 6, -12, -2, 0, 4],\n [-6, -12, 13, 4, 4, 3],\n [5, -2, 4, -12, -5, -6],\n [6, 0, 4, -5, 1, -12],\n [3, 4, 3, -6, -12, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[9, 9, -14, -12, -7, -12],\n [0, 13, 13, -3, -13, 4],\n [0, 0, 1, 13, 4, 14],\n [0, 0, 0, -5, -5, 7],\n [0, 0, 0, 0, 12, 14],\n [0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -9, 1, 3, -13, 2],\n [0, -6, 3, -1, 7, -12],\n [0, 0, 3, 4, 4, 7],\n [0, 0, 0, -8, -12, -2],\n [0, 0, 0, 0, 1, 11],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-10, 4, -10, -5, 8, -11],\n [4, 0, 0, -11, -2, -6],\n [-10, 0, 14, -2, -2, -10],\n [-5, -11, -2, 10, 7, -10],\n [8, -2, -2, 7, 0, -1],\n [-11, -6, -10, -10, -1, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, -4, 6, -6, 2, -3],\n [-4, 13, 6, 3, -1, 0],\n [6, 6, 10, -8, -4, 8],\n [-6, 3, -8, 13, -2, -2],\n [2, -1, -4, -2, 4, 2],\n [-3, 0, 8, -2, 2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-9, 15, 10, -10, -6, 11],\n [-10, 4, -2, -2, -1, 10],\n [2, -14, 14, -9, -13, -6],\n [-13, 11, -5, 6, -5, 12],\n [-3, -2, 4, 3, -10, -2],\n [1, -5, -2, -15, 8, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "975", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -9, -2, 15, 6, 15],\n [0, 11, -6, 11, -6, 3],\n [0, 0, -10, -15, -7, 7],\n [0, 0, 0, 1, 10, -5],\n [0, 0, 0, 0, 13, 9],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, 11, 7, -7, -1, -11],\n [-2, -4, -9, 11, -1, -14],\n [5, 11, -10, 11, 4, 5],\n [2, 6, 7, -14, -13, -7],\n [5, 10, 8, -6, -11, 9],\n [-12, -12, 5, -1, -9, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -9, 12, 15, -1, -10],\n [6, 7, -14, -5, -6, -6],\n [13, -5, -13, 0, 0, -8],\n [-1, 3, -13, -11, -3, 8],\n [-7, -2, 14, -11, 6, 3],\n [10, -5, 3, -14, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "445", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, 2, 4, -8, 1, -10],\n [2, -6, 10, -4, 2, 9],\n [4, 10, 4, -2, 8, -10],\n [-8, -4, -2, -7, -10, -2],\n [1, 2, 8, -10, -3, -9],\n [-10, 9, -10, -2, -9, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "572", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, -12, -6, 2, 0],\n [8, 7, -6, -2, 1, 2],\n [-12, -6, -10, -2, 0, -6],\n [-6, -2, -2, -8, 4, -6],\n [2, 1, 0, 4, 11, 8],\n [0, 2, -6, -6, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "472", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[5, -14, 10, -4, 0, 13],\n [-14, 13, 4, 4, -1, 0],\n [10, 4, 14, -2, 7, 0],\n [-4, 4, -2, -13, -6, -2],\n [0, -1, 7, -6, 0, 0],\n [13, 0, 0, -2, 0, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "291", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-12, -12, -8, -3, 10, -2],\n [3, -7, -9, -1, -8, -11],\n [1, 12, -2, -3, 10, 13],\n [0, 6, 12, 8, 14, 10],\n [-11, -8, 2, 11, 0, -8],\n [-9, 7, -6, 9, -6, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, 11, -10, -1, 5, -12],\n [0, 5, -7, -11, 7, -15],\n [0, 0, -10, -10, -5, -15],\n [0, 0, 0, -13, 8, -11],\n [0, 0, 0, 0, 13, -5],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-6, -5, -11, 9, 5, 13],\n [0, -10, -1, -2, 5, 1],\n [0, 0, 13, 15, -15, -15],\n [0, 0, 0, 15, 0, 14],\n [0, 0, 0, 0, 11, -11],\n [0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-13, -12, -10, 7, -4, 3],\n [3, -5, -9, 1, -15, 4],\n [1, 8, 11, -6, -2, -10],\n [0, -10, -11, 9, 0, 9],\n [3, -5, 3, -1, -9, 3],\n [-10, -3, 8, -11, -7, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "988", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -9, 12, -1, 10, -5],\n [0, 13, -7, -11, 8, 15],\n [0, 0, -2, -7, 11, -15],\n [0, 0, 0, 15, 14, 4],\n [0, 0, 0, 0, 8, 7],\n [0, 0, 0, 0, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 0, 11, -11, 0, 10],\n [-12, -10, 15, 13, 10, 15],\n [-8, 14, -12, -7, -11, 4],\n [14, 2, 0, 7, -12, -9],\n [9, -2, 12, -8, -7, 13],\n [-12, 11, -6, -13, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, -6, 3, 2, 3, 0],\n [-6, -3, -6, 4, 0, 4],\n [3, -6, -5, -2, -2, 4],\n [2, 4, -2, -13, -2, -2],\n [3, 0, -2, -2, -5, 7],\n [0, 4, 4, -2, 7, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, -4, -6, -3, -11, 10],\n [-4, -3, 5, 0, 2, 3],\n [-6, 5, -14, -2, 2, 2],\n [-3, 0, -2, 3, 8, 9],\n [-11, 2, 2, 8, -15, -2],\n [10, 3, 2, 9, -2, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 2, 9, -6, -5, 14],\n [13, -8, -6, 0, -4, 10],\n [12, -5, 12, -6, 6, 12],\n [7, -4, -5, -7, 8, 14],\n [-10, 1, -8, 11, 3, -10],\n [2, 0, 8, -12, 13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[2, -8, 7, 5, 7, 12],\n [-10, 13, -11, 10, -10, 15],\n [11, 1, -12, 11, -11, -7],\n [11, 2, -8, 12, 6, -14],\n [-3, 7, -3, -13, -2, -3],\n [0, 9, 6, -15, 13, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "420", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-8, 2, -3, 13, -4, 4],\n [0, 8, -12, 3, -15, -9],\n [0, 0, -1, -9, 8, 2],\n [0, 0, 0, 9, 11, -10],\n [0, 0, 0, 0, 4, 5],\n [0, 0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 5, -2, -13, 12, 11],\n [-1, 12, 12, -5, 1, 15],\n [-15, 4, 15, 2, 4, -3],\n [-7, 3, -4, 1, 1, 12],\n [-12, 9, 13, 3, 4, -12],\n [14, 10, 4, -1, 13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "740", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -5, -5, 4, 4, 15],\n [0, -9, 2, -1, 4, -5],\n [0, 0, 9, -11, 5, -8],\n [0, 0, 0, 12, -14, -10],\n [0, 0, 0, 0, -7, -4],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-15, -9, 0, 2, 4, -13],\n [6, -3, -13, -15, 8, 13],\n [11, -3, 12, -1, -13, 13],\n [-11, 13, -3, -14, -14, -6],\n [4, -9, -12, -5, -14, 3],\n [5, -1, 1, 6, -11, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, -9, 4, 12, -10, 6],\n [-7, 4, 7, 7, -7, -9],\n [-14, 6, 8, 9, -1, 2],\n [-8, 13, 5, 14, 10, 6],\n [1, -8, 15, 1, -5, 13],\n [1, -8, -5, 7, 14, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-8, 0, 0, 0, -3, 2],\n [0, 14, 6, 2, 3, -9],\n [0, 6, -9, -1, 8, 6],\n [0, 2, -1, 1, 2, 0],\n [-3, 3, 8, 2, -7, -10],\n [2, -9, 6, 0, -10, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, 4, -2, 4, -10],\n [4, 11, -8, 4, -6, 0],\n [4, -8, -14, -6, -10, -14],\n [-2, 4, -6, 7, -6, -6],\n [4, -6, -10, -6, 12, -8],\n [-10, 0, -14, -6, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, 2, 4, -6, -4, 0],\n [2, -10, -2, -6, 2, 2],\n [4, -2, 9, -2, -6, -4],\n [-6, -6, -2, 6, 0, 1],\n [-4, 2, -6, 0, 9, -4],\n [0, 2, -4, 1, -4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "592", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[5, -5, -12, -13, -3, -11],\n [0, -7, -1, -6, 14, -2],\n [0, 0, 5, 1, -15, -3],\n [0, 0, 0, 5, -15, 4],\n [0, 0, 0, 0, -14, -10],\n [0, 0, 0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "750", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[5, 9, 12, 2, -9, 3],\n [0, -3, 8, -12, -14, 8],\n [0, 0, -6, 3, 7, 3],\n [0, 0, 0, 13, -8, -11],\n [0, 0, 0, 0, 8, -4],\n [0, 0, 0, 0, 0, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -2, 3, 6, 10, -4],\n [9, 10, 12, -7, 6, -9],\n [-5, -11, -12, 1, 12, -4],\n [13, -3, -11, 13, -10, -2],\n [-13, -1, -11, -11, 0, 9],\n [2, 1, -5, -13, -11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -14, -14, -12, 3, -5],\n [-7, -8, 7, 4, -12, 0],\n [9, -7, 8, 14, -6, 6],\n [12, -11, -4, -9, 6, -8],\n [-9, -1, -6, -4, -8, -14],\n [-9, 8, -4, -1, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "860", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 2, 15, -5, 4, 4],\n [0, 1, -10, -13, 14, 8],\n [0, 0, -2, 1, 15, 13],\n [0, 0, 0, -6, -7, -9],\n [0, 0, 0, 0, -6, 8],\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -14, 15, -1, 8, -9],\n [0, -14, -8, 5, 0, 5],\n [0, 0, 1, 3, -6, -14],\n [0, 0, 0, 13, 14, 9],\n [0, 0, 0, 0, 2, 1],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[0, 8, 0, 6, 12, -2],\n [8, -1, 7, -10, -3, -4],\n [0, 7, -4, 2, 9, 8],\n [6, -10, 2, 15, -10, 10],\n [12, -3, 9, -10, -4, 4],\n [-2, -4, 8, 10, 4, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 7, -4, 15, -3, -15],\n [0, 3, 9, 13, 10, 8],\n [0, 0, 13, -14, 10, 8],\n [0, 0, 0, 1, 0, 9],\n [0, 0, 0, 0, -11, -2],\n [0, 0, 0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "426", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[12, -4, 4, 0, 2, -3],\n [-4, 1, 9, 4, -5, 7],\n [4, 9, -9, 9, 4, -2],\n [0, 4, 9, -11, -5, 2],\n [2, -5, 4, -5, -7, 6],\n [-3, 7, -2, 2, 6, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[14, -10, 0, -4, 6, 1],\n [-10, -3, 0, -2, -2, 6],\n [0, 0, -6, -8, -1, -12],\n [-4, -2, -8, -7, 2, 0],\n [6, -2, -1, 2, 15, 12],\n [1, 6, -12, 0, 12, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "327", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, 8, -8, 2, -4],\n [-4, -5, -10, 0, -8, 3],\n [8, -10, 7, -6, -11, -8],\n [-8, 0, -6, -1, -3, 6],\n [2, -8, -11, -3, -7, -4],\n [-4, 3, -8, 6, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -14, 0, -12, 1, 3],\n [0, 1, 9, -2, 10, -1],\n [0, 0, -10, 14, -3, -4],\n [0, 0, 0, -2, 6, 7],\n [0, 0, 0, 0, -12, -14],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, 1, -1, 4, -2, -2],\n [1, -9, 2, 11, 5, 0],\n [-1, 2, 13, 6, 10, -8],\n [4, 11, 6, 11, 0, -6],\n [-2, 5, 10, 0, 14, -2],\n [-2, 0, -8, -6, -2, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[9, 14, 9, -15, -3, -15],\n [10, 9, 0, 1, 7, 11],\n [-11, 10, -10, 4, -14, -13],\n [-6, 8, -14, 7, -4, 3],\n [-5, 15, -14, 10, 13, 14],\n [4, 9, -9, 9, 5, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-13, -14, 9, 2, -9, 12],\n [0, -11, -14, 11, 3, 12],\n [0, 0, -11, -11, 14, 8],\n [0, 0, 0, 4, 3, 1],\n [0, 0, 0, 0, -8, 13],\n [0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "656", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, -3, -6, -1, -7, 4],\n [-3, -12, 5, 4, 8, -14],\n [-6, 5, 13, 6, -4, -13],\n [-1, 4, 6, -6, 2, -6],\n [-7, 8, -4, 2, 0, -10],\n [4, -14, -13, -6, -10, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "830", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-13, -15, 6, 0, -2, -15],\n [0, -11, 13, 0, -12, -10],\n [0, 0, 2, 12, -11, -15],\n [0, 0, 0, 10, 13, -10],\n [0, 0, 0, 0, -5, 2],\n [0, 0, 0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, -15, -15, -15, -1, 8],\n [11, -15, -13, 14, 6, -4],\n [-14, -6, 11, -12, -10, 13],\n [-8, 13, -2, 14, -3, -12],\n [-1, 4, -15, -3, 14, 10],\n [10, 13, 6, 11, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, -4, -8, -4, 2, 1],\n [-4, -13, -8, 0, 2, 4],\n [-8, -8, -1, 8, 8, 8],\n [-4, 0, 8, 3, 6, 0],\n [2, 2, 8, 6, -11, 2],\n [1, 4, 8, 0, 2, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -5, 2, -11, 6, -11],\n [12, -9, -3, 6, 11, 5],\n [-7, 11, 3, 1, -4, -4],\n [-13, 8, 12, 14, 11, -5],\n [10, 5, -10, -8, -10, 15],\n [5, -15, -5, 5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "318", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[6, 7, -10, 3, 14, -8],\n [-2, -5, 1, 15, 13, 0],\n [3, -1, -4, 0, -4, 12],\n [9, 5, 11, -1, 15, 14],\n [9, -15, 1, 14, 5, 9],\n [12, 4, 3, 3, 13, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "910", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -7, 12, -3, 3, 3],\n [-9, 8, -10, 13, -14, 10],\n [-6, -11, 8, -9, -4, -5],\n [-9, 7, -9, -12, -13, -13],\n [0, -6, 7, -15, 14, -14],\n [-7, -13, 14, 12, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-4, 1, 3, -6, 2, 0],\n [1, 5, -4, 3, 2, -5],\n [3, -4, 3, -6, 6, 9],\n [-6, 3, -6, 0, 0, -6],\n [2, 2, 6, 0, -12, 4],\n [0, -5, 9, -6, 4, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 0, 3, 2, -8, -12],\n [0, 7, -2, 6, -2, -3],\n [3, -2, 13, -2, -2, -4],\n [2, 6, -2, -8, 4, 12],\n [-8, -2, -2, 4, -3, -1],\n [-12, -3, -4, 12, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, -2, 15, 3, 12, 2],\n [13, 6, -9, 11, -11, 3],\n [1, 1, -13, -3, -13, -14],\n [-13, 5, 11, -11, -5, 11],\n [-15, 12, 3, 5, 4, 12],\n [2, -6, -5, -11, 3, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "862", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-2, 12, -15, 11, -4, -5],\n [0, -11, -5, 9, -9, -5],\n [0, 0, 14, 12, -8, 7],\n [0, 0, 0, -2, 1, 2],\n [0, 0, 0, 0, 9, 2],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 10, 6, -14, -2, -3],\n [-4, 11, 15, -5, -14, 6],\n [-11, -14, 9, 10, -14, 14],\n [-15, 8, -15, 10, 13, -7],\n [-12, -7, 11, -10, 9, 1],\n [8, 0, -4, 8, -11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, -7, -7, 3, 1, -7],\n [-7, -1, 4, -6, 8, -6],\n [-7, 4, 11, 6, -8, 6],\n [3, -6, 6, -15, 5, 2],\n [1, 8, -8, 5, -4, 6],\n [-7, -6, 6, 2, 6, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "718", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 9, 4, 12, 4, -12],\n [0, 1, 0, -15, 1, 5],\n [0, 0, -11, -2, -2, -9],\n [0, 0, 0, -6, 3, 8],\n [0, 0, 0, 0, 8, 14],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, -1, 11, 4, -7, 12],\n [0, 2, -4, -9, 7, 8],\n [0, 0, 6, 11, 7, 3],\n [0, 0, 0, 1, 8, -15],\n [0, 0, 0, 0, -14, 4],\n [0, 0, 0, 0, 0, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, -10, 5, -1, -10, -4],\n [0, -6, -11, -4, -3, -5],\n [0, 0, 4, 7, 2, -7],\n [0, 0, 0, -13, -13, -4],\n [0, 0, 0, 0, -4, -11],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, 0, -3, -14, 12, -12],\n [2, -9, -6, 0, -5, 1],\n [9, 12, 5, -11, 11, -1],\n [6, -11, 14, -12, -12, -8],\n [8, -2, 1, -5, -10, 15],\n [-4, -7, 3, -10, 11, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 13, 1, 14, 14, -3],\n [0, 12, 9, 8, 9, 13],\n [0, 0, -2, 6, 3, 1],\n [0, 0, 0, -3, -7, 6],\n [0, 0, 0, 0, 9, 7],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, 9, 4, 12, 10],\n [-1, 1, -2, 2, 0, 4],\n [9, -2, 3, -2, 8, -4],\n [4, 2, -2, -2, -6, 3],\n [12, 0, 8, -6, 1, 8],\n [10, 4, -4, 3, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 5, -10, -12, -2],\n [2, -5, 1, 0, 12, 4],\n [5, 1, 5, -7, -3, 0],\n [-10, 0, -7, -1, -6, 8],\n [-12, 12, -3, -6, 11, -6],\n [-2, 4, 0, 8, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "854", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[15, -2, 12, 1, -5, -8],\n [-2, 11, 9, -4, -6, 2],\n [12, 9, 5, -4, -12, 4],\n [1, -4, -4, 3, -10, 6],\n [-5, -6, -12, -10, 12, -4],\n [-8, 2, 4, 6, -4, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-11, 2, 4, 9, 2, 3],\n [2, -2, 3, 6, 2, -4],\n [4, 3, 3, -2, -4, -6],\n [9, 6, -2, 14, 0, 8],\n [2, 2, -4, 0, -6, 8],\n [3, -4, -6, 8, 8, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, 0, 4, 8, 0, 2],\n [0, -5, -4, 10, -4, -5],\n [4, -4, 3, 3, 2, 2],\n [8, 10, 3, 6, -1, 2],\n [0, -4, 2, -1, 6, -3],\n [2, -5, 2, 2, -3, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "725", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, 7, -8, 8, -2],\n [2, 0, 14, -11, 1, 8],\n [7, 14, -14, -6, -10, 0],\n [-8, -11, -6, 4, -2, 0],\n [8, 1, -10, -2, 15, 0],\n [-2, 8, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -6, 4, 11, 6],\n [2, 15, 4, -3, 4, 4],\n [-6, 4, -7, -6, 5, -4],\n [4, -3, -6, -7, -9, 10],\n [11, 4, 5, -9, -14, 10],\n [6, 4, -4, 10, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 7, 7, 0, 4, -7],\n [7, 1, 7, 1, -12, 0],\n [7, 7, -4, -8, 9, 2],\n [0, 1, -8, -6, 2, 8],\n [4, -12, 9, 2, -6, 4],\n [-7, 0, 2, 8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "253", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, -9, 1, -5, 4, 13],\n [0, 10, -9, -3, -9, 11],\n [0, 0, -2, 3, 3, -13],\n [0, 0, 0, 2, -3, -7],\n [0, 0, 0, 0, 14, 1],\n [0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, 6, -6, 6, 5, -8],\n [0, 2, -12, 2, -11, -2],\n [0, 0, -2, 0, -4, 14],\n [0, 0, 0, 12, 13, 10],\n [0, 0, 0, 0, -2, -8],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, -11, 0, -15, 8, 0],\n [12, 5, -10, 7, 7, -1],\n [-15, 6, -1, 1, 13, -7],\n [-2, 12, 0, -3, 10, 1],\n [4, -10, -11, -6, -9, 12],\n [15, -12, -13, -14, -11, 14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "628", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -5, -6, -12, 13, -10],\n [2, 9, 4, -5, -4, 7],\n [11, -5, 0, 9, 7, -13],\n [-14, 11, -2, -5, -10, 11],\n [12, -13, -4, -1, -10, 7],\n [-1, -12, 5, 1, 1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[6, -2, 2, -5, -9, 0],\n [-2, -6, 0, 9, 4, 5],\n [2, 0, 8, 4, 9, 2],\n [-5, 9, 4, -15, 4, -8],\n [-9, 4, 9, 4, 4, -7],\n [0, 5, 2, -8, -7, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "433", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[13, -2, -2, -9, 2, 8],\n [-2, -5, 10, 4, 1, -2],\n [-2, 10, -12, -3, 0, 1],\n [-9, 4, -3, 2, 2, -5],\n [2, 1, 0, 2, -4, 2],\n [8, -2, 1, -5, 2, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, 0, -13, 9, 12, 1],\n [-13, -3, -4, -2, 13, -11],\n [0, -5, 3, 3, -7, 14],\n [11, -6, 15, 9, 6, -3],\n [7, -4, -7, 11, 6, -10],\n [10, -15, 12, 1, 13, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, 2, -6, 10, -1, 5],\n [2, -8, 2, -12, 0, 2],\n [-6, 2, 9, 0, -10, -4],\n [10, -12, 0, 6, 5, 9],\n [-1, 0, -10, 5, 5, 2],\n [5, 2, -4, 9, 2, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[15, -13, -6, 6, 12, -15],\n [14, 6, 1, -7, 4, -12],\n [9, 4, 2, 6, 3, -11],\n [7, 0, -4, -6, -14, -7],\n [-11, -13, -4, 12, -15, -14],\n [-3, -13, -8, 10, 3, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 10, 14, -10, 15, -8],\n [13, -4, 9, -7, 4, 15],\n [-2, 3, 4, -2, -10, 13],\n [0, -11, -8, -11, -12, 12],\n [2, -13, -14, -11, -8, 4],\n [-11, -4, 2, 11, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 3, -8, 2, 2, -12],\n [0, 13, 2, -11, 13, 13],\n [0, 0, -7, 9, -15, -3],\n [0, 0, 0, -2, 3, -7],\n [0, 0, 0, 0, -10, 1],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, -8, 0, 0, -3, 12],\n [0, 4, 1, 10, 8, -7],\n [0, 0, 14, 13, 7, 13],\n [0, 0, 0, 12, 2, 1],\n [0, 0, 0, 0, -3, -2],\n [0, 0, 0, 0, 0, 15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[5, -11, 2, -4, -13, 13],\n [-14, 1, 8, -10, 10, -14],\n [-7, 8, -2, 7, 0, -9],\n [-5, -6, -14, -10, -6, 4],\n [13, 4, 14, -8, 8, -9],\n [14, 15, 10, 2, -10, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 6, 2, -4, 0, -4],\n [6, -9, -4, -6, 8, 3],\n [2, -4, -12, -2, -4, 9],\n [-4, -6, -2, -8, 0, 0],\n [0, 8, -4, 0, 0, 10],\n [-4, 3, 9, 0, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, -6, 5, -6, -8, 4],\n [-13, 8, 14, 2, 2, -3],\n [-3, -1, 12, 11, 14, 6],\n [-11, -13, 3, 15, 5, -6],\n [-7, 7, 14, -10, -12, -13],\n [-6, 7, -5, -3, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "814", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-12, 2, -9, -13, -14, -1],\n [5, 9, -3, -13, 1, 1],\n [14, 7, 1, 5, -1, 7],\n [3, 9, 2, 6, 7, 1],\n [-3, 2, 11, -1, -5, 5],\n [9, 3, -4, 9, -2, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 9, -11, -10, 13, -8],\n [-13, -6, 4, 5, -9, 5],\n [-11, -7, -2, -5, 6, 4],\n [-10, 10, -13, -10, 9, -13],\n [1, -7, -13, -4, -8, 9],\n [-14, 12, 5, 4, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "517", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 12, -15, 6, -2, -7],\n [0, -5, -10, -1, -8, 0],\n [0, 0, 2, 15, 14, 8],\n [0, 0, 0, 9, -5, 13],\n [0, 0, 0, 0, -12, 7],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 15, 6, 15, 3, -8],\n [0, -4, 2, -3, 3, -14],\n [0, 0, 7, -2, 8, -7],\n [0, 0, 0, -6, -14, -2],\n [0, 0, 0, 0, 7, -15],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, -3, 5, 9, 9, 14],\n [-10, 1, 6, 8, -4, -11],\n [8, 8, 0, 14, -13, -6],\n [13, 3, -15, 2, 7, 7],\n [-3, -6, 0, 14, 12, 7],\n [-6, -3, -8, 1, -1, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-14, -4, 6, -4, -4, -8],\n [-4, 0, -4, 1, -14, -3],\n [6, -4, -9, -2, 6, -6],\n [-4, 1, -2, 14, -3, -4],\n [-4, -14, 6, -3, 14, -1],\n [-8, -3, -6, -4, -1, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, 9, 7, -4, 9, 1],\n [0, -7, 2, 9, 10, 13],\n [0, 0, -3, 1, -11, -4],\n [0, 0, 0, 6, -1, -9],\n [0, 0, 0, 0, -11, 14],\n [0, 0, 0, 0, 0, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "790", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, 3, 2, -4, -10, -3],\n [0, -6, -2, 13, 9, -8],\n [0, 0, 13, -7, 14, 6],\n [0, 0, 0, 1, 2, -14],\n [0, 0, 0, 0, -2, -7],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[6, 12, -2, -15, -10, -10],\n [0, -4, 2, 13, -13, 0],\n [0, 0, -11, 14, -5, 11],\n [0, 0, 0, -12, 5, -14],\n [0, 0, 0, 0, -9, 11],\n [0, 0, 0, 0, 0, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, 11, -8, 9, 0, -4],\n [11, 7, -2, 9, 9, 4],\n [-8, -2, -13, 0, 2, 6],\n [9, 9, 0, 14, -11, -2],\n [0, 9, 2, -11, -5, 0],\n [-4, 4, 6, -2, 0, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[11, 10, -1, -14, -7, 11],\n [-8, -11, -13, -7, -1, -8],\n [-13, 12, -13, -13, -15, 3],\n [12, 0, 14, -5, -1, 14],\n [10, -8, -12, -13, 13, 6],\n [-5, 8, 7, -9, -6, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[1, -14, -8, -12, 3, -1],\n [9, 14, -4, 0, 14, -13],\n [-1, 7, -2, 2, 9, -3],\n [13, 8, -5, 7, 9, 11],\n [2, 2, -12, 14, 12, -4],\n [12, 5, 4, 13, 10, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[3, 2, 8, -7, 6, 7],\n [2, 14, 3, -7, 0, 12],\n [8, 3, 5, -4, 10, -8],\n [-7, -7, -4, -15, -5, -5],\n [6, 0, 10, -5, 12, 10],\n [7, 12, -8, -5, 10, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "657", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-10, -6, 0, -3, 8, -1],\n [-6, -13, -6, 2, -4, -6],\n [0, -6, -2, 6, 4, 4],\n [-3, 2, 6, -11, 8, -1],\n [8, -4, 4, 8, 9, 8],\n [-1, -6, 4, -1, 8, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, 4, 0, -15, -11, -9],\n [-14, -15, -7, 14, -6, -3],\n [-13, 9, -1, -7, -6, 12],\n [-12, -13, -13, 7, -11, -13],\n [-10, 12, -4, 13, 10, -15],\n [10, 5, 10, 14, 14, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 15, -2, -8, -3, -11],\n [0, -6, 4, 15, -7, 4],\n [0, 0, -7, -2, -9, 3],\n [0, 0, 0, -2, 11, -4],\n [0, 0, 0, 0, -15, 4],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[13, 2, 0, 0, 10, -6],\n [2, -9, 8, -6, 5, -1],\n [0, 8, -8, 4, -6, 4],\n [0, -6, 4, 4, 1, 6],\n [10, 5, -6, 1, 0, 10],\n [-6, -1, 4, 6, 10, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, -3, 6, -1, 6],\n [2, 2, 0, -4, -1, 1],\n [-3, 0, 3, -2, -10, -12],\n [6, -4, -2, 13, 4, -7],\n [-1, -1, -10, 4, 11, 4],\n [6, 1, -12, -7, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "959", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[2, -13, 1, -5, -4, 9],\n [-11, 1, -4, -14, 4, 10],\n [1, 4, -13, -15, 12, -1],\n [-10, 9, 9, -10, -4, 6],\n [9, -3, -8, -12, -3, 8],\n [-6, 1, -6, -14, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 11, 2, 2, 0, 0],\n [11, 3, -2, 7, 4, -1],\n [2, -2, 2, -6, 0, 6],\n [2, 7, -6, -9, -2, 6],\n [0, 4, 0, -2, -5, 4],\n [0, -1, 6, 6, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 5, -14, -14, 1, 1],\n [0, -3, 7, -11, 15, 5],\n [0, 0, 1, 0, -2, 0],\n [0, 0, 0, 8, 2, 15],\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": "880", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, 0, 1, 15, 6, -5],\n [0, -3, 12, -13, 14, 7],\n [0, 0, -6, 12, 12, -1],\n [0, 0, 0, -9, 10, -13],\n [0, 0, 0, 0, -6, 10],\n [0, 0, 0, 0, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, 11, 0, -12, 15, 10],\n [0, -5, 1, -8, 11, 6],\n [0, 0, 1, -7, 10, 3],\n [0, 0, 0, 13, -8, 11],\n [0, 0, 0, 0, -2, -6],\n [0, 0, 0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, 4, -2, -10, 0, 8],\n [4, 3, 6, -9, 2, 7],\n [-2, 6, -11, 8, 1, 0],\n [-10, -9, 8, 7, 4, -4],\n [0, 2, 1, 4, 6, 0],\n [8, 7, 0, -4, 0, 15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 2, 11, 3, 14, 12],\n [0, -11, 10, -12, -10, 13],\n [0, 0, -1, 8, -10, 8],\n [0, 0, 0, 1, 11, -4],\n [0, 0, 0, 0, 15, -2],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, 6, 2, 8, 10, -12],\n [6, -1, 2, -2, 0, 3],\n [2, 2, 8, 0, 0, 2],\n [8, -2, 0, 0, 4, 4],\n [10, 0, 0, 4, 13, 2],\n [-12, 3, 2, 4, 2, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 5, 15, -3, 4, 7],\n [0, 2, -2, 12, -10, 10],\n [0, 0, -12, -14, 7, 6],\n [0, 0, 0, -13, -8, 9],\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": "800", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-3, -4, -1, 1, -2, 1],\n [-4, -11, -11, -2, 8, 2],\n [-1, -11, 10, 13, -6, 1],\n [1, -2, 13, 14, -5, -6],\n [-2, 8, -6, -5, 12, -6],\n [1, 2, 1, -6, -6, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, -8, 4, -4, -9, -11],\n [-8, -1, 3, 2, 0, 4],\n [4, 3, 3, 2, 0, 1],\n [-4, 2, 2, -11, 5, 7],\n [-9, 0, 0, 5, -8, -10],\n [-11, 4, 1, 7, -10, -15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 13, 8, 14, -5, 12],\n [-12, -3, 13, -1, 1, 11],\n [-4, 8, 4, -11, -1, -12],\n [-2, 10, 8, -3, -4, 15],\n [-10, -14, -11, -10, -9, 1],\n [4, 3, -1, -14, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -4, -7, 12, 8],\n [0, -8, -4, -2, 5, 3],\n [-4, -4, -2, 6, -3, -2],\n [-7, -2, 6, 2, -11, -4],\n [12, 5, -3, -11, 8, 8],\n [8, 3, -2, -4, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "381", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, 5, 0, 12, 2],\n [-2, 2, -8, -12, 2, -7],\n [5, -8, 8, -2, 9, 2],\n [0, -12, -2, 0, -1, 4],\n [12, 2, 9, -1, -15, 4],\n [2, -7, 2, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 8, 1, 13, -9, 6],\n [0, -2, 12, 13, -5, -1],\n [0, 0, -5, 10, -2, -11],\n [0, 0, 0, -14, 13, 11],\n [0, 0, 0, 0, -9, 0],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, -14, 13, 4, -3],\n [11, -7, 10, 6, 8, 15],\n [2, -8, 6, 1, 8, 4],\n [-8, -11, -14, 7, -2, -5],\n [-2, -14, 6, 6, 6, 9],\n [-5, -4, -6, -11, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-9, -1, -13, -14, -3, 7],\n [0, -3, 11, -11, -11, 2],\n [0, 0, 4, 0, 6, -3],\n [0, 0, 0, 3, 14, 10],\n [0, 0, 0, 0, 5, -8],\n [0, 0, 0, 0, 0, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, -10, -1, -12, -2, -9],\n [-10, 10, 10, -4, -2, -7],\n [-1, 10, -7, 8, -1, -3],\n [-12, -4, 8, -15, 6, -6],\n [-2, -2, -1, 6, 11, -12],\n [-9, -7, -3, -6, -12, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "747", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[12, -2, 1, -2, 9, 1],\n [0, 3, -2, -10, -4, 13],\n [0, 0, -7, -2, -4, 11],\n [0, 0, 0, -14, 5, 8],\n [0, 0, 0, 0, -8, -3],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-12, -10, 11, 10, -5, -8],\n [9, 15, 3, 12, 4, -3],\n [-15, -8, -15, 12, 5, -5],\n [11, -4, -1, 14, 9, 5],\n [-9, 7, -1, -11, -3, -13],\n [-2, -3, 10, 9, 3, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "780", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, -6, 2, 4, -8, 8],\n [-6, -1, -5, -6, 0, 0],\n [2, -5, -7, -6, 0, 2],\n [4, -6, -6, -13, 0, -2],\n [-8, 0, 0, 0, 4, 2],\n [8, 0, 2, -2, 2, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "976", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-13, 2, -4, -2, -2, 2],\n [2, -9, 10, -4, -3, 0],\n [-4, 10, -12, -1, -10, 0],\n [-2, -4, -1, 13, 7, 8],\n [-2, -3, -10, 7, -15, 7],\n [2, 0, 0, 8, 7, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, -1, -1, -14, -3, 3],\n [-1, 1, -2, 8, 3, 1],\n [-1, -2, 15, 6, -2, -2],\n [-14, 8, 6, 3, -3, 4],\n [-3, 3, -2, -3, 12, -4],\n [3, 1, -2, 4, -4, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-1, 0, 6, -10, 6, 1],\n [-4, -3, -11, -8, 9, -15],\n [-1, 7, 3, -14, 3, 9],\n [5, -11, -10, 5, -12, 4],\n [-6, 7, -14, 5, 7, 2],\n [-6, 13, -15, -7, 7, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[15, -2, -13, 13, 8, 9],\n [10, -7, 0, -9, -5, 15],\n [9, -3, 13, -13, -12, 15],\n [-9, -11, 7, -2, -7, 11],\n [-10, -10, -15, 0, -14, -2],\n [3, -7, -4, 14, 4, -15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "137", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-15, -13, 14, 10, 15, -10],\n [7, -7, -2, 10, 12, -5],\n [15, 6, -11, -2, -9, -13],\n [5, -1, 3, -13, 2, -3],\n [-3, 13, -13, 10, 6, -1],\n [10, -13, 9, -12, 11, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-7, -3, 11, 4, -14, 4],\n [0, -4, -14, -9, 7, 0],\n [0, 0, 12, -12, 7, -9],\n [0, 0, 0, -9, -13, -13],\n [0, 0, 0, 0, 3, 9],\n [0, 0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-13, -1, 6, 5, 1, 10],\n [-1, -6, 5, -4, -4, -2],\n [6, 5, 15, 11, -13, -4],\n [5, -4, 11, -14, 3, -2],\n [1, -4, -13, 3, -12, 9],\n [10, -2, -4, -2, 9, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-4, 15, -13, -3, 2, -8],\n [0, -12, -5, 3, 15, 2],\n [0, 0, 2, 5, 8, -4],\n [0, 0, 0, 3, -1, 2],\n [0, 0, 0, 0, -10, 8],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-5, -11, -10, -11, -12, -7],\n [0, -15, 2, -11, -2, 2],\n [14, 2, 8, -9, 11, 13],\n [8, 1, -2, 2, -3, 6],\n [-15, 5, 11, -3, 6, 5],\n [-1, -5, -6, 14, -14, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "817", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[1, 10, 6, 10, 3, -1],\n [-2, -15, -12, 8, 7, -10],\n [-15, 15, -15, 14, -14, 9],\n [-7, -3, -3, -4, 0, -7],\n [14, 3, 8, 9, 13, 10],\n [15, 0, -12, 14, 4, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 10, -15, -1, -8, -1],\n [0, -12, 1, 3, 7, -14],\n [0, 0, -10, -11, -5, -2],\n [0, 0, 0, -15, 11, 9],\n [0, 0, 0, 0, 5, -8],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, -12, 0, -11, -8, -4],\n [-12, 13, -7, -14, 6, 1],\n [0, -7, -13, -8, -14, -6],\n [-11, -14, -8, -11, 2, -9],\n [-8, 6, -14, 2, -6, -2],\n [-4, 1, -6, -9, -2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "478", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-10, -6, -1, 10, -7, -9],\n [0, 10, -13, 10, -15, 9],\n [0, 0, -4, 8, 14, -14],\n [0, 0, 0, -8, -6, -1],\n [0, 0, 0, 0, -3, -4],\n [0, 0, 0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[4, -2, 7, -14, 9, -6],\n [10, -15, -14, 13, 5, 13],\n [4, 9, 5, 12, -8, 2],\n [12, -3, -7, -1, -9, 13],\n [15, 13, -14, 5, 0, 11],\n [4, 1, 13, -4, 10, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 13, 2, -15, -14, 9],\n [0, -14, 8, -3, -10, -9],\n [0, 0, -9, 8, 6, 14],\n [0, 0, 0, -7, 11, -10],\n [0, 0, 0, 0, -7, 14],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "310", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[0, -3, 2, -6, -1, 0],\n [-3, 8, -6, 14, 5, -4],\n [2, -6, -9, -10, 2, 0],\n [-6, 14, -10, 7, 0, -4],\n [-1, 5, 2, 0, -12, 2],\n [0, -4, 0, -4, 2, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, 2, -4, 4, -2, -2],\n [2, -6, 6, -1, -2, -8],\n [-4, 6, 10, 2, 0, 5],\n [4, -1, 2, -6, 0, 3],\n [-2, -2, 0, 0, 11, 4],\n [-2, -8, 5, 3, 4, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -5, -5, 7, 6, 1],\n [-3, -7, 4, 7, 3, 2],\n [2, 6, 6, 1, 0, -3],\n [5, 14, -12, -12, 13, -8],\n [6, 0, -2, -12, -11, 6],\n [10, 3, 13, -14, -11, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-14, 10, -10, 15, -13, 2],\n [13, -7, 7, 3, -15, -2],\n [-14, 13, 11, 8, 6, 9],\n [-4, 9, 10, -10, -12, -15],\n [14, 7, -2, 14, -9, 11],\n [2, 5, -11, -10, 11, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "765", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[11, -11, 8, -6, 1, -14],\n [0, -15, 6, -2, -10, 14],\n [0, 0, 10, -7, 8, 1],\n [0, 0, 0, -2, -1, -2],\n [0, 0, 0, 0, 3, 8],\n [0, 0, 0, 0, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-15, 5, -7, -7, -7, -5],\n [-2, 4, 13, 14, -14, 9],\n [-12, 12, 12, -1, 4, 8],\n [6, -8, 4, -13, 5, -13],\n [14, 12, -6, 6, -5, 1],\n [-8, -13, 14, 6, -7, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -10, 4, 7, 0, -8],\n [-10, 2, -4, 4, 3, 0],\n [4, -4, 4, 8, -12, -12],\n [7, 4, 8, -7, -10, 0],\n [0, 3, -12, -10, -6, -4],\n [-8, 0, -12, 0, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[1, -13, -4, -11, -11, -10],\n [-11, -7, 11, -5, 6, 11],\n [5, 9, -2, 14, 4, 11],\n [9, 7, 8, -5, -8, 14],\n [13, 1, 7, -7, -8, 8],\n [2, 11, -8, -10, -7, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, 6, 5, -8, -10, -2],\n [6, -10, 4, 0, 0, 4],\n [5, 4, 4, -5, 0, 7],\n [-8, 0, -5, -12, -6, -7],\n [-10, 0, 0, -6, 0, -1],\n [-2, 4, 7, -7, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 9, -9, -8, 7, -15],\n [-9, -10, 9, -15, -15, -3],\n [5, 13, -1, -10, 6, -10],\n [1, -12, -3, -10, -4, 2],\n [7, -11, 3, 8, -3, 1],\n [2, 10, -7, 12, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -11, -10, -9, 11, -2],\n [-5, -8, 10, 12, -11, 7],\n [-13, 9, 10, 9, -13, 15],\n [-13, 12, 10, 14, -14, 15],\n [10, -3, 2, 12, 15, 5],\n [-15, 15, -1, 15, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, 5, 0, 2, 10],\n [0, -7, -8, -10, 12, 0],\n [5, -8, 4, -2, 2, -4],\n [0, -10, -2, 1, 5, -2],\n [2, 12, 2, 5, 6, 6],\n [10, 0, -4, -2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[12, -4, -6, -6, -9, 3],\n [0, 3, -1, -9, 6, 4],\n [0, 0, -6, -3, -2, -8],\n [0, 0, 0, -15, -3, -15],\n [0, 0, 0, 0, 4, -7],\n [0, 0, 0, 0, 0, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, 6, 3, 13, -5, 2],\n [0, -3, -2, -10, -11, -8],\n [0, 0, -12, -14, -8, -5],\n [0, 0, 0, 4, -14, 4],\n [0, 0, 0, 0, 11, 2],\n [0, 0, 0, 0, 0, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-13, -15, -11, -11, 7, -13],\n [-11, -3, -7, -11, -10, 0],\n [4, 15, 7, -4, 12, 5],\n [-12, 11, 0, 15, 8, 4],\n [8, -7, 3, -2, 5, 8],\n [1, -3, -1, 7, -6, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -10, -13, 3, -4, 5],\n [0, 8, -13, 14, -6, 1],\n [0, 0, 12, -3, -3, 0],\n [0, 0, 0, 2, -2, -15],\n [0, 0, 0, 0, 15, -10],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[13, -13, -7, -3, -10, 10],\n [0, 11, -10, -11, -10, -1],\n [0, 0, 9, -15, -9, 3],\n [0, 0, 0, -14, 9, 0],\n [0, 0, 0, 0, -11, -12],\n [0, 0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "406", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -8, 11, 0, 7, -3],\n [-6, 7, -2, 10, 8, -1],\n [-14, 7, 3, 6, 8, 7],\n [-1, 9, -13, 8, 11, 12],\n [-5, -6, 1, -8, -11, 3],\n [-3, 8, 15, -1, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, 5, -4, 2, 0, 0],\n [13, -10, -5, -3, 12, -11],\n [-8, -1, 2, 15, 5, 0],\n [8, 0, 9, -8, -1, 4],\n [-1, -10, 0, 1, -5, -15],\n [3, 1, -2, -8, -6, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "588", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, 4, 4, -14, -14, -10],\n [-4, 12, 5, -10, -9, 7],\n [1, -7, -8, 11, -8, 4],\n [1, 6, 7, 9, -3, 13],\n [15, 2, -2, 5, -12, 0],\n [-11, -6, 5, 15, 14, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[13, -1, -5, 12, 6, 9],\n [7, 7, 14, -13, -15, 0],\n [3, 7, -9, 13, -14, 2],\n [-11, 0, -6, 8, 7, -4],\n [6, -8, -4, -3, -4, -11],\n [13, -14, -13, 6, -12, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "568", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -12, -5, 6, 11, 12],\n [-12, 10, 2, -2, -6, -9],\n [-5, 2, 1, 5, -3, -9],\n [6, -2, 5, 6, -4, -6],\n [11, -6, -3, -4, 1, -1],\n [12, -9, -9, -6, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, 4, 12, -6, 2, 6],\n [4, 2, -2, -2, 14, 0],\n [12, -2, 6, 4, 2, -1],\n [-6, -2, 4, -15, 4, 12],\n [2, 14, 2, 4, -7, -9],\n [6, 0, -1, 12, -9, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[10, -5, 2, 6, -12, -14],\n [-5, -6, -1, 2, 0, 6],\n [2, -1, -2, -8, 4, 11],\n [6, 2, -8, 5, 2, 8],\n [-12, 0, 4, 2, 14, -2],\n [-14, 6, 11, 8, -2, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -4, 5, 11, -5, 0],\n [-14, -11, -10, -5, 1, -5],\n [0, -9, -13, 6, 12, -8],\n [-10, -13, 4, 13, -12, -2],\n [-5, -1, 3, -12, -1, -14],\n [-10, 3, -2, -4, -6, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, 3, 12, -11, -5, -12],\n [14, 12, 1, 10, 1, -7],\n [-11, 14, 10, 3, -3, -4],\n [1, 2, -14, 0, 5, -11],\n [-15, -1, -14, 4, -2, 6],\n [-3, 15, 15, -4, 6, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 3, 4, -10, 0, -2],\n [3, -2, 2, 0, -9, 4],\n [4, 2, -14, 8, 7, 4],\n [-10, 0, 8, 5, 13, -8],\n [0, -9, 7, 13, 3, 3],\n [-2, 4, 4, -8, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "414", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-9, 2, -10, 2, -3, -4],\n [2, 12, 5, 2, -2, 4],\n [-10, 5, 13, 7, 0, -2],\n [2, 2, 7, -4, 12, 10],\n [-3, -2, 0, 12, 9, -2],\n [-4, 4, -2, 10, -2, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, -6, 3, 4, 6, 1],\n [-6, 3, 2, -12, 2, -8],\n [3, 2, 11, -3, 4, 0],\n [4, -12, -3, 8, 1, -5],\n [6, 2, 4, 1, 11, -4],\n [1, -8, 0, -5, -4, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, -3, 0, 11, -6, -4],\n [-3, -4, 6, 4, -2, 4],\n [0, 6, -9, 2, 0, -1],\n [11, 4, 2, 5, 8, -3],\n [-6, -2, 0, 8, -8, 4],\n [-4, 4, -1, -3, 4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "996", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, 11, -2, 6, -10, -7],\n [0, 3, 0, -8, 10, 2],\n [0, 0, -11, 14, -12, 0],\n [0, 0, 0, 12, -6, -15],\n [0, 0, 0, 0, 4, 5],\n [0, 0, 0, 0, 0, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 6, 5, 2, -5, 2],\n [6, 8, -5, -3, 8, 10],\n [5, -5, 3, -4, -7, 7],\n [2, -3, -4, -2, -4, 9],\n [-5, 8, -7, -4, 0, 5],\n [2, 10, 7, 9, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-2, 2, 6, 0, -14, -8],\n [-14, 7, 15, -7, -15, -15],\n [15, 6, -14, -1, -12, -12],\n [11, 1, 1, 2, -8, -8],\n [4, 11, 6, 8, -12, -2],\n [-1, -9, 14, -8, 15, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[13, -10, 14, -6, 1, 14],\n [0, 15, 5, 5, -4, 6],\n [-3, 11, -9, 7, 8, 4],\n [12, 4, -7, -6, 1, 2],\n [7, 7, 6, -10, 1, 15],\n [6, 10, 11, 14, -14, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, -8, -14, -11, -14, 6],\n [-7, 1, -15, -11, -11, 13],\n [12, 0, 11, 9, 7, -10],\n [8, -5, 11, -13, 1, 10],\n [-2, 6, 10, -12, 6, 12],\n [-14, 0, 15, 2, -7, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, 10, -12, -3, -2, -8],\n [10, -13, 1, -2, 4, 8],\n [-12, 1, -9, 4, -4, 6],\n [-3, -2, 4, 10, 3, 12],\n [-2, 4, -4, 3, -2, -2],\n [-8, 8, 6, 12, -2, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[0, 4, 10, 1, -6, 5],\n [0, 0, -2, 10, -7, 1],\n [-7, 3, -4, -7, 2, -14],\n [-11, -14, 6, -14, -14, 3],\n [9, 5, 12, 11, -3, -4],\n [4, -3, 14, -3, 9, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-8, 5, 7, 5, 13, -1],\n [5, 3, 9, 4, 7, 15],\n [8, 0, -7, -11, -9, 7],\n [-2, 4, 1, -9, 1, -6],\n [-8, -10, 12, 11, 6, -14],\n [9, 4, 4, -7, 3, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -15, -12, -2, -5, -2],\n [-9, -1, -4, 6, 6, -3],\n [5, -9, -13, -11, 15, 8],\n [1, -6, -15, 14, -5, -14],\n [15, 10, -12, -9, -5, -3],\n [11, 14, 11, -2, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "698", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[0, 11, -8, -8, 10, 3],\n [11, 4, 0, -6, 0, -3],\n [-8, 0, 0, -14, 12, -6],\n [-8, -6, -14, 6, 4, 6],\n [10, 0, 12, 4, 9, 0],\n [3, -3, -6, 6, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -9, 3, 3, -13, 2],\n [0, 13, 3, 15, -3, -11],\n [0, 0, 7, 3, 2, 4],\n [0, 0, 0, 14, 7, 0],\n [0, 0, 0, 0, -3, 15],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -10, 1, 8, -7, 6],\n [-10, 8, 4, 10, 6, 11],\n [1, 4, 14, 3, -8, -2],\n [8, 10, 3, -6, -2, -2],\n [-7, 6, -8, -2, 14, -1],\n [6, 11, -2, -2, -1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[4, 12, -14, -3, -1, -7],\n [-10, -15, 14, -15, -8, 2],\n [13, 15, 9, 9, -1, -7],\n [13, 0, 14, -10, -6, 11],\n [6, 0, -3, -12, -4, -6],\n [-6, 6, -11, 3, 15, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "938", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -1, -2, 4, 2, 0],\n [-1, 9, -1, 1, 3, 2],\n [-2, -1, -9, 4, 12, 8],\n [4, 1, 4, -14, 8, 6],\n [2, 3, 12, 8, 10, -2],\n [0, 2, 8, 6, -2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -5, 2, 0, -5, -1],\n [-5, -4, 6, -2, -1, -10],\n [2, 6, 9, -10, 0, 1],\n [0, -2, -10, 6, 4, 8],\n [-5, -1, 0, 4, 9, -6],\n [-1, -10, 1, 8, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[5, -8, -1, -10, -3, -2],\n [-8, 1, 6, 8, -2, 5],\n [-1, 6, 0, 8, -4, 0],\n [-10, 8, 8, -11, -3, -5],\n [-3, -2, -4, -3, -9, 7],\n [-2, 5, 0, -5, 7, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "926", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, -11, 1, 2, -4],\n [2, 5, 0, 10, 0, -4],\n [-11, 0, 2, 6, -8, -2],\n [1, 10, 6, 6, 2, 10],\n [2, 0, -8, 2, 6, -11],\n [-4, -4, -2, 10, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "916", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 2, 9, -6, 6, 6],\n [2, -7, -3, 0, -4, 4],\n [9, -3, 9, -2, -3, -2],\n [-6, 0, -2, -9, 2, -2],\n [6, -4, -3, 2, -9, -3],\n [6, 4, -2, -2, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "413", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 2, -1, 13, -6, -6],\n [2, 9, -9, -10, 3, 12],\n [-1, -9, 7, 0, 2, 1],\n [13, -10, 0, 14, 8, -8],\n [-6, 3, 2, 8, 7, -2],\n [-6, 12, 1, -8, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "968", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[8, -1, 2, 2, -10, 6],\n [13, 6, 6, -1, 15, -8],\n [2, -12, -13, 15, 2, 15],\n [-5, -11, -9, -11, 4, 10],\n [-10, -4, -10, 11, 3, -1],\n [-10, 15, 14, -3, 8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, -9, 4, -9, 2, 4],\n [5, -11, -15, -9, -2, -14],\n [8, -2, 1, -9, -13, 5],\n [-14, 4, -6, -13, 7, 4],\n [14, -10, -7, 0, 11, -1],\n [8, 15, -7, -7, -3, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "619", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -15, -9, 2, 7, 9],\n [-3, -8, -5, 1, -6, 6],\n [-12, -11, 0, 4, 10, 2],\n [10, 2, 14, 8, -11, 14],\n [5, 9, 13, 9, 0, -7],\n [-13, -10, 9, 9, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "764", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, -11, 4, 8, 6, 0],\n [-14, -14, 4, -12, -14, 6],\n [-8, -14, -1, -6, -8, 4],\n [8, 14, -3, -15, 13, -15],\n [10, 0, -12, -14, 8, -11],\n [-10, 9, 7, 15, 11, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 0, -2, 12, 1, -1],\n [0, 3, 9, -4, -2, -6],\n [-2, 9, -14, 0, 5, -12],\n [12, -4, 0, -8, -8, -1],\n [1, -2, 5, -8, -7, 2],\n [-1, -6, -12, -1, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, -2, 13, -12, 3, 4],\n [0, 7, -9, -1, -2, -3],\n [0, 0, -1, 0, -9, 7],\n [0, 0, 0, -6, 0, -4],\n [0, 0, 0, 0, 14, 10],\n [0, 0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "812", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[10, 7, -2, -1, 2, -1],\n [7, 14, 3, 8, 0, 2],\n [-2, 3, -10, 2, 10, 0],\n [-1, 8, 2, -10, -2, -12],\n [2, 0, 10, -2, -7, -2],\n [-1, 2, 0, -12, -2, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 4, -2, 5, -8, 3],\n [-3, 10, -7, -12, 6, 2],\n [15, 14, 8, -5, 3, -5],\n [-1, 12, 3, 5, 15, 1],\n [-12, -15, -3, 7, -1, -7],\n [-12, 13, 0, -3, -10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "700", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, 2, -6, -4, -14, -6],\n [6, 1, -13, 9, 9, 12],\n [9, -14, 6, -8, -2, -6],\n [2, -8, -13, 6, -12, -14],\n [-4, -11, 10, 6, -9, 10],\n [9, 6, 5, 8, 2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 6, 7, 13, 11, 8],\n [3, 15, 14, 5, -3, 11],\n [10, 12, 0, -3, 9, -13],\n [4, -4, -4, -2, -13, 4],\n [-10, -12, 7, -11, -4, 12],\n [10, 10, 13, 11, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "663", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-7, -7, 13, -14, -5, 7],\n [0, 6, 2, -6, 1, 4],\n [0, 0, 15, 5, -1, -15],\n [0, 0, 0, -2, -3, -6],\n [0, 0, 0, 0, -11, -15],\n [0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[15, -13, -1, -14, -14, -5],\n [0, -1, 5, -9, -3, 0],\n [0, 0, -7, -6, 8, -7],\n [0, 0, 0, -5, 14, -14],\n [0, 0, 0, 0, -13, 7],\n [0, 0, 0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-2, -9, -8, -13, 11, 4],\n [-12, -14, -10, 10, -15, 5],\n [8, 5, 4, -5, -9, -14],\n [-1, -15, -2, -9, -2, -13],\n [0, 12, 8, 1, 10, 15],\n [0, -14, 5, -14, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-6, -1, 9, -1, 15, 3],\n [-7, 3, -11, -13, 10, 4],\n [-12, 10, -5, -9, -11, 4],\n [6, 10, 11, 3, 7, -11],\n [3, -13, -4, 3, -3, -12],\n [7, -15, 5, 7, 4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 10, 2, 6, -9],\n [9, 9, 10, 5, -14, 7],\n [0, 11, -3, -3, 9, -6],\n [-15, 14, 1, 9, 2, 0],\n [3, 0, 2, 5, 1, 0],\n [11, -6, 8, 12, 8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[0, -6, 9, -10, -7, -5],\n [4, -1, -12, -12, 4, -4],\n [-5, 2, -11, -15, 2, 5],\n [9, -13, 7, -3, -4, 0],\n [-7, 12, -1, -8, -6, 3],\n [15, 15, -4, -12, 0, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "731", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-12, 2, 14, 12, 15, -2],\n [0, 3, -2, 3, -12, -15],\n [0, 0, 4, 6, -5, 3],\n [0, 0, 0, 12, -14, 12],\n [0, 0, 0, 0, -13, -15],\n [0, 0, 0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, -2, 0, -2, -10, -8],\n [-2, -2, -3, 8, -6, 3],\n [0, -3, -4, -10, -1, 4],\n [-2, 8, -10, 1, -4, 2],\n [-10, -6, -1, -4, -12, -12],\n [-8, 3, 4, 2, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "791", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[14, -4, 9, -9, 0, -9],\n [13, -4, -15, -5, 11, 13],\n [-15, 0, 9, 11, 1, -14],\n [-2, -11, -15, -2, -6, -8],\n [-3, -14, 14, -11, 13, -11],\n [2, 0, -1, 1, 6, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, -9, 1, -13, 10, 1],\n [0, -14, 0, 7, 9, 4],\n [0, 0, 1, 2, -9, -7],\n [0, 0, 0, 9, 7, 0],\n [0, 0, 0, 0, 1, 3],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-13, 8, 5, -5, -13, -8],\n [10, 6, 0, -4, 0, -3],\n [-3, -11, -1, 7, -9, -5],\n [-5, -15, -5, 11, 6, 5],\n [-6, -4, -8, -15, -10, 13],\n [-14, -2, 2, 3, -5, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -4, 12, 0, -11, -7],\n [0, 2, 1, -10, -11, 3],\n [0, 0, -13, 13, -12, 0],\n [0, 0, 0, 10, 4, 0],\n [0, 0, 0, 0, 1, -1],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "880", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 12, -6, -1, -12, 10],\n [0, 9, 6, -14, 8, 0],\n [0, 0, -2, 0, 9, 11],\n [0, 0, 0, -7, 8, 10],\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": "32", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[0, 8, -2, -4, -4, -2],\n [8, -4, -5, 7, -4, -2],\n [-2, -5, 9, -4, -4, -2],\n [-4, 7, -4, -10, -14, 4],\n [-4, -4, -4, -14, -8, 2],\n [-2, -2, -2, 4, 2, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[6, 8, 5, -4, -12, -10],\n [-3, -9, 5, 5, 15, 4],\n [12, -7, 11, -8, 14, 8],\n [-2, 3, -12, -6, -5, -14],\n [-1, 4, -1, 3, -10, -10],\n [-2, 11, 3, -12, 9, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, 8, 2, -6, -6, -2],\n [8, -9, -3, -8, 6, 0],\n [2, -3, 8, -12, 4, -6],\n [-6, -8, -12, -8, 8, -1],\n [-6, 6, 4, 8, -15, 4],\n [-2, 0, -6, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "883", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[9, -15, -7, -4, 10, 7],\n [0, -14, -6, 12, 6, 12],\n [0, 0, 4, -12, 11, 6],\n [0, 0, 0, -10, -11, 2],\n [0, 0, 0, 0, 6, 12],\n [0, 0, 0, 0, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, -2, -4, 1, -14],\n [-10, 1, -9, -10, 0, 15],\n [11, -13, -10, 7, 6, -6],\n [-1, 3, -13, 9, -1, 7],\n [11, 2, -4, -11, 7, -8],\n [5, 1, 13, -5, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-4, -14, -6, -9, 5, 2],\n [0, 5, 3, 6, -12, 6],\n [0, 0, -13, 4, -11, -5],\n [0, 0, 0, -14, 10, 7],\n [0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[11, -1, 12, 5, -1, -10],\n [8, 13, 2, -15, 8, 5],\n [7, 5, 8, 1, -3, -8],\n [12, -14, 9, -13, 5, -12],\n [2, 15, -1, 5, -13, -15],\n [9, -10, -1, 4, -1, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-10, -15, 2, 5, -4, 1],\n [0, -13, 9, 7, -8, 14],\n [0, 0, 15, -11, -15, -1],\n [0, 0, 0, -3, -3, -10],\n [0, 0, 0, 0, -4, 0],\n [0, 0, 0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-8, -3, 15, -14, -2, 15],\n [0, -4, -5, 0, 9, -10],\n [0, 0, -10, -8, -4, 9],\n [0, 0, 0, -4, 9, 10],\n [0, 0, 0, 0, -8, -2],\n [0, 0, 0, 0, 0, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[8, -3, 8, -3, 11, -11],\n [-5, 0, 13, -7, 12, -5],\n [-8, 14, 8, 5, 10, -14],\n [-14, 5, 0, 7, -14, 10],\n [-4, -9, 3, 11, -2, -9],\n [5, -12, 6, 3, -13, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, -3, -4, 2, -5],\n [0, 9, 0, -4, 0, -2],\n [-3, 0, -6, 1, -7, 8],\n [-4, -4, 1, 5, -4, -2],\n [2, 0, -7, -4, 2, -3],\n [-5, -2, 8, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[10, -6, -3, -11, 10, -1],\n [0, -3, 0, 2, 11, 9],\n [0, 0, -3, -13, -6, -3],\n [0, 0, 0, -4, 3, 4],\n [0, 0, 0, 0, -4, 10],\n [0, 0, 0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-3, 1, 5, 2, 4, 6],\n [1, 6, -2, 3, 0, -8],\n [5, -2, -6, -4, -6, -8],\n [2, 3, -4, 4, -12, -2],\n [4, 0, -6, -12, 9, -4],\n [6, -8, -8, -2, -4, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 15, 10, -9, 12, -6],\n [0, 10, 4, -6, -8, 0],\n [0, 0, -5, -1, -2, 7],\n [0, 0, 0, -15, 5, -9],\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": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -4, 14, -4, -7, 3],\n [-4, -11, 2, -8, 3, -6],\n [14, 2, -7, 6, -5, 4],\n [-4, -8, 6, 2, -9, 4],\n [-7, 3, -5, -9, 7, 13],\n [3, -6, 4, 4, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "575", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 4, 5, 2, 0, -10],\n [4, -3, 7, -14, -2, -4],\n [5, 7, -1, 5, -5, 10],\n [2, -14, 5, 3, -3, -8],\n [0, -2, -5, -3, -1, -4],\n [-10, -4, 10, -8, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -9, 11, 13, -10, 3],\n [0, 7, -11, -2, 7, -15],\n [0, 0, 9, 6, 10, 8],\n [0, 0, 0, -4, -3, 1],\n [0, 0, 0, 0, -13, 10],\n [0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "792", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-5, -11, 8, 1, 4, 5],\n [0, -6, -4, 3, 4, -9],\n [0, 0, -2, -8, -12, -9],\n [0, 0, 0, 10, -6, 15],\n [0, 0, 0, 0, 2, 8],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 14, -14, 1, 2, 9],\n [1, -9, 5, 3, 2, -4],\n [7, 8, -9, -9, -13, 12],\n [-7, 5, 0, 3, 15, -13],\n [1, -10, 12, -9, -4, 0],\n [-3, -12, 15, -12, -5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "Determine the value of det(A) where A =\n[[-1, 0, 4, 5, -2, 0],\n [0, -9, -3, 6, 6, 12],\n [4, -3, -14, -10, 0, 1],\n [5, 6, -10, -12, -10, -3],\n [-2, 6, 0, -10, -9, 2],\n [0, 12, 1, -3, 2, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "443", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 2, -12, -10, -3, -11],\n [2, 4, 2, -1, 2, -5],\n [-12, 2, -3, 2, 2, -10],\n [-10, -1, 2, 10, 6, 0],\n [-3, 2, 2, 6, 7, -8],\n [-11, -5, -10, 0, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "617", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, -12, -2, -15, 3, 0],\n [0, 12, -6, 11, -12, -7],\n [0, 0, 8, -12, 7, -2],\n [0, 0, 0, 2, 9, 4],\n [0, 0, 0, 0, -1, 9],\n [0, 0, 0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-5, -2, 5, 5, -14, 12],\n [0, 8, -4, -15, -15, 4],\n [0, 0, 8, -15, 2, 0],\n [0, 0, 0, 15, -5, 15],\n [0, 0, 0, 0, 9, 11],\n [0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 13, -10, -15, -13, -15],\n [0, 12, -12, -5, 4, 0],\n [0, 0, 4, 5, -13, -2],\n [0, 0, 0, 1, 10, 13],\n [0, 0, 0, 0, -8, -15],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -1, 0, -1, 1, 4],\n [-4, -5, 7, -6, -11, -6],\n [-14, -5, 10, 9, -7, 13],\n [1, 1, 7, 14, -1, 6],\n [-10, 6, -9, 11, -2, 8],\n [-11, 2, 0, 13, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-1, -13, -6, 11, -11, -2],\n [0, -11, -11, -3, -6, -4],\n [0, 0, -10, -8, 12, -10],\n [0, 0, 0, 7, 10, 15],\n [0, 0, 0, 0, -5, 4],\n [0, 0, 0, 0, 0, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-7, 3, -5, -6, 10, -11],\n [-7, 9, 14, -13, 13, -2],\n [5, 7, 9, -2, 5, -1],\n [-4, 15, 12, 14, 13, 2],\n [-3, 4, 5, 2, 5, 6],\n [-8, -10, -5, 5, 2, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 15, -5, -4, -6, -1],\n [0, -2, -13, 12, -3, -5],\n [15, 9, 11, -4, 14, 10],\n [-15, -15, -7, -10, -7, 10],\n [-11, -14, 5, -13, 13, 2],\n [14, 9, -1, -2, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -8, -8, 0, -5, 10],\n [14, -8, -8, 3, 5, 10],\n [11, -12, 9, -3, 15, -6],\n [5, 1, 12, 12, 2, -14],\n [5, 12, 9, -10, 0, -5],\n [-5, 11, -7, 3, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "983", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-13, 2, -6, -6, -7, -2],\n [2, 2, -2, 3, 2, 3],\n [-6, -2, 3, 2, 8, 4],\n [-6, 3, 2, 3, 2, 3],\n [-7, 2, 8, 2, -7, -3],\n [-2, 3, 4, 3, -3, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[12, -14, 6, 7, 14, 3],\n [0, -4, 8, -11, 10, 0],\n [0, 0, 6, 14, -7, -2],\n [0, 0, 0, -4, -8, -7],\n [0, 0, 0, 0, -1, 0],\n [0, 0, 0, 0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, -4, 10, -12, 14, 9],\n [0, 15, -8, 6, -12, 9],\n [0, 0, 6, -2, 13, -6],\n [0, 0, 0, -5, -1, 9],\n [0, 0, 0, 0, 13, 8],\n [0, 0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 8, 4, -2, -8, -12],\n [8, 8, -2, -7, 10, -4],\n [4, -2, -8, 0, -6, 4],\n [-2, -7, 0, -6, 12, -2],\n [-8, 10, -6, 12, 7, 6],\n [-12, -4, 4, -2, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 14, -12, -6, 2, -5],\n [0, -8, -11, -3, 11, -11],\n [0, 0, 4, -5, 3, 2],\n [0, 0, 0, -4, -12, 10],\n [0, 0, 0, 0, -10, 9],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[-9, 7, 4, 0, -2, -12],\n [7, -3, -14, -4, -8, 11],\n [4, -14, -3, -5, 4, 3],\n [0, -4, -5, 1, 0, -7],\n [-2, -8, 4, 0, 9, -2],\n [-12, 11, 3, -7, -2, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[4, -14, 11, -7, 12, -12],\n [-11, 10, 15, -5, -12, 4],\n [-1, 11, 0, -15, 11, -13],\n [11, -4, -14, -15, 7, 14],\n [-11, 4, 7, -2, -3, 8],\n [5, 9, -11, -12, 5, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336", "dataset": "MATH"}
{"messages": [{"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 12, -12, -1, -2, 4],\n [12, 0, -6, 3, 6, -6],\n [-12, -6, -15, 4, 12, 2],\n [-1, 3, 4, -1, 11, -10],\n [-2, 6, 12, 11, -10, 5],\n [4, -6, 2, -10, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "459", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[2, 6, 5, 0, -3, -2],\n [6, -12, 8, -4, -2, -2],\n [5, 8, -11, -8, 2, 0],\n [0, -4, -8, 10, -8, 2],\n [-3, -2, 2, -8, -7, -2],\n [-2, -2, 0, 2, -2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[-6, 4, -6, -4, -2, 8],\n [4, 1, 0, 0, 3, -6],\n [-6, 0, 5, 6, 3, -6],\n [-4, 0, 6, -2, -3, 7],\n [-2, 3, 3, -3, 10, 2],\n [8, -6, -6, 7, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Compute |A| for the matrix A =\n[[10, -2, -4, 4, 3, 1],\n [-2, -7, -4, -3, -4, 2],\n [-4, -4, 0, -8, -3, 2],\n [4, -3, -8, 4, 5, -4],\n [3, -4, -3, 5, 0, 3],\n [1, 2, 2, -4, 3, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867", "dataset": "MATH"}
{"messages": [{"content": "What is the determinant of the matrix:\n[[7, 3, 6, 14, -4, 3],\n [10, -1, 11, -1, 15, 3],\n [-12, -2, 6, -10, 12, -5],\n [-11, 0, 3, -10, 3, -2],\n [-7, 11, -9, -15, 2, -1],\n [-3, -12, -15, 4, 12, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607", "dataset": "MATH"}