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[ { "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 ...
96
MATH
[ { "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: \\...
51
MATH
[ { "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{You...
584
MATH
[ { "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: \\boxe...
664
MATH
[ { "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: \\bo...
320
MATH
[ { "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: \\bo...
192
MATH
[ { "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 forma...
690
MATH
[ { "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: \\bo...
888
MATH
[ { "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 answ...
400
MATH
[ { "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 form...
760
MATH
[ { "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...
832
MATH
[ { "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...
52
MATH
[ { "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 form...
443
MATH
[ { "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: \\...
241
MATH
[ { "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 LaTe...
623
MATH
[ { "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...
280
MATH
[ { "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{You...
712
MATH
[ { "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{Yo...
500
MATH
[ { "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 forma...
626
MATH
[ { "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 form...
376
MATH
[ { "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: \...
872
MATH
[ { "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 form...
400
MATH
[ { "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: \\...
4
MATH
[ { "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 ...
600
MATH
[ { "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 an...
267
MATH
[ { "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...
490
MATH
[ { "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: ...
616
MATH
[ { "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: \\...
200
MATH
[ { "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:...
850
MATH
[ { "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 forma...
442
MATH
[ { "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 ans...
806
MATH
[ { "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: \\...
686
MATH
[ { "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: ...
372
MATH
[ { "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 f...
464
MATH
[ { "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...
768
MATH
[ { "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 ...
490
MATH
[ { "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 form...
224
MATH
[ { "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: \\boxe...
640
MATH
[ { "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 forma...
530
MATH
[ { "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: \\b...
774
MATH
[ { "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 ...
0
MATH
[ { "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 fo...
622
MATH
[ { "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 ans...
700
MATH
[ { "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 LaTe...
738
MATH
[ { "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...
752
MATH
[ { "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 LaTe...
664
MATH
[ { "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...
329
MATH
[ { "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: \\boxe...
736
MATH
[ { "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...
493
MATH
[ { "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 an...
80
MATH
[ { "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: \...
500
MATH
[ { "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 a...
825
MATH
[ { "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 answe...
136
MATH
[ { "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 f...
867
MATH
[ { "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 for...
850
MATH
[ { "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...
161
MATH
[ { "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 ...
950
MATH
[ { "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: ...
850
MATH
[ { "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{...
800
MATH
[ { "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 f...
200
MATH
[ { "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 answe...
838
MATH
[ { "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...
288
MATH
[ { "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 forma...
994
MATH
[ { "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:...
32
MATH
[ { "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 ans...
345
MATH
[ { "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 i...
573
MATH
[ { "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}", ...
496
MATH
[ { "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: \\b...
848
MATH
[ { "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 ...
120
MATH
[ { "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: \...
120
MATH
[ { "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 form...
669
MATH
[ { "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 forma...
914
MATH
[ { "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: \\boxe...
11
MATH
[ { "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: \\...
10
MATH
[ { "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...
236
MATH
[ { "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 L...
356
MATH
[ { "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 f...
246
MATH
[ { "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 a...
480
MATH
[ { "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 ...
200
MATH
[ { "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 L...
950
MATH
[ { "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...
793
MATH
[ { "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 L...
8
MATH
[ { "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...
158
MATH
[ { "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...
900
MATH
[ { "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 i...
66
MATH
[ { "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 form...
420
MATH
[ { "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...
592
MATH
[ { "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 LaTe...
724
MATH
[ { "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 LaT...
800
MATH
[ { "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 forma...
260
MATH
[ { "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: \\box...
230
MATH
[ { "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 answ...
98
MATH
[ { "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 f...
290
MATH
[ { "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 L...
128
MATH
[ { "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 ans...
860
MATH
[ { "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 f...
164
MATH
[ { "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: \\box...
200
MATH
[ { "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 i...
509
MATH
[ { "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 f...
388
MATH
[ { "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{You...
544
MATH