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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, 10, -6],\n [-8, -12, -5, 9],\n [-9, 1, -11, -11],\n [10, -10, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 1, -12, -3],\n [0, 12, 8, -11],\n [0, 0, -4, -1],\n [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" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 11, 10, 1],\n [3, 2, -2, 2],\n [-6, -8, -12, 11],\n [0, 11, -12, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
284
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 7, 6, -10],\n [-11, 0, 4, 3],\n [7, 9, 11, -9],\n [-1, -11, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 4, -6, 6],\n [4, 10, 3, 4],\n [-6, 3, -1, 3],\n [6, 4, 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" } ]
371
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -8, -10, 9],\n [0, 10, -4, 0],\n [0, 0, -11, 0],\n [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" } ]
520
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -5, 8, 6],\n [-2, 2, 3, 1],\n [-8, 1, -10, 11],\n [-10, 9, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 2, -8, -2],\n [0, 7, -6, 3],\n [0, 0, -6, 12],\n [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" } ]
706
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 12, -1, 11],\n [-12, -5, 11, -11],\n [7, 8, -2, 1],\n [-6, -1, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
444
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 11, 9, -12],\n [0, 9, -7, 2],\n [0, 0, -8, 11],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
576
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 12, -9, -4],\n [0, -5, -9, 10],\n [0, 0, -4, 7],\n [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" } ]
780
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, -1, -11, 4],\n [0, 5, 4, 8],\n [0, 0, -12, 0],\n [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" } ]
920
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -10, 10, 6],\n [3, 9, -8, 9],\n [2, 2, -6, -10],\n [-5, 0, 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" } ]
872
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 9, 2, 8],\n [9, -11, 0, 8],\n [2, 0, -12, 4],\n [8, 8, 4, 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" } ]
144
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -12, 10, 7],\n [-8, 7, -4, 12],\n [5, 11, -12, -4],\n [-2, -3, -7, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 6, 4, -12],\n [10, 1, -6, 2],\n [-1, 5, -10, -10],\n [4, 0, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
752
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 2, 2, 7],\n [6, 1, -12, -3],\n [-11, -3, -8, 10],\n [8, -2, 6, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
444
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -9, -11, -3],\n [0, 9, -7, 4],\n [0, 0, -6, -5],\n [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" } ]
840
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 6, 11, 8],\n [6, 12, 11, -4],\n [11, 11, 7, -2],\n [8, -4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
770
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 7, -12, -12],\n [0, -5, -11, 9],\n [0, 0, 4, 3],\n [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" } ]
480
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -9, 10, 10],\n [0, -4, 11, -6],\n [0, 0, 4, 10],\n [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" } ]
96
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 6, 11, -6],\n [6, 2, 2, -7],\n [11, 2, 5, -12],\n [-6, -7, -12, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
94
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 3, 5, 6],\n [0, 6, -11, 1],\n [0, 0, 2, -2],\n [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" } ]
76
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 6, 3, -5],\n [6, -5, 0, -2],\n [3, 0, -4, -3],\n [-5, -2, -3, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
822
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -4, -11, 4],\n [8, -3, -8, 6],\n [11, -10, -12, -10],\n [11, -8, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
77
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -6, -1, 10],\n [-7, -8, -12, 3],\n [0, -4, 6, 1],\n [3, 7, -1, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
689
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 7, -4, 4],\n [7, 3, -2, 6],\n [-4, -2, 6, 4],\n [4, 6, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -4, 9, -11],\n [-6, -4, -3, 10],\n [-2, -1, 6, 0],\n [-6, -10, -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" } ]
341
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -9, -7, 9],\n [0, -6, 6, 2],\n [0, 0, 5, -1],\n [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" } ]
300
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -11, -8, -1],\n [5, 5, -6, -4],\n [4, 4, -2, 7],\n [3, 2, 8, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 2, 0, -6],\n [-1, 4, 0, 3],\n [3, 0, 1, 5],\n [10, 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" } ]
76
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 4, -8, 1],\n [4, 10, 6, 0],\n [-8, 6, 11, -6],\n [1, 0, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
864
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -6, 0, -2],\n [-6, -12, 8, -3],\n [0, 8, 5, -8],\n [-2, -3, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
347
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 1, -7, -6],\n [-6, -2, 12, -8],\n [1, 12, 4, 7],\n [4, 11, 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" } ]
838
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 7, -7, -11],\n [0, 2, -1, 9],\n [0, 0, -1, -11],\n [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" } ]
24
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 5, 0, -3],\n [0, -12, -7, 8],\n [0, 7, 2, 8],\n [11, -3, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
433
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, 6, 0],\n [2, -12, 2, 6],\n [6, 2, -12, 0],\n [0, 6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 11, 0, -11],\n [0, 4, 4, 4],\n [0, 0, 1, 12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
692
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -6, -2, -6],\n [-6, -3, -4, 0],\n [-2, -4, -1, 4],\n [-6, 0, 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" } ]
650
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -12, -10, -5],\n [0, -5, -6, -1],\n [0, 0, -10, -6],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
750
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 9, 7, -10],\n [-9, 9, -10, -3],\n [0, -6, 4, -9],\n [-4, 10, -11, 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" } ]
395
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, 0, 2],\n [0, 2, 3, -11],\n [0, 0, -4, 6],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -10, 12, 11],\n [0, -6, 4, -5],\n [0, 0, -6, 1],\n [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" } ]
756
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 1, -2, 4],\n [1, -3, 6, -4],\n [-2, 6, 6, -8],\n [4, -4, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -12, 11, 7],\n [0, -12, 7, -1],\n [0, 0, -3, -11],\n [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" } ]
712
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 9, -3, 0],\n [-8, -5, -12, -12],\n [-10, 5, -6, 1],\n [-8, 10, -8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -6, -8, 4],\n [-6, 11, -2, -3],\n [-8, -2, 9, -6],\n [4, -3, -6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 12, -4, 6],\n [12, -11, -12, -4],\n [-4, -12, 2, 0],\n [6, -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" } ]
184
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -1, -1, 3],\n [-1, 1, -10, 8],\n [-3, 8, -1, 4],\n [-11, 9, -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" } ]
610
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 7, 5, 2],\n [0, 11, -9, -5],\n [0, 0, -6, -3],\n [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" } ]
396
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 4, 5, 10],\n [4, 2, 0, -6],\n [5, 0, 12, -6],\n [10, -6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
690
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -2, 9, -5],\n [0, -4, -5, -9],\n [0, 0, 2, -2],\n [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" } ]
392
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -4, 10, 3],\n [-4, -8, 0, -5],\n [10, 0, 1, 6],\n [3, -5, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
772
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -3, -6, 6],\n [-3, -1, -10, 0],\n [-6, -10, 11, -2],\n [6, 0, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
456
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 6, 12],\n [-2, 0, -3, -4],\n [-4, 12, 1, 10],\n [8, -6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
864
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -11, 6, 3],\n [0, 7, 8, 10],\n [0, 0, 4, 11],\n [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" } ]
112
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -5, 10, 5],\n [-5, -7, -2, 4],\n [10, -2, 11, -8],\n [5, 4, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
334
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 0, -4, -3],\n [0, 1, 3, 6],\n [-4, 3, -9, 0],\n [-3, 6, 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" } ]
824
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 1, -6, 10],\n [1, -10, 1, 2],\n [-6, 1, -5, 0],\n [10, 2, 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" } ]
480
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, 12, 3],\n [0, 9, -7, -9],\n [0, 0, 4, 2],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 10, -3, 3],\n [2, 4, 10, 3],\n [1, 11, 10, 2],\n [-5, -6, -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" } ]
752
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 10, 5, 6],\n [0, -8, -4, 4],\n [0, 0, 3, -3],\n [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" } ]
712
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 3, 0, 9],\n [3, -6, 0, -2],\n [0, 0, -4, -8],\n [9, -2, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -9, 5, 11],\n [-9, -8, 9, -8],\n [5, 6, -5, 11],\n [6, -1, 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" } ]
155
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 6, 6, 4],\n [6, 12, 4, -2],\n [6, 4, 0, -3],\n [4, -2, -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" } ]
276
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 0, 4, 2],\n [0, 4, 0, -4],\n [4, 0, -11, -4],\n [2, -4, -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" } ]
368
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, 1, 3],\n [4, 8, -6, 1],\n [1, -6, 2, -8],\n [3, 1, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
621
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -7, 12, 3],\n [0, 7, 1, -1],\n [0, 0, -6, 8],\n [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" } ]
100
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -10, -10, -9],\n [0, 3, -7, 0],\n [0, 0, 10, 1],\n [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" } ]
730
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, 0, -1],\n [-2, -5, 6, -6],\n [0, 6, 8, 10],\n [-1, -6, 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" } ]
780
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 8, 5, -12],\n [0, -7, 8, 8],\n [0, 0, 9, 11],\n [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" } ]
118
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -2, 5, -1],\n [-2, -1, 10, 10],\n [5, 10, 5, -12],\n [-1, 10, -12, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
797
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -11, -12, 5],\n [0, -3, 12, 10],\n [0, 0, 6, -4],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -10, -11, 11],\n [0, 10, 6, -12],\n [0, 0, 1, 5],\n [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" } ]
200
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 4, 10, 0],\n [0, 1, -2, -6],\n [0, 0, -6, 11],\n [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" } ]
48
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 2, 3, 10],\n [0, 2, -7, -4],\n [-8, -3, -8, 2],\n [12, -8, 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" } ]
768
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -10, -4, -2],\n [0, 1, -7, -2],\n [0, 0, -1, 11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -9, -8, 11],\n [0, -7, -4, 1],\n [0, 0, -3, 4],\n [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" } ]
664
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -1, 1, -11],\n [11, 10, -6, -3],\n [-4, -12, 6, -4],\n [3, -4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
580
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 4, -8, 6],\n [0, -9, 11, -5],\n [0, 0, 1, -9],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
838
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 10, -6, -2],\n [10, -8, -4, 0],\n [-6, -4, -3, 8],\n [-2, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -10, 0, -1],\n [-3, -7, 1, -4],\n [3, 7, 9, 3],\n [-7, 1, 5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 12, 0, -10],\n [0, 1, 2, 1],\n [0, 0, -11, 0],\n [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" } ]
548
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -10, 4, -8],\n [-10, 8, 4, -2],\n [4, 4, 8, 8],\n [-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" } ]
936
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -6, 2, 6],\n [-6, -12, -1, -5],\n [2, -1, 6, -8],\n [6, -5, -8, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
844
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 10, -6, 11],\n [0, -12, -7, -12],\n [10, -12, -1, 11],\n [-5, 1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -10, 5, -11],\n [4, 4, 4, -8],\n [9, 6, -6, -8],\n [-9, -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" } ]
20
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -10, -12, 0],\n [0, 6, 10, -4],\n [0, 0, 9, -9],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 0, 4, -5],\n [0, -1, 10, 7],\n [4, 10, 6, -6],\n [-5, 7, -6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
802
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -8, 3, -10],\n [0, -12, -8, 2],\n [0, 0, 2, 1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 12, -4, 12],\n [0, 1, -6, -6],\n [0, 0, 1, 3],\n [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" } ]
901
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -12, 11, -8],\n [0, -2, 0, -8],\n [0, 0, 9, 12],\n [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" } ]
324
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -4, -6, 9],\n [-11, -9, -9, 4],\n [-3, -1, -3, -7],\n [10, -5, -9, 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" } ]
744
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, -5, -4],\n [0, -1, 2, 11],\n [6, 8, 2, 9],\n [3, 3, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
833
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -4, -1, 0],\n [-4, -7, -6, -4],\n [-1, -6, -8, -6],\n [0, -4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
47
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 8, 6, 5],\n [8, 1, -6, -2],\n [6, -6, 11, -8],\n [5, -2, -8, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
793
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 4, -10, -11],\n [-12, -9, 9, 7],\n [11, 0, -7, -3],\n [-9, 4, 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" } ]
20
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -12, 5, 8],\n [-1, -5, -4, -8],\n [2, -1, 2, 5],\n [11, 11, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -3, -5, 12],\n [0, -7, 10, -2],\n [0, 0, -12, -2],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
684
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, -4, 6],\n [4, -4, 9, 11],\n [-3, 6, -7, -10],\n [12, 3, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
859
MATH