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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0],\n [-2, 3, 2],\n [0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
958
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 10, -9],\n [5, 1, -8],\n [6, 10, -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" } ]
924
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 10, -8],\n [0, 8, -2],\n [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" } ]
920
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, 4],\n [-4, -9, -2],\n [4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
404
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -4, -4],\n [0, -9, 9],\n [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" } ]
838
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -8, 3],\n [-8, 4, 0],\n [3, 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" } ]
640
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 4, 6],\n [4, 4, 4],\n [6, 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" } ]
864
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, 5],\n [9, 8, 3],\n [9, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
881
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, -2],\n [3, 5, 9],\n [3, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
382
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, 8],\n [0, -4, -8],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -3, 2],\n [-4, 8, -4],\n [-10, 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" } ]
652
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -7, -5],\n [0, 7, 3],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 1, -2],\n [1, 8, -2],\n [-2, -2, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
328
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -1],\n [0, -7, 0],\n [-1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
154
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -2, 9],\n [3, 4, -7],\n [-6, 5, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
257
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -8, -7],\n [0, -3, -3],\n [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" } ]
730
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -8, 1],\n [6, 4, 2],\n [-3, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
402
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 6, 6],\n [-7, 8, -6],\n [-2, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -5, 4],\n [-5, 6, -1],\n [4, -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" } ]
219
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, -2],\n [6, 9, -8],\n [-2, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
65
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 1, 7],\n [0, -8, 4],\n [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" } ]
256
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 4, -4],\n [4, -4, 1],\n [-4, 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" } ]
168
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -2, 0],\n [-2, 0, 0],\n [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" } ]
980
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -3, 2],\n [-3, 2, 8],\n [2, 8, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
377
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 5, 2],\n [-7, 5, 6],\n [9, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
748
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -6, 10],\n [10, 4, 7],\n [-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" } ]
646
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 4, -6],\n [0, 7, 9],\n [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" } ]
70
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, 6],\n [4, 9, -1],\n [7, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
352
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, -4],\n [6, 10, -4],\n [-4, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
416
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 1, -4],\n [1, -3, 1],\n [-4, 1, -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" } ]
910
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -2, -6],\n [-2, -2, 6],\n [-6, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -8, -2],\n [-8, 1, -2],\n [-2, -2, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
268
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 7],\n [9, -5, 8],\n [-3, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
943
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -9, -3],\n [0, 8, -5],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 7, -9],\n [4, -9, 6],\n [-3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -7, -5],\n [-4, 7, 3],\n [10, -6, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 9, -1],\n [0, -8, -8],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -9, 6],\n [-9, -5, -2],\n [6, -2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 4, 8],\n [4, -2, 4],\n [8, 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" } ]
242
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -4, 10],\n [-4, -10, 2],\n [10, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
904
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -6, -9],\n [-6, 8, 0],\n [-9, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
172
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 5, -8],\n [0, 3, -2],\n [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" } ]
832
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 9, -3],\n [0, -9, 1],\n [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" } ]
838
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -1, 2],\n [0, -7, 1],\n [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" } ]
860
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -8, 0],\n [-8, -2, 0],\n [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" } ]
932
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 10, 6],\n [0, 8, -4],\n [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" } ]
64
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 2, 6],\n [2, -6, -1],\n [6, -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" } ]
706
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 8, 6],\n [0, 4, 5],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -1, 8],\n [-3, -2, -10],\n [-6, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 8, -2],\n [0, 3, -2],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
985
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -5, -6],\n [-5, 5, 9],\n [-6, 9, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
683
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -2, -2],\n [-2, 0, -4],\n [-2, -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" } ]
956
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 3, -10],\n [-1, 4, -4],\n [2, 9, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
881
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -7, -6],\n [-7, 6, 2],\n [-6, 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" } ]
905
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -6, -5],\n [10, 4, 1],\n [1, -10, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
412
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -4, -3],\n [1, 6, -3],\n [5, -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" } ]
347
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -5, -3],\n [4, 8, -10],\n [3, 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" } ]
146
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -3, -5],\n [0, 1, -1],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 2, -6],\n [-9, 7, 1],\n [-8, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
71
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -6, 0],\n [-6, -2, 2],\n [0, 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" } ]
176
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -6, 0],\n [3, 5, 7],\n [-6, -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" } ]
798
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -3, 9],\n [-8, -2, -10],\n [4, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
936
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, 8],\n [0, -4, 2],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 7, 5],\n [8, 6, 3],\n [0, 2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
996
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -9, -6],\n [-7, -5, 0],\n [0, -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" } ]
456
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 3, 7],\n [0, 5, 6],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 5, -9],\n [2, 6, 10],\n [-5, 5, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 10, -6],\n [10, -7, 2],\n [-6, 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" } ]
448
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -1, 6],\n [-1, -9, -8],\n [6, -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" } ]
963
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -3, 2],\n [-3, 1, -4],\n [2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -2, 2],\n [-2, 8, 6],\n [2, 6, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, 6],\n [-7, 3, 1],\n [2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
877
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, -6],\n [0, 8, -2],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
512
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, 6],\n [4, -1, 9],\n [6, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
889
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -3, 8],\n [0, 7, 10],\n [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" } ]
657
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -7, -2],\n [-7, -2, -2],\n [-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" } ]
992
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -9, 4],\n [-9, -9, 5],\n [4, 5, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
163
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -4],\n [-2, 4, 0],\n [-4, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, -7],\n [0, 6, 1],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -4, 1],\n [-4, -1, 0],\n [1, 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" } ]
97
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 2, 5],\n [2, 5, -8],\n [5, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
468
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 6, -9],\n [0, -10, 0],\n [-7, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 10, -8],\n [0, 2, -2],\n [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" } ]
90
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 2, -5],\n [2, -9, 3],\n [-5, 3, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
707
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -2, 7],\n [0, -3, -9],\n [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" } ]
952
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 10, -5],\n [1, -5, -2],\n [3, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 6, 7],\n [0, -1, -5],\n [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" } ]
49
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 3, 4],\n [3, 9, 10],\n [4, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
996
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 5, -4],\n [5, -5, 7],\n [-4, 7, -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" } ]
9
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 0, -2],\n [0, 6, 6],\n [-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" } ]
928
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 0, 1],\n [0, 10, -2],\n [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" } ]
270
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 8, -4],\n [8, -4, 2],\n [-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" } ]
756
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -4, -9],\n [0, 9, 0],\n [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" } ]
216
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, 9],\n [0, -2, 8],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 4, -9],\n [4, 4, -6],\n [-9, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 6, -10],\n [0, -5, 7],\n [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" } ]
910
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 0, 6],\n [-5, 10, -9],\n [-10, 9, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
117
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 0, 1],\n [0, -4, 0],\n [1, 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" } ]
244
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -2, 8],\n [0, 2, -3],\n [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" } ]
20
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -5, -1],\n [0, -7, 9],\n [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" } ]
433
MATH