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[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 9, 1],\n [6, -3, -4],\n [-5, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
484
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 4, 3],\n [4, 2, -2],\n [3, -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" } ]
992
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -9, -10],\n [9, 5, 2],\n [-4, 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" } ]
460
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -10, 3],\n [3, 6, 6],\n [9, 1, -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" } ]
385
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -8, 2],\n [1, -10, -5],\n [0, 8, 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" } ]
48
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0],\n [0, 4, 10],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 2, -10],\n [2, 9, 3],\n [2, -1, -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" } ]
228
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 2, 9],\n [-10, 3, -1],\n [8, -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" } ]
773
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 9, -5],\n [-10, 7, -6],\n [-10, -4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, -2],\n [0, -10, 5],\n [-2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
190
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 3, 8],\n [-7, -6, 7],\n [-10, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
373
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 9, -6],\n [9, -2, 0],\n [-6, 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" } ]
630
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -9, 0],\n [0, 9, 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" } ]
973
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 4, -6],\n [-6, -7, -10],\n [9, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
922
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -2, -2],\n [-2, 0, 0],\n [-2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, -8],\n [0, 10, 0],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 6, -3],\n [0, 7, 5],\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" } ]
252
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -4, -2],\n [0, 8, 8],\n [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": "What is the determinant of the matrix:\n[[7, 6, 1],\n [0, -6, -10],\n [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" } ]
126
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -4, 9],\n [0, 1, 7],\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" } ]
982
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 5, -4],\n [-6, 9, -8],\n [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" } ]
200
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, -3],\n [8, -8, -1],\n [-3, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
348
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 3, -5],\n [0, -5, -7],\n [2, -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" } ]
244
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 2, 5],\n [0, -6, 8],\n [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" } ]
892
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -8, -5],\n [-8, -6, 9],\n [-5, 9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
967
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, -7],\n [-2, 6, -8],\n [-10, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
170
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -2, -6],\n [-2, -3, 1],\n [7, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
618
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 9, 9],\n [0, 6, 6],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -1, 4],\n [4, 0, -10],\n [3, 2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
958
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 3, -10],\n [3, -6, -2],\n [-10, -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" } ]
403
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, 0],\n [-2, 10, 8],\n [-5, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
882
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 5, -5],\n [0, 5, 1],\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" } ]
30
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -8, -6],\n [0, 6, -1],\n [0, 0, 2]]\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[[4, -4, -5],\n [-4, 1, 2],\n [-5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 8, -1],\n [8, 6, 3],\n [-1, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 1, -1],\n [0, 9, 1],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
865
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -1, 2],\n [-1, 3, 0],\n [2, 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" } ]
19
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 4, 9],\n [4, 9, 0],\n [9, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
726
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -6, -6],\n [7, 1, 1],\n [6, -2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
648
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 8, -10],\n [-3, 4, -8],\n [-1, 1, 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" } ]
246
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -3, 6],\n [-3, -7, -2],\n [6, -2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\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[[-5, 10, -6],\n [4, 7, -4],\n [-7, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -3, 9],\n [5, -9, 7],\n [0, -9, 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" } ]
700
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -6, 0],\n [-6, 6, -2],\n [0, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
808
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 4, 2],\n [4, 6, 8],\n [2, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
388
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -10, -4],\n [2, 3, -8],\n [-7, -9, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
676
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 5, -2],\n [5, 1, 6],\n [-2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 10, 4],\n [0, -5, 2],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, 6],\n [8, -2, -3],\n [-1, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 2, 0],\n [2, -10, 2],\n [0, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
342
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 0, -9],\n [0, 6, -3],\n [-2, -6, 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" } ]
102
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, -3],\n [0, -10, -1],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -6, 4],\n [-10, 6, -1],\n [5, 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" } ]
601
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -1, -4],\n [10, 4, -4],\n [1, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
676
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -3, -8],\n [0, 5, -5],\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" } ]
250
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 3, 2],\n [-1, -2, 5],\n [-8, -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" } ]
613
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 2, -6],\n [2, 1, 4],\n [-6, 4, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
708
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -7, 4],\n [-4, -7, 10],\n [5, 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" } ]
986
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -4, 10],\n [8, 8, -6],\n [0, 8, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
64
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 1, 4],\n [5, -10, 8],\n [-4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
868
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 0, -3],\n [0, 4, 4],\n [-3, 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" } ]
676
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -3, -6],\n [0, -2, -2],\n [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" } ]
60
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, -8],\n [0, -6, 1],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, -3],\n [0, 5, 1],\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" } ]
225
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 4, 1],\n [-1, -5, -8],\n [0, -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" } ]
838
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, -9],\n [-2, 8, -3],\n [-9, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
812
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 4, -2],\n [4, -9, 3],\n [-2, 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" } ]
934
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 5, 4],\n [0, 9, -3],\n [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" } ]
90
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -2, -1],\n [0, -5, -6],\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" } ]
90
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, -3],\n [0, 8, 0],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -8, -4],\n [2, -2, 8],\n [-2, 8, -9]]\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, 5, 8],\n [0, -6, -7],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -2, -8],\n [0, -5, 3],\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" } ]
225
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 7, 0],\n [7, -6, -5],\n [0, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -3, 2],\n [0, -6, 7],\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" } ]
84
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 2, 2],\n [2, -10, -2],\n [2, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
736
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -1, 2],\n [-1, 1, 4],\n [2, 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" } ]
982
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 6, -10],\n [0, 8, 0],\n [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" } ]
160
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 3, 1],\n [0, 2, 0],\n [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" } ]
984
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 2, 2],\n [2, -10, 0],\n [2, 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" } ]
256
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 5, -4],\n [0, -10, -7],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 2, 6],\n [0, 9, 2],\n [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" } ]
18
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 4, 9],\n [0, -5, 1],\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" } ]
840
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -4, -8],\n [10, 0, -9],\n [10, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -7, 9],\n [0, 9, -6],\n [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" } ]
630
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -10, 10],\n [0, -6, 6],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -1, 6],\n [0, -7, 4],\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" } ]
790
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, -6],\n [0, -10, 4],\n [-6, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 0, -6],\n [0, 9, 3],\n [-6, 3, -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" } ]
244
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -7, 1],\n [0, 9, 7],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -8, 3],\n [-7, 2, 8],\n [-5, -7, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 4, -2],\n [4, 9, -2],\n [-2, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
639
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, 10],\n [2, -9, -2],\n [10, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
390
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -5, 4],\n [9, -4, 6],\n [9, -3, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
624
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 8, 0],\n [0, -3, 5],\n [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" } ]
757
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 1, 2],\n [1, -10, -2],\n [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" } ]
126
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 2, -4],\n [2, -10, 2],\n [-4, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
628
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, -10],\n [0, 10, 0],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -3, 0],\n [9, -2, 8],\n [-8, -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" } ]
799
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -5, -10],\n [-3, 9, 8],\n [9, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
404
MATH