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[ { "content": "What is the determinant of the matrix:\n[[6, 2, 9],\n [0, -4, -7],\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" } ]
240
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 3, -6],\n [10, -1, 4],\n [-7, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -10, -6],\n [0, 7, 6],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
559
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 2, 10],\n [-1, 7, 10],\n [7, 9, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -3, -8],\n [0, 1, -4],\n [0, 0, -10]]\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, 7, 0],\n [7, -1, 4],\n [0, 4, -5]]\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[[-3, 7, 8],\n [0, -8, -6],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 0, -2],\n [0, -5, 8],\n [-2, 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" } ]
492
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -3, 4],\n [-3, -6, 8],\n [4, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
340
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 5, -6],\n [5, -6, -6],\n [-6, -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" } ]
876
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 5, -4],\n [0, -9, 1],\n [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" } ]
135
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -6, -2],\n [0, -3, 7],\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[[8, -6, -10],\n [0, -4, 8],\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" } ]
32
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -5, -1],\n [-10, -8, 3],\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" } ]
738
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -4, -2],\n [-4, 7, 0],\n [-2, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
442
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, -4],\n [0, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
190
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -3, -4],\n [-3, 9, 2],\n [-4, 2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
714
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 0, 4],\n [0, 10, 4],\n [4, 4, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
892
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -7, -2],\n [0, 7, -9],\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" } ]
552
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -1, 5],\n [-1, 6, -10],\n [10, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, 7],\n [-9, 4, 7],\n [6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
918
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -4, 5],\n [0, -6, 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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -2, -2],\n [-2, 3, 4],\n [-2, 4, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
159
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 4, 8],\n [4, 6, -2],\n [8, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
516
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -9, 4],\n [0, -5, 0],\n [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" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 4, 9],\n [0, -5, 1],\n [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" } ]
40
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, 0],\n [0, -5, 7],\n [0, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 4, 7],\n [4, 4, 0],\n [7, 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" } ]
168
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 10, 3],\n [0, -3, 9],\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" } ]
6
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 6, -2],\n [6, -4, 0],\n [-2, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
576
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 8, 0],\n [8, -3, 0],\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" } ]
536
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -2, -2],\n [-2, -8, 0],\n [-2, 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" } ]
20
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 1, 2],\n [1, 5, 2],\n [2, 2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
801
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, -7],\n [1, 5, 4],\n [5, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
925
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 9, -2],\n [5, -3, 2],\n [-3, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
636
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 5, -7],\n [8, -1, -1],\n [0, 6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 8, -2],\n [8, -3, -10],\n [-2, -10, -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" } ]
396
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -4, 0],\n [0, -1, 5],\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" } ]
1
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 0],\n [2, -2, 0],\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" } ]
32
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, 0],\n [-6, 1, 0],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
378
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, -7, -9],\n [2, -9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, 2],\n [0, 0, -2],\n [2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 8, 2],\n [8, -10, 2],\n [2, 2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -7, -2],\n [-3, -10, -4],\n [-4, 10, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
154
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 3, -5],\n [0, -9, 0],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -8, -9],\n [0, 2, 0],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 10, -6],\n [0, -2, 6],\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" } ]
888
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, 6],\n [8, 4, -6],\n [3, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -9, -9],\n [-5, -9, 1],\n [8, 7, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
464
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 9, -4],\n [9, 1, 2],\n [-4, 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" } ]
38
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 3, -5],\n [0, -6, 0],\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" } ]
622
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, -6],\n [0, 6, 4],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
892
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 3, -4],\n [0, -10, 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" } ]
100
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, -3],\n [2, 7, -3],\n [-10, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 2, 9],\n [6, -9, -3],\n [9, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
405
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 8, 0],\n [6, -6, -10],\n [0, -1, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 0, -2],\n [0, 9, -8],\n [-2, -8, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
631
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -1, 10],\n [-8, -7, -2],\n [-1, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
424
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -2, 8],\n [0, 3, -10],\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" } ]
874
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 5, -10],\n [0, -1, -3],\n [0, 0, -7]]\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[[6, -4, 4],\n [0, 4, 1],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -2, 3],\n [0, 4, 7],\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" } ]
60
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -4, -3],\n [-4, -9, 1],\n [-3, 1, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
769
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -4, -5],\n [6, -10, -2],\n [10, -9, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
618
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -4, 4],\n [0, -5, 6],\n [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" } ]
800
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 6, 0],\n [6, 7, -1],\n [0, -1, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
207
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 0, 2],\n [0, -2, -6],\n [0, 0, 4]]\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[[-3, -7, 1],\n [0, 2, 5],\n [0, 0, -6]]\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, -6, -7],\n [0, -1, -4],\n [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" } ]
40
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, 0],\n [-6, -1, -8],\n [0, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
606
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -9, 9],\n [0, -3, -7],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -8, -5],\n [5, 9, 8],\n [8, 7, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
601
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -3, 4],\n [-1, 1, 9],\n [7, 8, -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" } ]
15
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 2, 0],\n [2, 1, -6],\n [0, -6, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
246
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 4, 4],\n [4, -10, -2],\n [4, -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" } ]
708
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -5, 0],\n [1, -6, -7],\n [7, -4, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
167
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -3, -9],\n [0, 1, -10],\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" } ]
993
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 8, 0],\n [-5, 8, -10],\n [-5, 10, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
276
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 6, -8],\n [6, -1, -5],\n [-8, -5, -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" } ]
868
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -9, -6],\n [0, -1, 6],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -7, -3],\n [0, -8, 8],\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" } ]
352
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 0, 7],\n [4, 7, 8],\n [9, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
515
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -7, 4],\n [0, -3, -1],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -2, 0],\n [-2, 3, 4],\n [0, 4, -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" } ]
175
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -4, 2],\n [-7, 0, 4],\n [9, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
740
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -6, 2],\n [4, -9, 0],\n [-10, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
886
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 0, -2],\n [9, -8, -1],\n [7, 8, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 5, -5],\n [1, 8, -8],\n [-3, -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" } ]
828
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 2, 6],\n [-9, -4, -6],\n [-6, -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" } ]
996
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 2, 4],\n [2, 6, -8],\n [4, -8, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
924
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -1, -4],\n [0, 4, -7],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -9, 3],\n [0, 2, -9],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
994
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 7, 2],\n [7, -3, 0],\n [2, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
878
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -7, 3],\n [0, 4, 0],\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" } ]
240
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -4, 6],\n [9, 10, 10],\n [0, -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" } ]
766
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, -3],\n [2, 6, -5],\n [-3, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 1, -1],\n [-2, -2, 9],\n [5, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -1, 2],\n [-1, 3, 0],\n [2, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
205
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -4, -5],\n [0, -8, -5],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 8, 4],\n [0, -6, -6],\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" } ]
96
MATH