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[ { "content": "What is the determinant of the matrix:\n[[-6, 4, -5],\n [0, -2, 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" } ]
48
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, 4],\n [7, -2, 5],\n [4, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
632
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 8, -3],\n [0, -3, 6],\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" } ]
955
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 6, -4],\n [-1, 2, -8],\n [-3, 4, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 10, 5],\n [0, -6, -7],\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" } ]
126
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 8, 6],\n [0, -9, 6],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
595
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -4, 6],\n [0, 7, 2],\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" } ]
245
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -4, 0],\n [0, 3, 3],\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" } ]
90
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 8, -3],\n [0, 4, 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" } ]
808
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, -5],\n [-2, 10, -2],\n [-3, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
786
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, 10],\n [-7, 3, 8],\n [3, 8, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
617
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, 9],\n [-6, -5, -7],\n [-6, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 2, 0],\n [10, -6, -2],\n [-7, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
258
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 6, -3],\n [6, -2, -3],\n [-3, -3, -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" } ]
264
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 2, 0],\n [3, -9, 8],\n [-10, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
677
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 1, -4],\n [1, 7, 4],\n [-4, 4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
792
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, 4],\n [2, 5, -8],\n [3, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
896
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -2, 8],\n [0, 8, -3],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
616
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 5, -2],\n [0, -7, -10],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 3, -2],\n [3, 8, 4],\n [-2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
731
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -1, 10],\n [0, 3, 0],\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" } ]
30
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -3, 10],\n [0, 10, -4],\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" } ]
970
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -7, 9],\n [0, -8, 4],\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" } ]
960
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 5, 1],\n [5, 4, 4],\n [1, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
521
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -9, 2],\n [-6, -4, 2],\n [-9, 9, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 0],\n [2, -1, 6],\n [0, 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" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 9, -4],\n [-4, -10, -1],\n [8, -6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
472
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -7, 4],\n [1, -3, -9],\n [7, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
551
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 3, 1],\n [0, 9, -2],\n [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" } ]
54
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -10, 8],\n [0, 5, 2],\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" } ]
860
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 6, -10],\n [-5, 7, -5],\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" } ]
12
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -10, 4],\n [-10, 8, -1],\n [-6, 6, 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" } ]
572
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -1, 3],\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[[7, 3, 0],\n [3, -9, 0],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
352
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 2, 3],\n [10, -7, 8],\n [-3, -8, -7]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, -4],\n [4, 3, 6],\n [-4, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
526
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -8, 2],\n [-8, 9, 3],\n [2, 3, -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" } ]
623
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, 6, 5],\n [2, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
451
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -7, 5],\n [0, 9, -9],\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" } ]
946
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 2, 2],\n [0, -5, -1],\n [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" } ]
820
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -6, -3],\n [7, 0, 8],\n [3, -3, 0]]? 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[[5, -10, 0],\n [0, -8, -6],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 9, -9],\n [0, -8, 3],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
616
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -4, -6],\n [-4, 7, 0],\n [-6, 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" } ]
301
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 2, 4],\n [4, -4, 9],\n [8, -5, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, 0],\n [0, 8, -8],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 10, -7],\n [-3, -7, 1],\n [10, 5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
727
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 4, 1],\n [0, -5, -4],\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" } ]
5
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 3, 3],\n [3, -10, 4],\n [3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
156
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, -2],\n [0, -5, 0],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -5, 3],\n [-1, 9, 9],\n [-3, -4, -2]]\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": "What is the determinant of the matrix:\n[[-7, 1, 3],\n [0, 6, -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" } ]
42
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, -4],\n [2, 4, -4],\n [-4, -4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
632
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 3, 0],\n [0, 2, -1],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -3, -4],\n [-3, 10, 6],\n [-4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
230
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, -3],\n [5, 0, -10],\n [2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
945
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 4, -4],\n [0, 2, 3],\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" } ]
72
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 3, -6],\n [3, 3, 2],\n [-6, 2, 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" } ]
948
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 6, 8],\n [6, 10, -8],\n [8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -2, 10],\n [8, -7, 9],\n [7, -3, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -5, -3],\n [9, 9, -8],\n [1, -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" } ]
701
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 4, -2],\n [0, 6, -9],\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" } ]
622
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -2, -7],\n [-2, 5, -2],\n [-7, -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" } ]
599
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -3, -2],\n [0, -9, 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" } ]
36
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 0, 9],\n [0, 2, 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" } ]
60
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -5, -3],\n [10, 4, 3],\n [10, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
68
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 7, 4],\n [7, -9, -8],\n [4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
254
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -10, 7],\n [-10, -7, 2],\n [7, 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" } ]
763
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -3, 8],\n [3, -5, -10],\n [-8, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
862
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 1, -2],\n [1, -6, 6],\n [-2, 6, 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": "Compute |A| for the matrix A =\n[[-5, 3, 3],\n [3, 3, 4],\n [3, 4, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
957
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 4, -3],\n [6, -5, 8],\n [7, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
939
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -3, 2],\n [-3, 3, 2],\n [2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -8, 9],\n [-9, 5, 4],\n [4, 7, 4]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 8],\n [-2, 1, 7],\n [8, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
555
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -6, -6],\n [0, -9, 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" } ]
378
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 0, -5],\n [0, 8, -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" } ]
984
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 6, -9],\n [1, -8, -8],\n [-2, -9, 8]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, 2],\n [-7, -10, -2],\n [-9, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
616
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -9, 9],\n [0, 8, 7],\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" } ]
288
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -10, -2],\n [0, -3, 5],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 2, 3],\n [-8, -7, 8],\n [4, 7, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
228
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -3, 2],\n [-3, 4, 4],\n [2, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
955
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -4, -2],\n [-4, -9, -1],\n [-2, -1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
49
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -8, 5],\n [0, 9, 0],\n [-9, -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" } ]
333
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, -5],\n [0, 7, 8],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
804
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, -9],\n [0, 8, 8],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -1, 4],\n [-1, 8, 5],\n [4, 5, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
272
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -8, 0],\n [0, 2, 8],\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" } ]
950
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 7, -8],\n [0, 4, -6],\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" } ]
192
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 1, -7],\n [-7, 1, -3],\n [-5, -10, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
236
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 6],\n [-2, -3, 5],\n [6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
860
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 6],\n [-6, -5, -5],\n [-3, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
881
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -5, 8],\n [-1, 8, 1],\n [-3, -4, 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" } ]
63
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 10, 8],\n [-8, -8, 1],\n [7, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
854
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, 1],\n [0, -5, 0],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 3, 5],\n [0, -2, -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" } ]
70
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -10, 1],\n [-3, 0, 2],\n [0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
157
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 9, 8],\n [3, -6, 8],\n [-8, 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" } ]
334
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -4, 10],\n [-4, -6, -2],\n [10, -2, 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" } ]
112
MATH