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[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, 4],\n [-2, 4, 8],\n [4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -3, -6],\n [-3, -9, 0],\n [-6, 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" } ]
424
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -4, -10],\n [-4, -4, -4],\n [-10, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -4, 4],\n [-4, 7, 0],\n [4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
888
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -3, 10],\n [0, 10, -9],\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" } ]
680
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -1, 8],\n [1, 10, 5],\n [-2, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
275
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 4, -4],\n [4, 3, 2],\n [-4, 2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 0, -3],\n [0, -10, -4],\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" } ]
300
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 4, 0],\n [4, 2, -2],\n [0, -2, 0]]\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[[5, 0, -4],\n [0, 4, 4],\n [-4, 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" } ]
996
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -2, 2],\n [-2, -10, 4],\n [2, 4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 5, 7],\n [5, -3, 10],\n [7, 10, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
639
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, -10],\n [2, 4, 6],\n [-10, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
328
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 3, -5],\n [0, 10, -2],\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" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 8, -4],\n [0, -1, -10],\n [0, 0, -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" } ]
9
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 7, -3],\n [0, 1, -6],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
997
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 3, 0],\n [3, 10, 2],\n [0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
369
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -4, 2],\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" } ]
916
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -4, 0],\n [6, 6, 9],\n [-2, 7, 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" } ]
964
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 5, 6],\n [4, 5, 1],\n [10, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 5, -1],\n [5, 7, -4],\n [-1, -4, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
969
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 1, -3],\n [1, 9, -3],\n [-3, -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" } ]
584
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 0, -4],\n [0, 6, -4],\n [-4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, 5],\n [5, -3, 9],\n [-3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
978
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, -1],\n [0, -9, -6],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
622
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 3, -6],\n [0, 10, 0],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 4, -4],\n [4, 9, -6],\n [-4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
466
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -2, -2],\n [0, -2, -7],\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" } ]
96
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 2],\n [0, -7, -5],\n [2, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 4, 0],\n [4, -1, -2],\n [0, -2, -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" } ]
189
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -6, 4],\n [6, -2, 3],\n [2, -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" } ]
926
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, -7],\n [0, -1, 6],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 8, -9],\n [0, 4, -7],\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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 9, -10],\n [0, 3, -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" } ]
958
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -2, -5],\n [0, 1, -7],\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" } ]
998
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 4, 8],\n [0, 8, 6],\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" } ]
808
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -7, -9],\n [0, -9, 5],\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" } ]
180
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 4, -5],\n [0, -7, -1],\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" } ]
56
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 4, -8],\n [10, 3, 9],\n [4, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
595
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -5, 2],\n [-5, -9, -2],\n [2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
76
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 10, -9],\n [-9, -1, 9],\n [-4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
201
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 1, 2],\n [1, -5, 0],\n [2, 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" } ]
78
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -1, -3],\n [0, 5, 4],\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" } ]
270
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -10, -1],\n [9, -4, 10],\n [10, -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" } ]
592
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 8, -5],\n [0, 10, 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" } ]
550
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 1, 10],\n [0, -9, -10],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 8, -7],\n [0, 10, 3],\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" } ]
40
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 8, 5],\n [5, 7, -10],\n [1, 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" } ]
689
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -5, 9],\n [-4, 1, 5],\n [-7, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
762
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -4, 7],\n [0, -8, -1],\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" } ]
928
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 0, -4],\n [0, 9, 6],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
370
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, 8],\n [-2, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -2, 0],\n [-2, -5, 2],\n [0, 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" } ]
68
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, 0],\n [0, 10, -2],\n [-2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 2, -8],\n [2, 0, 4],\n [-8, 4, 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" } ]
836
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 5, 1],\n [5, 5, 0],\n [1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
995
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, -4],\n [-10, -4, -7],\n [-9, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
373
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, 4],\n [4, 4, 4],\n [4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 5, 9],\n [9, -8, 6],\n [3, -3, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -4, 4],\n [-8, 9, -9],\n [1, 3, 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" } ]
76
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, -3],\n [2, -7, 7],\n [-7, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
275
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -10, -4],\n [0, 10, -3],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -10, -2],\n [0, 3, 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" } ]
757
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -9, 4],\n [2, -3, 4],\n [4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -8, -7],\n [-8, 1, -6],\n [-7, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
711
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -8, 6],\n [-7, -9, -5],\n [-8, 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" } ]
247
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -6, 2],\n [-6, 8, 8],\n [2, 8, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 4, -9],\n [3, 2, 9],\n [-5, 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" } ]
973
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 1, 6],\n [-3, 1, 10],\n [3, 5, -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" } ]
182
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -8, -6],\n [7, -5, 6],\n [-10, 4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
366
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 2, 9],\n [7, -4, 8],\n [-5, 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" } ]
230
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 6, 5],\n [0, -8, -5],\n [0, 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" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -1, 0],\n [-1, -3, 0],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -2, 9],\n [-9, 1, -7],\n [1, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 1, -1],\n [-6, -7, -10],\n [-9, 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" } ]
357
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, 5],\n [-2, 6, 4],\n [5, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 10, -6],\n [-9, 9, -3],\n [5, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
904
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -7, -6],\n [0, -9, -9],\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" } ]
784
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -5, 2],\n [5, 3, 9],\n [10, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
685
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 1, -9],\n [-9, 2, 6],\n [10, -5, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
871
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 0, 1],\n [0, -5, -8],\n [1, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
910
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -6, 2],\n [-6, 10, -1],\n [2, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
770
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 4, 4],\n [4, 9, 9],\n [4, 9, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
718
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -4, 3],\n [8, -2, 4],\n [-7, -1, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
350
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -3, -4],\n [6, 5, 0],\n [-8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, 7],\n [0, -7, -6],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 0, 3],\n [0, -5, -8],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 6, -7],\n [0, -3, 10],\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" } ]
850
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 3, -5],\n [8, -5, -5],\n [3, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
444
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -7, 3],\n [-7, 10, -3],\n [-7, 5, -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" } ]
483
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 6, -2],\n [6, -9, 2],\n [-2, 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" } ]
236
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 5, -2],\n [10, -6, -2],\n [-2, 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" } ]
212
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -4, -9],\n [-1, 5, -8],\n [8, 8, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
944
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 1, 6],\n [0, 5, 8],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
135
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 2, -4],\n [2, -9, 0],\n [-4, 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" } ]
916
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 2, -3],\n [2, -8, 4],\n [-3, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
828
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 4, -8],\n [0, -9, -2],\n [-4, 5, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
322
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 2, 0],\n [-8, 4, -1],\n [-10, 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" } ]
668
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -3, -6],\n [-3, 10, -8],\n [-6, -8, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
378
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -1, -8],\n [-6, -9, 3],\n [-5, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH