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[ { "content": "Compute |A| for the matrix A =\n[[3, 2, -2],\n [-10, -9, 5],\n [-4, 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" } ]
96
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -6, -9],\n [0, -6, 7],\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" } ]
790
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, 10, -2],\n [-3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
918
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 1, 3],\n [1, 1, -3],\n [3, -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" } ]
962
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 0, -5],\n [0, -7, 0],\n [-5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 1, 9],\n [7, 0, -2],\n [-8, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
387
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -4, -9],\n [0, 10, -7],\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" } ]
930
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 9, -4],\n [-9, 0, 10],\n [-10, -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" } ]
226
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, 2],\n [0, 5, 2],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -5, 9],\n [0, 5, 1],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -9, 4],\n [-1, 4, -7],\n [5, 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" } ]
527
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 7, 10],\n [0, -10, 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" } ]
700
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -9, 1],\n [-1, -10, -8],\n [1, -3, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
949
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 6, 10],\n [0, 5, -4],\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" } ]
600
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 [-4, 2, 0],\n [2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 2, 3],\n [1, -8, 10],\n [1, 1, 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" } ]
837
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 7, 7],\n [0, 6, -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" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 1, -8],\n [0, -10, 7],\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" } ]
640
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, -4],\n [-2, -6, -3],\n [-8, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
786
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 8, -2],\n [8, -2, 0],\n [-2, 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" } ]
600
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -6, -9],\n [6, -1, -4],\n [-5, 5, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
555
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 7, 3],\n [0, 10, -5],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
500
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 9, 9],\n [-9, -3, 1],\n [0, 10, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
284
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -6, -4],\n [0, 4, -2],\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" } ]
988
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 8, -5],\n [-1, 3, 3],\n [-5, -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" } ]
904
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, 8],\n [3, 4, -3],\n [-4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -6, 5],\n [0, 8, -5],\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" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -9, 3],\n [9, 2, 0],\n [-5, -3, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
459
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -7, -2],\n [-7, 0, 5],\n [-2, 5, 9]]\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": "What is the determinant of the matrix:\n[[-10, 10, -8],\n [9, -4, 1],\n [-6, 9, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
374
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -5, 6],\n [0, -1, -4],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
993
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, 4],\n [0, -8, 2],\n [4, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
812
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -2, 5],\n [-4, 4, 2],\n [-3, 9, 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" } ]
854
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 6, -6],\n [-1, -6, -8],\n [2, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "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, -6, -8],\n [-6, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
502
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -5, 1],\n [0, -7, -10],\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" } ]
552
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 4, 6],\n [4, -6, -4],\n [6, -4, 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" } ]
104
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 0, 2],\n [0, 6, 4],\n [2, 4, 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" } ]
116
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -6, -6],\n [0, 6, 9],\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" } ]
30
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -4, 0],\n [-4, -8, 3],\n [0, 3, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
83
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 7, 8],\n [0, -1, 6],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
992
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, 2],\n [-2, -6, -8],\n [2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 10, 9],\n [0, -6, -4],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
970
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -10, 7],\n [0, 9, 1],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
946
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 4, -7],\n [4, -7, -7],\n [-7, -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" } ]
673
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -8, 6],\n [0, 5, -4],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -4, 0],\n [0, -1, -2],\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" } ]
980
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -2, 8],\n [-2, 0, -7],\n [8, -7, -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" } ]
946
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -3, -7],\n [0, -9, 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" } ]
324
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -3, -2],\n [0, -10, 6],\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" } ]
300
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -2, 0],\n [-5, -9, 10],\n [6, 1, 0]]\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[[-10, 4, 1],\n [4, -8, -4],\n [1, -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" } ]
8
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -8, 6],\n [-8, 10, -1],\n [6, -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" } ]
324
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -3, 10],\n [0, -4, 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" } ]
56
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, 2],\n [-2, 3, -5],\n [2, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
993
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -2, -3],\n [-1, 3, 2],\n [-9, -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" } ]
951
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -6, 4],\n [-6, 7, -2],\n [4, -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" } ]
476
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -5, 8],\n [0, -7, -7],\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" } ]
916
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -1, 2],\n [0, -4, 10],\n [-5, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
780
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 3, 2],\n [-6, -6, 0],\n [-9, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
718
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 8, -5],\n [1, 1, -6],\n [-8, 10, 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" } ]
568
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 9, 2],\n [-5, -4, -6],\n [-7, 4, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
192
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 5, -1],\n [5, -5, 0],\n [-1, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
155
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 0, 10],\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" } ]
96
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 4, 2],\n [4, -6, -1],\n [2, -1, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
175
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -1, -1],\n [0, 5, -5],\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" } ]
940
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -1, -2],\n [0, -3, 8],\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" } ]
910
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -5, -9],\n [0, -6, -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" } ]
622
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 1, 2],\n [6, -4, 3],\n [0, 4, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
304
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 4, 7],\n [0, -2, 4],\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" } ]
54
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 [9, -9, 4],\n [7, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
541
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -2, -9],\n [-2, 10, 4],\n [-9, 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" } ]
468
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -2, 8],\n [-6, 10, -3],\n [8, -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" } ]
284
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -1, 0],\n [-1, 3, -1],\n [0, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
903
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 5, -1],\n [0, 1, 8],\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" } ]
18
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 6, 4],\n [6, -10, -8],\n [4, -8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
956
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 6, 3],\n [6, 5, -4],\n [3, -4, 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" } ]
710
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 2, 4],\n [2, 7, -6],\n [4, -6, 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" } ]
556
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, -10],\n [-5, -10, -10],\n [5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
970
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 8, 4],\n [8, 8, 4],\n [4, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
272
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -9, -3],\n [-9, 0, -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" } ]
519
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 4],\n [2, -7, -4],\n [4, -4, -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" } ]
70
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -8, -5],\n [9, 0, -3],\n [-5, 9, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -4, 0],\n [-4, -9, 6],\n [0, 6, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
904
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 1, -3],\n [0, 9, 10],\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": "Compute |A| for the matrix A =\n[[10, -2, -10],\n [-2, 5, 0],\n [-10, 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" } ]
316
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -8, 10],\n [0, 5, -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" } ]
950
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 8, 2],\n [8, 1, 4],\n [2, 4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
841
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 7, 6],\n [-5, -6, -5],\n [5, -5, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 1, 8],\n [1, 2, -4],\n [8, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
785
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 4, -9],\n [0, 5, -5],\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" } ]
210
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 3],\n [0, 3, -8],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -2, -7],\n [9, -10, 10],\n [-10, 10, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
430
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -6, -7],\n [0, -10, 8],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -6, -7],\n [-8, -7, 8],\n [-6, 2, -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" } ]
858
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 7, 6],\n [7, -3, 8],\n [6, 8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
166
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 1, 6],\n [-10, 6, -2],\n [-9, 5, -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" } ]
36
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 6, 4],\n [0, 4, 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" } ]
992
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 4, -6],\n [4, -7, -7],\n [-6, -7, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
668
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -10, 9],\n [0, 5, 4],\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" } ]
800
MATH