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[ { "content": "Compute |A| for the matrix A =\n[[0, -2, -6],\n [-2, 1, 2],\n [-6, 2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -10, -7],\n [2, 1, -9],\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" } ]
882
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 [-8, 3, 9],\n [-4, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
899
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -10, -4],\n [0, -8, -4],\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" } ]
256
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -6, -3],\n [-6, -10, 4],\n [-3, 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" } ]
114
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 0, 0],\n [0, 2, -2],\n [0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 3, 4],\n [3, -1, 4],\n [4, 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" } ]
123
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, -4],\n [2, 6, -4],\n [-4, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
564
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -8, 1],\n [-3, 7, -9],\n [10, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
416
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, 2, -6],\n [-4, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
148
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 10, 3],\n [0, 8, -3],\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" } ]
952
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -10, 5],\n [0, -5, 8],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -1, -5],\n [-1, -8, 3],\n [-5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
353
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 7, -5],\n [7, 8, 8],\n [-5, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
497
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 4, -2],\n [8, -10, 3],\n [8, 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" } ]
682
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 1, 0],\n [1, 9, 0],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
138
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 4, -4],\n [0, 10, -9],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -8, 3],\n [7, -4, 7],\n [8, 4, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
660
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 1, -5],\n [0, -4, -1],\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" } ]
676
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, 8],\n [4, -7, 2],\n [8, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
786
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 10, 8],\n [0, 8, -2],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
504
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -7, 6],\n [0, -3, 6],\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" } ]
27
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -8, -4],\n [-8, -4, 6],\n [-4, 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" } ]
496
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 1, 8],\n [1, -1, 4],\n [8, 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" } ]
144
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 4, 6],\n [4, 6, -3],\n [6, -3, 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" } ]
648
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 6, 4],\n [6, -4, -4],\n [4, -4, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 8, 9],\n [0, 4, -8],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -4, 0],\n [-4, -9, -3],\n [0, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 5, 0],\n [0, 2, 6],\n [7, 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" } ]
146
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -1, 7],\n [-1, 2, 4],\n [7, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
948
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 2, 2],\n [2, 2, 6],\n [2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 7, 0],\n [7, -4, 4],\n [0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
484
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -5, -8],\n [-5, -8, 2],\n [-8, 2, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
677
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 1, -4],\n [1, 10, 0],\n [-4, 0, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 2, -5],\n [0, -10, -3],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
550
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -1, 3],\n [7, -1, -6],\n [5, 3, 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" } ]
282
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -7, -4],\n [10, 2, -9],\n [-9, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
249
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 2, 6],\n [-7, 2, -5],\n [3, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 2, 2],\n [2, 8, -2],\n [2, -2, 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" } ]
912
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -7, 4],\n [0, 6, -8],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
420
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -10, 10],\n [0, 5, -3],\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" } ]
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -1, 5],\n [-10, 0, -4],\n [-5, -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" } ]
180
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 4, 0],\n [4, -3, 1],\n [0, 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" } ]
20
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 5, -2],\n [0, 1, 7],\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" } ]
928
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 [0, -1, -10],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -7, 1],\n [-2, 4, 4],\n [-5, -2, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
220
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -4, -6],\n [0, -7, 2],\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" } ]
441
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 7, -3],\n [0, -8, -7],\n [0, -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" } ]
928
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 5, 8],\n [0, -9, -6],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 2, -5],\n [0, -4, 3],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 2, -8],\n [0, 10, -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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -7, 5],\n [5, 1, 0],\n [4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 5, -6],\n [8, 6, 3],\n [4, -9, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
977
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, -7],\n [-3, 6, 10],\n [8, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -7, 8],\n [0, 8, -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" } ]
504
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, 1],\n [2, 9, -1],\n [1, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
951
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -7, 5],\n [0, 2, 6],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -6, -3],\n [-6, -8, 5],\n [-3, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
247
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -3, -10],\n [-9, 3, 2],\n [5, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
129
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 0, 2],\n [1, 3, -4],\n [5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
946
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 4, -5],\n [4, 7, 0],\n [-5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 6, -2],\n [6, 5, -10],\n [-2, -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" } ]
304
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -2, -8],\n [-10, 0, -1],\n [-4, -2, 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" } ]
730
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -9, 8],\n [0, -1, 0],\n [-5, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
970
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 6, 2],\n [6, 8, -1],\n [2, -1, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
310
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 9, -6],\n [5, -3, 1],\n [-1, 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" } ]
114
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -1, 6],\n [0, 3, -4],\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" } ]
937
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -7, 1],\n [-6, -8, 0],\n [-8, 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" } ]
852
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -5, 3],\n [9, 6, -1],\n [-4, 1, -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" } ]
69
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 3, 2],\n [2, 0, 4],\n [10, 2, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -10, 3],\n [0, 5, -10],\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" } ]
240
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -6, 7],\n [0, -2, -5],\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" } ]
126
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -2, 6],\n [4, -4, 4],\n [3, -7, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 0, 0],\n [0, -2, -6],\n [0, -6, 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" } ]
676
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 4, 6],\n [0, 10, -10],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
980
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -1, 2],\n [-1, 5, 2],\n [2, 2, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
330
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 9, -6],\n [-3, 3, -2],\n [5, -4, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 7, -7],\n [0, 2, -4],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 2, -1],\n [2, 9, 4],\n [-1, 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" } ]
18
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -2, -4],\n [-2, 6, -7],\n [-4, -7, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
521
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 9, 5],\n [-9, -9, -2],\n [5, 9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
514
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 7, -2],\n [7, -4, 6],\n [-2, 6, 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" } ]
662
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 10, -9],\n [0, 9, 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" } ]
424
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 10, -6],\n [-9, -9, 0],\n [-3, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
676
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 8, 0],\n [8, -7, -1],\n [0, -1, 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" } ]
536
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, -6],\n [0, 7, 1],\n [5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
382
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -2, 5],\n [-2, 8, 3],\n [5, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
118
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 6, 6],\n [6, -6, 0],\n [6, 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" } ]
288
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 10, 2],\n [-4, -1, -3],\n [5, -3, 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" } ]
84
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 [-6, 10, 5],\n [0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
864
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -2, 1],\n [0, -7, 10],\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" } ]
937
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -6, -1],\n [0, -7, 6],\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" } ]
28
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, -5],\n [0, 4, 6],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 4, 3],\n [4, 7, -6],\n [3, -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" } ]
67
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 0, 6],\n [0, 9, 0],\n [6, 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" } ]
405
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 9, -5],\n [0, -10, -1],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -9, -4],\n [0, -2, 8],\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" } ]
984
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 6, 0],\n [0, -7, -9],\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" } ]
350
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 6, -5],\n [7, -4, -1],\n [4, 5, 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" } ]
686
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 0, 6],\n [0, 6, -2],\n [6, -2, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
804
MATH