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[ { "content": "Compute |A| for the matrix A =\n[[1, -8, 4],\n [-8, 5, 5],\n [4, 5, 5]]\nRound to the nearest integer, then take the result 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, 4],\n [5, 4, -10],\n [2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
93
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 4, -4],\n [4, 6, 10],\n [-4, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
226
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 0, -6],\n [0, -3, 2],\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" } ]
850
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 0, 8],\n [0, -2, -2],\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" } ]
892
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, -1],\n [-4, -9, 8],\n [8, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
610
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 9, 6],\n [0, 5, -9],\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" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -8, 7],\n [0, 4, -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" } ]
168
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 5, 9],\n [-1, 8, 1],\n [4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
523
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -3, 4],\n [-3, 0, 2],\n [4, 2, 0]]? Round to the nearest integer, then express your answer modulo 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[[5, -7, 8],\n [0, -6, 3],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -4, 6],\n [-4, 10, 4],\n [6, 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" } ]
426
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 1, -8],\n [6, 1, 3],\n [-6, -9, 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" } ]
108
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 0, -2],\n [2, -10, 3],\n [-5, -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" } ]
140
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -4, -3],\n [-4, 0, 2],\n [-3, 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" } ]
944
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -4, -4],\n [0, -2, 5],\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" } ]
960
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -8, -6],\n [-5, 5, -6],\n [9, -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" } ]
230
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 1, -2],\n [0, -9, -3],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
324
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 4, -10],\n [-7, 5, 0],\n [3, -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" } ]
702
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 8, 8],\n [10, 6, 7],\n [10, -9, 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" } ]
68
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 10, -2],\n [-6, 2, 5],\n [10, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
374
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 2, 2],\n [2, 3, 2],\n [2, 2, 4]]? 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[[-7, 3, -10],\n [0, -9, 4],\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" } ]
496
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 0, -1],\n [0, -5, -3],\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" } ]
350
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 1, 8],\n [-5, -7, 7],\n [-9, -2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
613
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 7, 5],\n [5, -10, -1],\n [10, -6, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
461
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -8, 8],\n [-8, -7, 4],\n [8, 4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
465
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 10],\n [-6, 1, 2],\n [-6, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
450
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, 0],\n [10, -10, 2],\n [0, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
444
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -2, 2],\n [-2, -1, 2],\n [2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
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 [-4, -7, -10],\n [8, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
735
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, -6],\n [-4, -2, -9],\n [-1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
402
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -1, -4],\n [0, 4, 10],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -4, -4],\n [-4, -2, 4],\n [-4, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
898
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -4, -10],\n [-4, -7, 2],\n [-10, 2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -5, -8],\n [-2, 0, -2],\n [3, 5, -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" } ]
100
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 3, -1],\n [0, -7, 1],\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" } ]
140
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 4, 2],\n [4, 8, 0],\n [2, 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" } ]
48
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, 4],\n [0, 8, 4],\n [4, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
752
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 0, 3],\n [0, 9, 0],\n [3, 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" } ]
847
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 0, -3],\n [-8, -7, -4],\n [5, 9, 5]]? Round to the nearest integer, then express your answer modulo 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[[7, 4, 6],\n [4, 10, 4],\n [6, 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" } ]
882
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -10, -2],\n [4, 6, -1],\n [6, -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" } ]
178
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 2, 6],\n [2, -4, 3],\n [6, 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" } ]
156
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -1, -4],\n [4, -4, 9],\n [0, -5, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
64
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 6, -6],\n [6, 9, 4],\n [-6, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
218
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 10, -9],\n [1, 1, 2],\n [-9, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
875
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -1, 2],\n [0, 6, 2],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, 10],\n [0, -5, -10],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 4, 10],\n [10, -10, -2],\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" } ]
252
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, -6],\n [2, 3, 3],\n [-6, 3, 9]]\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": "What is the determinant of the matrix:\n[[-8, -9, 6],\n [-6, 10, -9],\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" } ]
442
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 4, 2],\n [4, 1, -2],\n [2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -8, -10],\n [0, -5, 7],\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" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 6, 7],\n [-1, 3, 7],\n [-4, -3, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
895
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, -7],\n [0, 2, -5],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 2, 0],\n [6, -6, -3],\n [4, 4, -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" } ]
456
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 9, -4],\n [0, -3, 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" } ]
910
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -6, 4],\n [-6, -3, 0],\n [4, 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" } ]
210
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, -3],\n [-1, -10, 8],\n [-1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, 4],\n [-2, -5, -2],\n [4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
111
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -10, -2],\n [2, -1, -10],\n [-4, 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" } ]
478
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -5, 0],\n [-10, 1, 5],\n [-8, 9, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 9, 8],\n [0, 7, -9],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
294
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, -2],\n [2, 0, -4],\n [-2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -6, 10],\n [-7, -3, 10],\n [7, 9, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
985
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 7, -4],\n [0, 10, 9],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -2, 0],\n [-2, 0, 2],\n [0, 2, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, 3],\n [-6, 3, 2],\n [3, 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" } ]
261
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 8, 6],\n [8, -8, -3],\n [6, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
145
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -8, -3],\n [-3, 6, -7],\n [-9, -9, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
893
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -4, -9],\n [0, -8, -9],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 9, 3],\n [4, -9, 1],\n [3, 7, 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" } ]
250
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 2, 8],\n [5, 8, -10],\n [-4, -3, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
656
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -3, -10],\n [0, 2, 4],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
128
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 0, -5],\n [0, 9, 5],\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" } ]
919
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, -5],\n [1, -8, -3],\n [2, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
875
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 7, 9],\n [-7, -2, -10],\n [-5, 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" } ]
395
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -3, 2],\n [0, 10, -9],\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" } ]
370
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -4, -1],\n [6, 3, -1],\n [6, -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" } ]
574
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 9, -1],\n [0, 6, 4],\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" } ]
730
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 5, -7],\n [5, -7, 2],\n [-7, 2, -5]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 5, 5],\n [2, -9, 1],\n [-6, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
329
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -9, -2],\n [0, 7, -4],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
895
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 1],\n [0, 3, -2],\n [1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 4, 8],\n [0, -1, -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" } ]
42
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, -2],\n [-1, 4, 10],\n [6, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -8, -2],\n [-8, -7, -2],\n [-2, -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" } ]
481
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 9, 2],\n [9, -1, -3],\n [2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
485
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -2, 1],\n [0, -3, 0],\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" } ]
21
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 [0, 5, 2],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
865
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -10, -4],\n [0, -6, 2],\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" } ]
294
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -6, 4],\n [-6, 1, 0],\n [4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
194
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -10, -8],\n [0, -1, 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" } ]
5
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -7, 9],\n [0, 10, 6],\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" } ]
910
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 7],\n [2, 2, 2],\n [7, 2, 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" } ]
950
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 4],\n [0, -2, 6],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 0, 4],\n [0, -8, 9],\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" } ]
968
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -2, 5],\n [0, -4, 2],\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" } ]
96
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 4, 10],\n [4, -3, 4],\n [10, 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" } ]
456
MATH