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[ { "content": "Compute |A| for the matrix A =\n[[-5, 8, -2],\n [8, 7, 6],\n [-2, 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" } ]
257
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 6, -2],\n [-3, -10, 10],\n [-7, -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" } ]
176
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 2, 0],\n [2, 8, 9],\n [0, 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" } ]
62
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -4, 7],\n [-4, 5, -4],\n [7, -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" } ]
935
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -6, -4],\n [-6, -8, 6],\n [-4, 6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
716
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -5, -6],\n [7, 6, -2],\n [3, 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" } ]
869
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 6, -2],\n [6, -8, -6],\n [-2, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
536
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, 7],\n [0, 2, 4],\n [-10, 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" } ]
380
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 6, 2],\n [6, -7, 8],\n [2, 8, 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" } ]
412
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -10, 4],\n [-10, 5, -8],\n [4, -8, -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" } ]
526
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 [1, -4, -1],\n [2, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 5, -3],\n [5, 8, -2],\n [-3, -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" } ]
748
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, -5, -3],\n [-2, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
62
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 6, -4],\n [6, -8, -8],\n [-4, -8, -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" } ]
800
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, 8],\n [4, 3, 10],\n [-5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 8, 5],\n [0, -1, -2],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -1, 6],\n [3, 10, 4],\n [-9, 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" } ]
405
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 [-2, -7, 1],\n [9, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
265
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, -6],\n [0, -6, 4],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
568
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, 5],\n [0, -3, -6],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -5, 0],\n [-5, -3, 0],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
974
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -5, -8],\n [8, -2, 2],\n [-5, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
738
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 2, 8],\n [-10, 10, 3],\n [-1, 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" } ]
670
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -2, -2],\n [-2, 6, -4],\n [-2, -4, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
984
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -6, -9],\n [7, -2, -1],\n [-9, 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" } ]
108
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, 6, -6],\n [-2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
886
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -9, 10],\n [10, -9, 10],\n [6, -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" } ]
300
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -5, -1],\n [4, -1, 8],\n [8, 3, 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" } ]
908
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -1, 2],\n [-1, -9, 8],\n [2, 8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -7, 9],\n [-9, 8, -10],\n [9, 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" } ]
461
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 5, -8],\n [0, -10, 3],\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" } ]
200
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 3, -3],\n [-7, -9, -10],\n [-9, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
891
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 5, 10],\n [0, 6, 6],\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" } ]
480
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 9, 6],\n [1, -1, -7],\n [9, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
490
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 6, 5],\n [5, 1, 7],\n [6, 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" } ]
601
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -7, 0],\n [-7, -4, -4],\n [0, -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" } ]
580
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 1, 10],\n [-5, -3, 10],\n [-7, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
260
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -2, 2],\n [-2, -9, -4],\n [2, -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" } ]
812
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -4, 5],\n [0, -10, -2],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 10, 9],\n [0, 3, -2],\n [0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -7, -6],\n [0, -4, 7],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -6, -8],\n [0, -1, 5],\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" } ]
999
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -4, -7],\n [-4, -3, -3],\n [-7, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
899
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 6, -6],\n [6, 0, 2],\n [-6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
744
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 9, -3],\n [0, 8, -10],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -2, -8],\n [-2, 5, 2],\n [-8, 2, 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" } ]
741
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -6, 5],\n [-2, 4, 10],\n [-7, -10, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -4, 6],\n [-4, 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" } ]
290
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -5, -1],\n [0, -3, 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" } ]
946
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 4, -2],\n [4, 6, 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" } ]
976
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 3, -2],\n [3, 2, 3],\n [-2, 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" } ]
893
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -5, -8],\n [4, 10, -6],\n [-3, -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" } ]
514
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 0, 2],\n [-9, 7, -7],\n [-2, -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" } ]
334
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 1, 3],\n [0, -4, 2],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -1],\n [2, 1, 4],\n [-1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
939
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -3, -9],\n [-10, 10, 4],\n [5, 1, 4]]? 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": "Compute |A| for the matrix A =\n[[8, 9, -10],\n [-9, -1, 1],\n [4, 8, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
725
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 4, 5],\n [0, 3, -10],\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" } ]
979
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -2, -4],\n [-2, -1, -4],\n [-4, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
816
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 6, 4],\n [0, -1, -3],\n [-8, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -2, -3],\n [-2, 5, -3],\n [-3, -3, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
793
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 7, -4],\n [-10, -9, 10],\n [-5, -6, -7]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, -5],\n [3, 8, -9],\n [1, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
101
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 9, -2],\n [-4, -1, 10],\n [6, 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" } ]
914
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, 7],\n [4, -2, 0],\n [8, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 0],\n [0, -2, 6],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -7, -6],\n [-4, 2, 9],\n [0, 8, -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" } ]
200
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -3, 5],\n [-9, -5, -3],\n [-1, 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" } ]
300
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -6, -3],\n [0, -4, -6],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -5, 10],\n [0, 6, 4],\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" } ]
24
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 7, -8],\n [5, 9, 6],\n [-1, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
186
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 1, 9],\n [0, -8, 4],\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" } ]
904
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, -9],\n [0, 5, 6],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, -6],\n [6, -5, 3],\n [-5, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
396
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -8, 9],\n [-6, 4, 10],\n [-4, 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" } ]
188
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -4, 6],\n [-4, 10, 6],\n [6, 6, 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" } ]
244
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 0, 2],\n [0, 0, 2],\n [2, 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" } ]
980
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -2, -4],\n [-2, -1, -6],\n [-4, -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" } ]
106
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 2, 4],\n [8, -3, 9],\n [5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
134
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 9, 10],\n [0, -8, 2],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 3, 3],\n [7, 2, 9],\n [-10, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 1, 4],\n [0, 9, -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" } ]
216
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -8, 8],\n [0, -5, -3],\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" } ]
760
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, -7],\n [0, 7, -8],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -2, 4],\n [0, 7, -9],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -8, -1],\n [5, 10, 7],\n [-5, 4, 7]]\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, -9, 1],\n [0, -5, -7],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 8, -3],\n [0, 10, 7],\n [-3, 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" } ]
672
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 1, -4],\n [1, 10, 4],\n [-4, 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" } ]
863
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -2, -2],\n [-2, -7, 8],\n [-2, 8, -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" } ]
119
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 8, 1],\n [8, 2, -7],\n [1, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
730
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 8, -5],\n [0, -10, 7],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 0, -4],\n [0, -1, 0],\n [-4, 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" } ]
16
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 3, 6],\n [10, -10, 2],\n [-6, -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" } ]
334
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -2, -2],\n [-2, 6, 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" } ]
40
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 8, 3],\n [9, -4, 3],\n [-3, -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" } ]
439
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -1, 5],\n [2, 8, -5],\n [-9, 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" } ]
837
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 8, 7],\n [8, 10, -9],\n [7, -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" } ]
968
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 1, 10],\n [0, 9, -3],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 8, -2],\n [8, -7, 4],\n [-2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH