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[ { "content": "Determine the value of det(A) where A =\n[[1, 6, 7],\n [7, 3, -9],\n [4, 9, 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" } ]
871
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 4, -1],\n [4, -6, 2],\n [-1, 2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
206
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 2, 0],\n [2, -7, 2],\n [0, 2, -8]]\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[[6, 0, -2],\n [9, 0, 2],\n [6, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -9],\n [0, -10, 7],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -6, 0],\n [-6, 5, 7],\n [0, 7, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -9, -10],\n [10, -1, -8],\n [-10, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
229
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -7, 10],\n [0, 9, 5],\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" } ]
460
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 [-4, 2, -8],\n [-4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -1, 2],\n [-1, 2, -6],\n [2, -6, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
457
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, 3],\n [-4, -2, 4],\n [3, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
836
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 1, 7],\n [8, -10, -9],\n [-5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
295
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, 6],\n [-2, -1, -4],\n [6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
956
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -5, 6],\n [-10, -2, 4],\n [-7, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
406
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -4, 5],\n [-4, -10, 2],\n [5, 2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
918
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 0, -3],\n [0, 3, -10],\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" } ]
973
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 6, -10],\n [6, 9, 4],\n [-10, 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" } ]
416
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 9, -3],\n [0, 6, -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" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, -5],\n [0, 1, -5],\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[[-10, 8, 8],\n [0, -4, -5],\n [0, 0, -5]]\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, -4, -9],\n [6, 5, -10],\n [-6, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
298
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 0, -2],\n [-2, 0, 4],\n [2, -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" } ]
944
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -3, 1],\n [1, 0, -3],\n [9, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 9, -8],\n [-3, -6, -8],\n [-6, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
326
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -5, 10],\n [0, -2, 1],\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": "Compute |A| for the matrix A =\n[[4, 4, 1],\n [3, 0, -6],\n [0, -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" } ]
907
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -10, 10],\n [0, 5, 0],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 9, 8],\n [2, -4, 1],\n [8, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
268
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 10, -7],\n [0, -6, -9],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 10, -10],\n [0, 6, -3],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 2, 8],\n [4, -8, -1],\n [-2, 9, 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" } ]
275
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -10, -7],\n [0, -6, -1],\n [0, 0, -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" } ]
892
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -3, -4],\n [-9, 5, -10],\n [-3, -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" } ]
58
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -7, 4],\n [-7, -8, -4],\n [4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
506
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -4, 1],\n [0, 10, -10],\n [0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 9, 7],\n [0, 7, -4],\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" } ]
63
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 8, -3],\n [8, 7, 0],\n [-3, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
857
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, -7],\n [0, 8, -3],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 0, -2],\n [0, 6, -2],\n [-2, -2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
844
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 6, -1],\n [6, 0, 0],\n [-1, 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" } ]
324
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 4, -10],\n [4, 0, 2],\n [-10, 2, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
932
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -8, 5],\n [0, 6, 0],\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" } ]
108
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -2, 10],\n [0, 8, 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[[9, 5, -5],\n [-4, -2, -1],\n [4, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
946
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 3, -8],\n [6, 2, 10],\n [7, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
660
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 2, -6],\n [0, 4, 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" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -3, 0],\n [-3, 0, -4],\n [0, -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" } ]
159
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 6, 4],\n [-8, 7, 0],\n [-7, -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" } ]
912
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 9, 5],\n [0, 9, 7],\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" } ]
324
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -8, -4],\n [-8, -7, 5],\n [-4, 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" } ]
123
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 1, -2],\n [0, 4, -8],\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" } ]
168
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -8, -9],\n [0, 1, -1],\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" } ]
990
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 5, -8],\n [0, 2, -7],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, 5],\n [-8, -4, 9],\n [5, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
731
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 1, -3],\n [0, 3, 5],\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" } ]
952
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 6, 0],\n [6, -4, 0],\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" } ]
940
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 8, 2],\n [8, -9, 4],\n [2, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
297
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 6, 0],\n [6, -4, -2],\n [0, -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" } ]
108
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 4, -4],\n [0, -2, -9],\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" } ]
980
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, -6],\n [-2, -3, -4],\n [4, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
414
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 2, 4],\n [2, -7, 1],\n [4, 1, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
582
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -3, -8],\n [0, 9, -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" } ]
640
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -10, 0],\n [-7, 7, -5],\n [-4, 5, -5]]\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[[-9, 5, 10],\n [10, 7, 6],\n [2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
259
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -6, -9],\n [-7, 7, -10],\n [-3, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
770
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -1, 2],\n [0, 4, -6],\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" } ]
776
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -8, -2],\n [0, 7, -3],\n [5, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
370
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 4, -2],\n [4, 4, 9],\n [-2, 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" } ]
121
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -6, 2],\n [-5, -3, -2],\n [-3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
826
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -1, -2],\n [-1, -2, -7],\n [-2, -7, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, 6],\n [0, -6, 8],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -4, 2],\n [-4, -1, 3],\n [2, 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" } ]
845
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -3, -9],\n [6, -10, 0],\n [-10, 2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
936
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -8, 1],\n [-8, 0, -6],\n [1, -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" } ]
840
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -9, -4],\n [-2, 8, -2],\n [-6, -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" } ]
820
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 0, -4],\n [0, -3, 0],\n [-4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
66
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 6, -6],\n [6, 4, 5],\n [-6, 5, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
406
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -7, 9],\n [9, 4, -10],\n [7, 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" } ]
753
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, 1],\n [2, 8, -4],\n [1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
908
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 2, 0],\n [2, 9, 4],\n [0, 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" } ]
318
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 4, 0],\n [4, 8, -5],\n [0, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -10, 7],\n [6, 0, -4],\n [5, 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" } ]
86
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -5, -10],\n [0, 9, 6],\n [0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
820
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -5, -5],\n [5, -7, -9],\n [1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
819
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 4, 3],\n [4, 8, 5],\n [3, 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" } ]
511
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -5, -9],\n [0, -8, 8],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 3, 6],\n [3, 5, -2],\n [6, -2, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
870
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 7, 4],\n [0, -1, 3],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
985
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 7, 4],\n [0, -3, 10],\n [0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
940
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, -3],\n [2, -7, -6],\n [-3, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
471
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, -2, 4],\n [2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -6, -8],\n [0, -6, -7],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 6, -6],\n [6, 4, 5],\n [-6, 5, 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" } ]
275
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 9, 3],\n [7, -10, -1],\n [-8, -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" } ]
913
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 5, -9],\n [5, 6, 5],\n [-9, 5, -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" } ]
458
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -7, -10],\n [0, 6, -4],\n [0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -4, 6],\n [-4, 5, 0],\n [6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
820
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 9, -3],\n [-7, 4, -1],\n [-7, 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" } ]
914
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, -4],\n [0, -7, -9],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
776
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -2, -2],\n [-2, 8, 6],\n [-2, 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" } ]
40
MATH