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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, -1],\n [0, -6, 7],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 6, 1],\n [0, -8, -10],\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" } ]
520
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, -2],\n [0, 1, 4],\n [-2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -6, -10],\n [-9, 8, -2],\n [0, -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" } ]
52
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -7, 1],\n [6, 6, 4],\n [-10, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
382
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 8, 4],\n [0, 6, -6],\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" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 4, 7],\n [0, 3, -5],\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" } ]
120
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -4, -6],\n [-4, 7, -3],\n [-6, -3, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
797
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -5, -4],\n [-5, -8, -2],\n [-4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
372
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, 2],\n [0, -6, -4],\n [2, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
632
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -10, 7],\n [0, -7, -7],\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" } ]
930
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -5, 2],\n [0, -2, -6],\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" } ]
140
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, 4],\n [0, 4, -2],\n [4, -2, 0]]\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[[3, -1, 1],\n [-1, -4, -9],\n [1, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
831
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 3, -9],\n [3, -10, 6],\n [-9, 6, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
755
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 1, 5],\n [2, -6, -6],\n [3, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
544
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 9, 6],\n [3, -2, 3],\n [-6, 10, 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" } ]
721
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 5, -2],\n [5, 10, 2],\n [-2, 2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -2, 1],\n [-2, 7, 4],\n [1, 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" } ]
767
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -1, 0],\n [-1, 8, -6],\n [0, -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" } ]
833
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 6, 2],\n [2, 3, -3],\n [-5, -5, -3]]\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[[-3, 2, -4],\n [2, -4, 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" } ]
64
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 4, -4],\n [4, -9, -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" } ]
544
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 3, 6],\n [0, -6, 9],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 7, -3],\n [0, 9, 5],\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" } ]
955
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 2, -8],\n [2, -1, 6],\n [-8, 6, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
902
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 0, 6],\n [0, -2, 8],\n [6, 8, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -3, 6],\n [7, -6, 8],\n [0, 8, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
878
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 1, 6],\n [-2, 7, -9],\n [3, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
681
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 9, -9],\n [-8, 4, -3],\n [1, -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" } ]
671
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -1, 6],\n [-3, -7, -4],\n [10, 5, -9]]\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, 1, -9],\n [-6, -8, -7],\n [-1, 9, -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" } ]
731
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -3, 9],\n [2, 7, -3],\n [3, -7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
925
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -7, 8],\n [-2, 3, 5],\n [-8, 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" } ]
762
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, -5, 2],\n [2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
919
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 10, 6],\n [10, 10, -2],\n [6, -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" } ]
48
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -2, 1],\n [-2, 7, 1],\n [1, 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" } ]
71
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, -4],\n [0, 3, -2],\n [-4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 2, 4],\n [-4, 1, 0],\n [4, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
867
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -1, -10],\n [-9, -6, 5],\n [4, -9, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
825
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 7, 6],\n [0, 1, 9],\n [10, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
860
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, -8],\n [0, -3, 5],\n [0, 0, -2]]\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[[-6, 2, 2],\n [0, -8, 8],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 3, 1],\n [-6, 8, -1],\n [3, 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" } ]
83
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 5, 0],\n [9, -10, 10],\n [3, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
410
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 8, 8],\n [8, 0, -6],\n [8, -6, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -6, -2],\n [-6, 7, 1],\n [-2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
918
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -7, 10],\n [0, -3, -9],\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" } ]
63
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 10, 10],\n [-9, 0, 10],\n [4, 8, -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" } ]
60
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -4, 7],\n [-1, -3, -8],\n [-5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
556
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -2, 10],\n [-7, -1, -4],\n [4, -9, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
810
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -7, -8],\n [0, -6, -4],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -3, -1],\n [0, 7, 3],\n [0, 0, 5]]\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[[5, -7, -7],\n [-7, 4, 4],\n [-7, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
174
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -1, -1],\n [8, 4, 8],\n [2, 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" } ]
608
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -8, 9],\n [0, -3, 9],\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" } ]
126
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -10, -4],\n [0, 2, 0],\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" } ]
976
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -2, 2],\n [2, 9, 7],\n [-3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 10, -1],\n [0, -8, -8],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -2, -4],\n [-4, 8, -8],\n [1, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 1, 0],\n [0, 8, -2],\n [0, 0, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -7, -2],\n [-7, 10, -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" } ]
844
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 0, 0],\n [-2, -7, -10],\n [0, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
826
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 6, -3],\n [6, -2, -9],\n [-3, -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" } ]
843
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 4, 3],\n [0, 3, -6],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 3, 0],\n [0, 4, 7],\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" } ]
600
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 2, 2],\n [2, -9, -6],\n [2, -6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -4, -4],\n [-4, 4, -4],\n [-4, -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" } ]
160
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 0, -8],\n [-5, 2, 10],\n [2, -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" } ]
32
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 9, -10],\n [0, -7, 0],\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" } ]
147
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -6, 4],\n [-6, -6, -6],\n [4, -6, -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" } ]
444
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, -5],\n [0, -6, -9],\n [1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -5, 7],\n [6, 4, -7],\n [9, 10, -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" } ]
183
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -6, -10],\n [-8, 6, 10],\n [0, -10, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -5, -10],\n [2, 1, 9],\n [7, 10, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
265
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, 1],\n [0, 4, -4],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
940
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 2, -7],\n [2, 2, 4],\n [-7, 4, -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" } ]
678
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 3, -10],\n [0, -1, -8],\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" } ]
4
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, -9],\n [0, 3, -3],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
135
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 4, -2],\n [4, -9, 2],\n [-2, 2, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -6, 0],\n [0, -4, -6],\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" } ]
128
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -10, -1],\n [0, -5, -3],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -7, -6],\n [0, 8, 5],\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" } ]
904
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -9, -5],\n [0, 9, 1],\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" } ]
676
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 5, 8],\n [-8, 4, -6],\n [7, -9, 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" } ]
222
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 4, -7],\n [-4, -8, -10],\n [6, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
812
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 0, 8],\n [4, -4, -10],\n [9, -6, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 10, 4],\n [0, 7, -4],\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" } ]
496
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -3, 0],\n [-6, -2, 1],\n [5, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
877
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -1, 1],\n [-1, -3, 6],\n [1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
283
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 6, 2],\n [6, -9, 6],\n [2, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
486
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, 10],\n [0, -10, -1],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 5, -7],\n [0, 10, 0],\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" } ]
680
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -7, 1],\n [0, 5, 6],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -2, 1],\n [6, 0, -5],\n [7, 2, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
942
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -2, -3],\n [-6, 6, -10],\n [8, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
430
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 0, -2],\n [0, 10, -1],\n [-2, -1, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -7, 0],\n [-7, 1, 2],\n [0, 2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -8, 8],\n [0, 6, 4],\n [0, 0, -4]]\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[[-10, -8, 5],\n [0, 6, 2],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH