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[ { "content": "Determine the value of det(A) where A =\n[[-1, -9, -8],\n [0, -5, 8],\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" } ]
970
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 5, 3],\n [0, -7, -5],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
378
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -1, -4],\n [0, 3, 8],\n [2, -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" } ]
134
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -1, -2],\n [-1, -1, -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" } ]
996
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -4, 7],\n [-4, -9, 8],\n [7, 8, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -5, 4],\n [0, 4, 7],\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" } ]
256
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -6, -8],\n [0, -4, -5],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 3, 3],\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" } ]
4
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -4, 5],\n [-2, 2, -4],\n [-8, 5, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -9, -3],\n [0, 1, -9],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, 0],\n [4, -10, -8],\n [-5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
876
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 6, 4],\n [0, 3, -7],\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" } ]
976
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 7, -6],\n [7, -1, -7],\n [5, 3, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
131
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 2, -7],\n [9, 3, 8],\n [-6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
549
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 3, 2],\n [3, 4, 0],\n [2, 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" } ]
906
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -9, -6],\n [0, 2, 3],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 5, 0],\n [0, -9, 3],\n [0, 0, -3]]\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, 6],\n [2, 6, -5],\n [6, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
551
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 2, 0],\n [-7, 0, -5],\n [-9, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
212
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 1, 4],\n [1, -9, -4],\n [4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
827
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -3, 5],\n [0, 8, 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[[1, 5, -2],\n [0, 3, 4],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
27
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -2, 6],\n [0, 6, 4],\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" } ]
946
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -4, -1],\n [-4, 1, 2],\n [-1, 2, 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" } ]
970
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -8, -8],\n [-8, -2, 1],\n [-8, 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" } ]
914
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, 2],\n [1, 7, 0],\n [2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 4, 4],\n [7, -7, -9],\n [5, 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" } ]
220
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -3, -5],\n [-3, 9, -8],\n [-5, -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" } ]
389
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 2, 2],\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, 3],\n [0, 1, -6],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
996
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 0, 7],\n [0, -10, 9],\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" } ]
980
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, -9],\n [-4, -4, 3],\n [-9, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
618
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -2, -4],\n [-8, 1, 0],\n [10, -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" } ]
824
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 0, -2],\n [0, 4, -6],\n [-2, -6, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -5, 1],\n [-2, 7, -5],\n [8, -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" } ]
624
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -7, -7],\n [0, 5, 8],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, 5],\n [-10, -8, 0],\n [5, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
278
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 10, -7],\n [-3, -1, 2],\n [-10, -1, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
849
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -7, 8],\n [-7, 5, 0],\n [8, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
340
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -6, 7],\n [8, 8, -9],\n [-5, 1, 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" } ]
85
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -10, -7],\n [8, -10, 0],\n [-1, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
614
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 9, -3],\n [0, 4, 8],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, -7],\n [0, -2, -6],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
984
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 3, -2],\n [3, 6, 0],\n [-2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
922
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -3, 7],\n [0, 9, 10],\n [-5, -6, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
255
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -3, -6],\n [-3, -10, 0],\n [-6, 0, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
71
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 1, 4],\n [0, 2, 7],\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" } ]
32
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 3, -4],\n [-8, 0, -10],\n [0, -3, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -3, 2],\n [-3, 0, -2],\n [2, -2, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 6, -1],\n [0, 5, 9],\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" } ]
955
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -7, -1],\n [0, -2, -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" } ]
970
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -8, 0],\n [-8, -9, -2],\n [0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
500
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -3, -4],\n [-3, 6, 0],\n [-4, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
387
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 2, 1],\n [2, -5, 8],\n [1, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
781
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -2, 8],\n [0, -8, -9],\n [0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 3, -4],\n [0, -3, -2],\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" } ]
30
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 0, 2],\n [0, -2, -6],\n [2, -6, -10]]\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": "Compute |A| for the matrix A =\n[[-3, 0, -2],\n [9, 2, 8],\n [7, 4, 6]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -4, -4],\n [-4, 4, 3],\n [-4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 6, 8],\n [0, 1, -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" } ]
90
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -6, 0],\n [-6, -8, 2],\n [0, 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" } ]
948
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 0, 2],\n [5, -6, -2],\n [-8, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
826
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, -7],\n [-6, 2, 0],\n [0, 10, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
132
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 4, 8],\n [-3, 7, 6],\n [3, 2, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
962
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -6, 1],\n [7, -5, 3],\n [-10, 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" } ]
102
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 0, -2],\n [0, -10, -3],\n [-2, -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" } ]
258
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 1, -1],\n [-7, -5, 5],\n [1, 3, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
312
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -7, -10],\n [0, 10, 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" } ]
100
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 8, 7],\n [-2, -3, 7],\n [4, 8, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 4, -8],\n [0, 2, 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" } ]
988
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -3, 3],\n [-5, 2, -3],\n [10, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 0, 5],\n [0, 1, -4],\n [5, -4, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
75
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -6, 10],\n [0, -9, 6],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
567
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -6, 8],\n [6, -7, -4],\n [-6, 7, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -5, -6],\n [-5, -3, 4],\n [-6, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
285
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 2, -2],\n [2, -5, 3],\n [-2, 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" } ]
212
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 [-7, 10, 6],\n [9, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
450
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 1, -6],\n [5, 7, 6],\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" } ]
988
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 9, 10],\n [0, 8, 5],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 8, -2],\n [5, -4, 9],\n [-4, 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" } ]
676
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 4, 4],\n [4, 1, -2],\n [4, -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" } ]
996
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -2, -6],\n [8, 3, -10],\n [-6, 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" } ]
737
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 0, 6],\n [0, -3, -1],\n [6, -1, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
76
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -10, 9],\n [-3, -4, 5],\n [-6, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
47
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 3, 7],\n [0, 1, -7],\n [-2, -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" } ]
56
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -5, 2],\n [0, -4, -1],\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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 0, -2],\n [0, 7, -4],\n [-2, -4, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
777
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -8, 4],\n [-8, -9, 0],\n [4, 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" } ]
882
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 3, 4],\n [0, -1, -6],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 5, 0],\n [5, -9, -4],\n [0, -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" } ]
864
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -6, 8],\n [5, -3, -5],\n [9, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 3, -7],\n [0, 10, -9],\n [0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
420
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 0, -2],\n [0, -1, 4],\n [-2, 4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
958
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 4, -2],\n [4, -9, 0],\n [-2, 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" } ]
76
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 4, 7],\n [4, 1, -2],\n [7, -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" } ]
943
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 3, 3],\n [0, 3, 1],\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" } ]
12
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -5, -1],\n [0, -2, -1],\n [0, 0, -8]]\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[[4, -5, 10],\n [0, 5, 2],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 1, -10],\n [7, -4, -7],\n [-4, 8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -2, -4],\n [0, -9, 6],\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