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[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -9, 2],\n [3, 8, 9],\n [-6, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
477
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -10, 4],\n [0, -5, -6],\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" } ]
895
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 1, 1],\n [0, 7, 10],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -8, -10],\n [0, 6, 0],\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" } ]
622
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 6, -4],\n [0, -2, -2],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -8, -6],\n [-7, 2, 10],\n [9, 9, 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" } ]
836
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -9, 5],\n [0, -4, 5],\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" } ]
976
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 4, -8],\n [0, 7, 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" } ]
147
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -5, 6],\n [0, -2, 3],\n [4, -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" } ]
128
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -5, -2],\n [-5, -4, 1],\n [-2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
971
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 9, -8],\n [-7, 1, 7],\n [-1, 7, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
552
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -5, -1],\n [10, -6, 2],\n [9, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
74
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, 1],\n [4, 4, -2],\n [-1, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
106
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -2, -6],\n [-2, -5, -5],\n [-6, -5, -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" } ]
75
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 7, 4],\n [7, -6, 10],\n [4, 10, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
349
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -2, 1],\n [-5, 5, -2],\n [-9, -10, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
719
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -9, 2],\n [4, -7, 3],\n [0, 3, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
772
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -2, 3],\n [-2, 0, 6],\n [3, 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" } ]
540
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 3, 4],\n [0, -4, -4],\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" } ]
960
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 [-3, 4, -2],\n [-1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
59
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -4, 9],\n [6, -5, 1],\n [9, -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" } ]
916
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -2, 0],\n [-2, 1, 4],\n [0, 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" } ]
26
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -3, 8],\n [0, -10, -8],\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[[-10, -2, -2],\n [-2, 5, 0],\n [-2, 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" } ]
412
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -2, -4],\n [-2, 10, -4],\n [-4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
332
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 1, 2],\n [1, 5, 0],\n [2, 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" } ]
390
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -6, -4],\n [-6, -5, 4],\n [-4, 4, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
374
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 3, 3],\n [0, 6, -1],\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" } ]
72
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -1, -2],\n [-1, 4, 5],\n [-2, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 6, 4],\n [0, 4, 3],\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" } ]
20
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 3, 9],\n [0, 4, 5],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -7, -8],\n [-8, -2, 0],\n [-5, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 0, -4],\n [0, -3, -6],\n [-4, -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" } ]
748
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 8, -8],\n [10, -10, -6],\n [4, 10, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 6, -6],\n [0, -6, -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" } ]
748
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -1, 8],\n [0, -7, 7],\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" } ]
196
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, -4],\n [-4, 6, 2],\n [-4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
992
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 0, -2],\n [0, 0, -2],\n [-2, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
996
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 6, 5],\n [0, 7, 10],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
608
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -9, -9],\n [0, 5, 5],\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" } ]
60
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -6, -6],\n [2, 6, -1],\n [7, 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" } ]
210
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -2, -4],\n [-2, 5, 8],\n [-4, 8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
978
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 5, 6],\n [-10, 4, 8],\n [1, -2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -9, -6],\n [3, 4, -7],\n [2, 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" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, 0],\n [-6, 10, -3],\n [0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
39
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -2, -5],\n [-2, -7, -2],\n [-5, -2, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 10, 8],\n [3, 7, -10],\n [-7, -9, -5]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 1, -2],\n [1, -1, 6],\n [-2, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
286
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 0, 7],\n [-5, -2, 8],\n [-10, 8, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
804
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 8, -7],\n [8, -4, 8],\n [-7, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -7, 0],\n [-7, -8, -2],\n [0, -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" } ]
657
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -3, -7],\n [7, -1, -8],\n [-10, 2, 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" } ]
820
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, 0],\n [0, 4, -8],\n [0, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
352
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 5, 4],\n [5, 7, 0],\n [4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
318
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -7, 10],\n [0, 8, -10],\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" } ]
520
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -6, -6],\n [-2, 9, -4],\n [1, 5, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
243
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 0, 4],\n [0, 8, 4],\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" } ]
400
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 7],\n [-2, -8, 4],\n [7, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -6, 0],\n [-6, 3, 5],\n [0, 5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -4, -5],\n [-6, 2, 8],\n [-7, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
750
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 6, -6],\n [6, -3, 6],\n [-6, 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" } ]
880
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 6, -8],\n [6, -10, -3],\n [-8, -3, 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" } ]
229
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -3, 2],\n [-3, 5, 2],\n [2, 2, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -1, 10],\n [0, -4, -8],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 9, -4],\n [0, -1, 6],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -5, 7],\n [-10, 7, 5],\n [2, -7, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
591
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -8, 1],\n [-8, 5, 3],\n [1, 3, -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" } ]
753
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 7, 4],\n [7, 6, -7],\n [4, -7, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
76
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 1, 7],\n [0, -10, -5],\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" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 6, -1],\n [7, -3, -10],\n [2, -6, 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" } ]
832
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -2, 0],\n [-2, -3, -2],\n [0, -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" } ]
86
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -10, -8],\n [-2, 8, -5],\n [-10, 1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -6, -2],\n [-6, 2, -2],\n [-2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -7, -9],\n [-4, 10, 7],\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" } ]
374
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 0, 2],\n [0, -5, 6],\n [2, 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" } ]
268
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -10, -6],\n [-9, -7, 5],\n [-1, -1, 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" } ]
896
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -3, -10],\n [0, -7, 10],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, 6],\n [0, 10, 6],\n [6, 6, -9]]\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[[-10, -2, -4],\n [-2, -10, 0],\n [-4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
352
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 8, 7],\n [-7, 10, 1],\n [1, 5, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
688
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 7, -5],\n [0, 3, -10],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
105
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, -7],\n [-3, 9, 3],\n [-2, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -4, 2],\n [-1, -2, 2],\n [7, 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" } ]
946
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -8, -6],\n [-8, -4, 6],\n [-6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 10, 7],\n [4, -10, 7],\n [-5, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -6, -4],\n [9, -9, -10],\n [9, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
291
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 10, 6],\n [-2, -4, 3],\n [-7, 7, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
208
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 6, -4],\n [0, 1, -10],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -7, -3],\n [10, -6, 1],\n [-6, 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" } ]
656
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -3, -5],\n [0, 7, -10],\n [7, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, -6],\n [0, 10, 6],\n [-6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
416
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -4, 3],\n [-4, -10, 2],\n [3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
962
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -9, 7],\n [0, 6, 9],\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" } ]
712
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -4, 6],\n [-8, -6, 9],\n [8, -1, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
993
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -2, 4],\n [-2, 6, 0],\n [4, 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" } ]
774
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -8, -3],\n [5, 4, -2],\n [0, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
715
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 6, -10],\n [0, -4, -8],\n [-8, -7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
752
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 10, -2],\n [9, 0, -7],\n [9, -6, -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" } ]
504
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -2, -4],\n [-2, -5, 8],\n [-4, 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" } ]
28
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 2, -4],\n [2, -8, -4],\n [-4, -4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
732
MATH