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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -2, 0],\n [-2, -1, 0],\n [0, 0, 5]]\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[[5, 2, 2],\n [0, 5, -10],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -5, -2],\n [-3, 10, -7],\n [-8, 3, 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" } ]
275
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -3, 2],\n [9, 0, 3],\n [7, 8, -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" } ]
171
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -10, -10],\n [-10, -9, -4],\n [-10, -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" } ]
714
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 2, -2],\n [0, -6, 4],\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" } ]
84
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -8, 2],\n [-7, -6, 4],\n [0, -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" } ]
364
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 5, -4],\n [0, 9, -3],\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" } ]
405
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -3, -3],\n [-3, 0, 4],\n [-3, 4, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -4, -6],\n [-6, 4, -4],\n [-8, 5, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -4, 0],\n [-4, 3, 2],\n [0, 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" } ]
32
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -4, 5],\n [-4, 9, 0],\n [5, 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" } ]
495
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 6, -1],\n [6, 4, -2],\n [-1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -7, 8],\n [0, 9, 9],\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" } ]
270
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 [-3, -4, 5],\n [-6, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
445
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 4, 3],\n [-8, 10, 9],\n [4, -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" } ]
312
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 0, 9],\n [0, 5, 2],\n [9, 2, 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" } ]
750
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 0, 4],\n [0, 3, 2],\n [4, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
127
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 10, -7],\n [1, 6, -2],\n [9, -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" } ]
364
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -3, 6],\n [-7, 2, 3],\n [2, -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" } ]
80
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -3, 1],\n [0, 3, -10],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
820
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -6, 3],\n [0, 10, 5],\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" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 6, -6],\n [6, -1, 4],\n [-6, 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" } ]
697
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -5, 5],\n [0, -4, -1],\n [0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -3, 1],\n [0, 9, -10],\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" } ]
568
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -1, -8],\n [0, 4, 3],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 4, -7],\n [0, -2, 6],\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" } ]
928
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 6, -5],\n [0, -3, 5],\n [0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
838
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 8, 6],\n [-4, 7, 0],\n [-5, 4, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
209
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -3, 4],\n [0, 2, -3],\n [0, 0, -2]]\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[[10, 2, -10],\n [9, -8, 10],\n [-1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, 2],\n [0, -1, 6],\n [2, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
294
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 5, 8],\n [5, 0, -7],\n [3, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
65
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 6, -8],\n [6, -10, 10],\n [-8, 10, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
172
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 4, 0],\n [4, 6, 2],\n [0, 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" } ]
842
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -8, 6],\n [7, -7, 7],\n [6, -7, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -4, 4],\n [-4, -7, -4],\n [4, -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" } ]
680
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 4, -1],\n [8, -10, 3],\n [10, 5, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -6, 9],\n [-2, 10, -1],\n [-1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
156
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 4, -2],\n [4, 3, -8],\n [-2, -8, 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" } ]
416
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 1, 8],\n [0, 6, 1],\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" } ]
288
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 [-10, -4, 8],\n [10, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 5, -3],\n [5, 5, -2],\n [-3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -7, -8],\n [-5, 8, 3],\n [-3, 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" } ]
331
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 0, 2],\n [0, 0, 2],\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" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -2, -3],\n [-2, 10, 4],\n [-3, 4, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
734
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -2, -3],\n [-2, -4, -3],\n [-3, -3, 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" } ]
764
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, 9],\n [0, -1, 8],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -5, 9],\n [-2, 9, 8],\n [-10, 10, -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" } ]
925
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -9, 2],\n [-9, -6, 0],\n [2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -7, 2],\n [-7, 4, 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" } ]
752
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -6, -4],\n [-6, -6, -2],\n [-4, -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" } ]
162
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, -2],\n [4, -7, -7],\n [-2, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 6, -8],\n [6, -3, 9],\n [-8, 9, -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" } ]
985
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, 2],\n [-4, -2, 1],\n [2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
901
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, -5],\n [0, -9, 6],\n [7, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
487
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 4, 5],\n [0, 1, 5],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 2, -3],\n [0, -6, -9],\n [10, 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" } ]
415
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -3, -2],\n [-3, -9, 10],\n [-2, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
799
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 2, -8],\n [0, -5, -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" } ]
200
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 3, 4],\n [-9, -9, 3],\n [-7, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
387
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 1, 9],\n [7, -1, -8],\n [1, 4, -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" } ]
309
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 1, -4],\n [0, 9, 3],\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" } ]
63
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, 0],\n [0, 3, -4],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 9, -4],\n [-2, 7, 5],\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" } ]
514
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 10, -5],\n [7, -2, -10],\n [10, 5, 10]]? 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": "Determine the value of det(A) where A =\n[[7, 8, 0],\n [0, -1, 2],\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" } ]
965
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -8, -10],\n [0, -5, -1],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
980
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 0, 3],\n [0, 2, -7],\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": "Compute |A| for the matrix A =\n[[6, -8, -6],\n [0, -9, -9],\n [0, 0, 6]]\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[[-6, -10, 2],\n [6, -9, 7],\n [-7, 3, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
754
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -1, 0],\n [9, 7, -5],\n [-1, 2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
38
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 2, -6],\n [0, 2, 7],\n [7, -5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\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, 0],\n [0, -7, 0],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 4, -8],\n [0, -1, 5],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -4, 3],\n [-4, 10, -5],\n [3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
155
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -10, -1],\n [0, -6, 5],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -2, -4],\n [0, 1, 6],\n [0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
990
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -1, 0],\n [3, -3, -6],\n [-4, 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" } ]
298
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 4, 5],\n [4, 0, -2],\n [5, -2, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 6, -6],\n [-3, 5, 1],\n [-5, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, -7],\n [2, 6, -5],\n [-7, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
734
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 10, -2],\n [0, -4, 4],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -7, 8],\n [0, 8, 4],\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" } ]
936
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -6, -6],\n [-6, 2, -1],\n [-6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
910
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -7, -4],\n [0, 7, 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" } ]
790
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 1, 6],\n [0, 5, 4],\n [6, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
550
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 5, -5],\n [0, -4, 2],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -3, -3],\n [0, -5, -7],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 1, 5],\n [0, 9, 5],\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" } ]
271
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 1, -5],\n [0, -7, 4],\n [0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
951
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -5, -2],\n [0, -1, -1],\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" } ]
970
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, -8],\n [4, -3, 8],\n [-8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
148
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 0, -4],\n [0, -7, -9],\n [0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 5, 8],\n [5, -10, 2],\n [8, 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" } ]
516
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 1, -3],\n [0, 5, -7],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
985
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 10, 10],\n [5, 6, -8],\n [-1, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
286
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 1, 10],\n [0, -1, -8],\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" } ]
35
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -7, 3],\n [-1, 9, 1],\n [-7, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 1, 3],\n [0, -3, -1],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
865
MATH