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[ { "content": "Determine the value of det(A) where A =\n[[0, 10, 1],\n [-5, 9, -2],\n [-8, -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" } ]
427
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 8, -4],\n [1, -1, -2],\n [6, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
148
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 2, -9],\n [-6, 10, 5],\n [-10, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
678
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -7, -10],\n [-7, 4, -4],\n [-10, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
889
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 10, -6],\n [0, -10, 1],\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" } ]
270
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 4, 9],\n [-9, -10, -3],\n [-4, 4, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
388
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 4, 5],\n [7, -2, 7],\n [-3, 3, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -4, 0],\n [-4, -3, -2],\n [0, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
208
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 0, -1],\n [0, -10, 2],\n [-1, 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" } ]
780
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, -10],\n [0, -3, 0],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -9, -6],\n [0, -2, 4],\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" } ]
12
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 5, 10],\n [0, -10, -9],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
500
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -8, -4],\n [-5, -9, -2],\n [-6, 3, -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" } ]
164
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 4, -2],\n [4, -8, 0],\n [-2, 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" } ]
96
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 9, 3],\n [-8, 8, 3],\n [-4, -3, 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" } ]
930
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, -1],\n [4, 0, 8],\n [-1, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 3, 0],\n [3, -9, -4],\n [0, -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" } ]
166
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -2, 3],\n [-2, 2, -4],\n [3, -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" } ]
928
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, -7],\n [7, 10, -4],\n [-6, 5, -3]]\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[[-8, 2, 10],\n [2, 1, 1],\n [10, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 10, -2],\n [0, -4, 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" } ]
128
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -10, 5],\n [-8, 5, -5],\n [0, -9, 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" } ]
800
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 8, 1],\n [-9, 1, 9],\n [-4, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
794
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -3, -5],\n [-3, 6, 6],\n [-5, 6, -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" } ]
934
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 6, 8],\n [6, 5, -9],\n [8, -9, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -5, 0],\n [5, -9, 10],\n [-3, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -10, 8],\n [-2, -6, 8],\n [9, -10, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -6, 3],\n [9, 7, -8],\n [10, 10, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
348
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 9, -6],\n [-3, -2, -7],\n [-6, 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" } ]
784
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 3, -3],\n [0, -9, -2],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
910
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -6, -8],\n [-6, -1, -2],\n [-8, -2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
878
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 2, 0],\n [0, 6, 7],\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" } ]
664
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 9, -8],\n [-10, -6, 0],\n [-7, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
504
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -4, 6],\n [-4, 6, 0],\n [6, 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" } ]
624
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 3, -4],\n [3, -1, 0],\n [-4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -4, -4],\n [-10, 9, 9],\n [-5, 7, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
450
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 5, -4],\n [5, 7, 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" } ]
729
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -9, 5],\n [0, 10, 5],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
810
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, -8],\n [4, 0, -4],\n [-8, -4, -6]]\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[[-2, 1, -2],\n [1, -3, -1],\n [-2, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -7, -5],\n [0, -8, 1],\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" } ]
384
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -6, -8],\n [10, -7, 2],\n [-3, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 0, 7],\n [0, -1, -8],\n [0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 0, 4],\n [0, 4, 4],\n [4, 4, 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" } ]
20
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -7, -4],\n [0, -4, 6],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -10, 2],\n [0, -5, 7],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -4, -1],\n [0, -2, 9],\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" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 10, -2],\n [0, 6, -1],\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" } ]
210
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 6, -4],\n [4, -6, -6],\n [8, 4, -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" } ]
450
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -3, -10],\n [0, -6, 4],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -7, 7],\n [-7, 2, 2],\n [7, 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" } ]
804
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, 8],\n [10, -6, -8],\n [9, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
440
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 1, 4],\n [0, -6, 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" } ]
108
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, 9],\n [0, -9, -9],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, 4],\n [10, 4, 2],\n [4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -3, 7],\n [0, -9, 10],\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" } ]
72
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -2, 3],\n [-2, 0, 6],\n [3, 6, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
268
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -10, -2],\n [-10, 9, 0],\n [-2, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -3, -2],\n [-3, -10, 3],\n [-2, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
509
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -4, -10],\n [0, -8, 5],\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" } ]
992
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -7, 2],\n [7, -10, -6],\n [-4, 5, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
718
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 10, -3],\n [0, 5, -2],\n [-3, 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" } ]
105
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 10, 6],\n [0, -2, 7],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 5, -9],\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" } ]
860
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, 4],\n [9, 2, -4],\n [-1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
689
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 7, -9],\n [0, 8, 0],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, -9],\n [3, 7, -7],\n [10, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
123
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 10, 0],\n [-10, 9, 5],\n [-9, 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" } ]
565
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -10, 9],\n [-1, -4, -4],\n [-9, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -6, 8],\n [-6, 0, 2],\n [8, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
156
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -3, 4],\n [0, -6, -3],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
108
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 9, 8],\n [-9, -1, -4],\n [-10, 4, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -3, -4],\n [0, 9, -3],\n [0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
910
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 6, 6],\n [4, 10, 6],\n [10, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -5, 4],\n [0, 8, -4],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
944
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, 0],\n [-2, 8, 0],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
796
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, -9],\n [0, -8, -6],\n [0, 0, -1]]\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[[-2, 1, 1],\n [0, -1, 2],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
984
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 0, 4],\n [0, 9, 6],\n [4, 6, -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" } ]
451
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 9, 9],\n [0, -9, 6],\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" } ]
180
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 5, 1],\n [4, 0, 5],\n [10, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
124
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -5, 8],\n [0, -10, 5],\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" } ]
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 2, 0],\n [2, -6, 0],\n [0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, -5],\n [4, 0, -10],\n [2, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
746
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -9, -2],\n [-6, 6, 4],\n [0, 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" } ]
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 3, -5],\n [0, -3, 6],\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" } ]
919
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -2, -2],\n [-2, -4, 0],\n [-2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -5, -8],\n [-5, 5, 5],\n [-8, 5, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
455
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 8, 6],\n [4, 3, -7],\n [-4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
551
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 2, 2],\n [2, -7, 0],\n [2, 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" } ]
677
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 8, 0],\n [8, 4, -2],\n [0, -2, -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" } ]
336
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -10, 8],\n [0, -10, -7],\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" } ]
920
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 1, -8],\n [9, -2, -7],\n [-7, 5, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
962
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -1, -6],\n [0, -3, -8],\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" } ]
30
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -8, -6],\n [-7, 9, 3],\n [5, 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" } ]
539
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 0, -10],\n [0, -1, 7],\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" } ]
3
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 5, -8],\n [-4, 5, 10],\n [3, -1, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
198
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 6, -1],\n [6, 7, 2],\n [-1, 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" } ]
6
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 2, 9],\n [0, 2, 9],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
936
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, 2],\n [-4, -7, -8],\n [2, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH