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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -9, 1],\n [0, 10, -10],\n [3, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -9, 3],\n [-5, 9, -2],\n [3, -6, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
597
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -10, 4],\n [0, -10, 0],\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" } ]
400
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 [-2, 5, 4],\n [7, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
587
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -6, -1],\n [3, -7, 9],\n [-1, 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" } ]
974
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, 1],\n [6, 2, -10],\n [9, 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" } ]
354
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 8, -3],\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" } ]
30
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 8, -2],\n [0, 10, -2],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
500
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -1, 7],\n [0, -1, -4],\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" } ]
994
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 3, 1],\n [-2, 5, -5],\n [7, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
858
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -2, -2],\n [0, -6, 7],\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" } ]
928
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 3, -6],\n [3, 9, 2],\n [-6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
502
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -9, 5],\n [0, -7, 5],\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" } ]
84
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -4, -1],\n [1, 1, -1],\n [-9, 5, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
942
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 3, 10],\n [0, -2, -2],\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" } ]
916
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 10, -6],\n [1, 4, 7],\n [-10, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 2, -9],\n [2, 0, -8],\n [4, 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" } ]
940
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, 3],\n [0, -8, 10],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -6, -8],\n [0, 4, -6],\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" } ]
128
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 1, -4],\n [1, -3, 4],\n [-4, 4, 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" } ]
7
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -5, -2],\n [5, 7, -3],\n [7, 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" } ]
233
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -9, -3],\n [-5, -10, -10],\n [-9, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
805
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 7, 10],\n [0, 5, -10],\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" } ]
360
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -10, 0],\n [6, 5, -10],\n [-10, 10, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
565
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 6, 1],\n [-2, 3, 3],\n [8, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
498
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 3, -8],\n [-1, 7, 2],\n [-7, 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" } ]
974
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -1, 4],\n [0, -2, -2],\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" } ]
820
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -9, -6],\n [3, -2, -3],\n [-4, -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" } ]
882
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -5, 0],\n [0, 9, 5],\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" } ]
486
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 5, -5],\n [2, -1, -5],\n [6, -10, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
731
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -1],\n [2, -6, 8],\n [-1, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
614
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, 2],\n [0, 1, -2],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
970
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 7, 10],\n [10, -3, -8],\n [-3, 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -2],\n [0, -2, -6],\n [-2, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
372
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -10, 9],\n [2, 9, 2],\n [-10, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
966
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, -3],\n [-2, 4, -1],\n [6, -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" } ]
982
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 6, -9],\n [0, -7, 8],\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" } ]
21
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 10, 7],\n [0, -7, 0],\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" } ]
378
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -8, -5],\n [-10, 0, -7],\n [-8, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 4],\n [0, 4, -6],\n [4, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
648
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -6, 5],\n [-6, -6, 3],\n [5, 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" } ]
484
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 3, -1],\n [0, -5, 6],\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" } ]
825
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -5, -10],\n [2, -6, 7],\n [-4, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
808
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -4, -3],\n [-4, -8, -2],\n [-3, -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" } ]
632
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -3, -4],\n [-3, 2, 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" } ]
10
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 3, 5],\n [10, 1, 0],\n [2, 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" } ]
52
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -2, 8],\n [-2, -3, -6],\n [8, -6, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 3, 2],\n [1, 2, 3],\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" } ]
926
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -10, 5],\n [-2, 6, -7],\n [-10, 5, -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" } ]
635
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -4, -1],\n [-4, -8, 0],\n [-1, 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" } ]
720
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -4, -6],\n [-4, -6, 2],\n [-6, 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" } ]
132
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -9, 6],\n [-8, -2, 9],\n [-5, 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" } ]
527
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 8, 9],\n [0, 9, -4],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 0, 7],\n [0, 1, -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" } ]
984
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -6, -7],\n [2, 5, 9],\n [-8, -1, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 7, 4],\n [0, 4, 5],\n [3, -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" } ]
93
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 9],\n [0, -3, -1],\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" } ]
958
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 4, 5],\n [5, 6, -1],\n [10, -10, -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" } ]
494
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 1, 2],\n [1, -6, -1],\n [2, -1, -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" } ]
863
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, -8],\n [0, 1, 4],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
994
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 8, 0],\n [0, 5, -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" } ]
880
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 3, -9],\n [9, -8, -8],\n [-5, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 1, 2],\n [1, -7, -4],\n [2, -4, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
346
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 8, 3],\n [0, -9, -10],\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": "Determine the value of det(A) where A =\n[[-2, -7, 5],\n [8, -8, -6],\n [-7, 7, 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" } ]
766
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -6, -2],\n [-6, 9, 2],\n [-2, 2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
524
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, 9],\n [0, 10, 9],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
440
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 8, 5],\n [8, 9, 4],\n [5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
919
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -4, 2],\n [-4, 2, 1],\n [2, 1, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
973
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 2, -5],\n [2, -6, -3],\n [-5, -3, 7]]\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[[6, -10, 7],\n [0, -6, 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" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -1, -7],\n [0, 8, 7],\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" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -7, -2],\n [0, -1, -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" } ]
16
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 1, -3],\n [-1, 10, 10],\n [-1, -10, -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" } ]
866
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -8, -3],\n [9, -6, 6],\n [-2, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
430
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 7, -7],\n [0, 6, -8],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -6, -2],\n [7, 3, 0],\n [8, 6, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 5, -5],\n [5, -7, 2],\n [-5, 2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 5, 1],\n [0, -4, 0],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -2, -5],\n [5, 4, -5],\n [-1, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 2, 7],\n [0, -3, 3],\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" } ]
90
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 8, 3],\n [9, -10, 0],\n [6, -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" } ]
132
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -8, -4],\n [-9, 1, 9],\n [-10, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 0, -4],\n [0, -5, 5],\n [-4, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
885
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, -4],\n [4, -3, 4],\n [-4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -3, 8],\n [0, 3, 10],\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" } ]
21
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0],\n [-2, 9, 0],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
161
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 2, -8],\n [3, 8, -7],\n [-5, 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" } ]
546
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -9, -10],\n [-1, -7, -8],\n [9, 2, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -1, -8],\n [0, -2, -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" } ]
856
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 8, -2],\n [8, -6, -6],\n [-2, -6, 9]]\nRound to the nearest integer, then take the result modulo 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[[7, -8, -3],\n [6, 3, -7],\n [-8, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, -3],\n [1, 1, 8],\n [-5, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
411
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 2, 4],\n [2, 7, 1],\n [4, 1, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
846
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -7, 0],\n [0, -9, -6],\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" } ]
27
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 4, 0],\n [4, -1, 2],\n [0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
938
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -5, 2],\n [-5, -3, 0],\n [2, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
356
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 3, 1],\n [5, -10, 1],\n [10, 10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 1, 2],\n [1, 5, 2],\n [2, 2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
389
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 9, -1],\n [-7, 6, -10],\n [-7, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH