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[ { "content": "What is the determinant of the matrix:\n[[-11, 2, -6, 12],\n [-6, -7, 4, 2],\n [-12, -8, -5, 5],\n [6, -4, -5, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
227
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -2, 0, -10],\n [-2, 11, 0, -10],\n [0, 0, 9, -9],\n [-10, -10, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 11, 6, 12],\n [-10, -4, 11, 3],\n [-1, -2, -8, -12],\n [-1, 7, -8, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
788
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -2, 7, -12],\n [-1, -8, -5, -10],\n [9, -8, -11, 9],\n [10, -9, -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" } ]
60
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -2, 8, -7],\n [-2, 12, -3, 4],\n [8, -3, -10, -2],\n [-7, 4, -2, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
689
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 0, -6, 6],\n [0, -7, 4, -8],\n [-6, 4, -9, 8],\n [6, -8, 8, -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" } ]
678
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -7, -10, 2],\n [-7, 3, 6, 2],\n [-10, 6, -9, -4],\n [2, 2, -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" } ]
222
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -4, -2, -2],\n [-4, 10, 5, 0],\n [-2, 5, 7, -4],\n [-2, 0, -4, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -12, -10, 3],\n [-7, -12, -8, -6],\n [11, 7, 7, 7],\n [9, -7, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
706
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -3, -9, 5],\n [-3, -1, 10, -7],\n [-5, -12, 4, -10],\n [-8, -8, 10, -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" } ]
130
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 12, 7, -12],\n [1, 12, -10, -12],\n [10, 11, 3, -12],\n [12, -7, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
255
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -4, -6, 0],\n [-4, 12, 0, 6],\n [-6, 0, 10, -2],\n [0, 6, -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" } ]
848
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 7, 11, 8],\n [0, 2, 8, -12],\n [0, 0, 4, 2],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 0, -2, -2],\n [0, -8, 10, 0],\n [-2, 10, 2, 6],\n [-2, 0, 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" } ]
856
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, -2, 4],\n [6, -1, -3, -11],\n [10, -1, 2, -5],\n [12, 5, 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" } ]
876
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -7, -11, -7],\n [-5, -6, -10, 11],\n [-7, 12, 9, 5],\n [-8, -6, 11, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
341
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -9, 7, -6],\n [0, 9, -12, -11],\n [0, 0, -1, -10],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -2, -7, 8],\n [0, 11, -12, -5],\n [0, 0, -6, 2],\n [0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
504
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -4, -9, 1],\n [9, -7, -3, 2],\n [-3, -12, -1, -2],\n [0, 11, -3, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
635
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -8, -7, -10],\n [0, 11, 8, -5],\n [0, 0, -9, 11],\n [0, 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" } ]
872
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -3, 3, 2],\n [0, -4, 11, 3],\n [0, 0, 10, 3],\n [0, 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" } ]
200
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 9, 8, -11],\n [5, 3, 10, 0],\n [-10, 9, -1, -9],\n [-11, -2, 11, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
766
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 7, 2, 6],\n [-10, 5, -2, 1],\n [-6, -9, 8, 12],\n [-3, -11, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
154
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -8, 9, -10],\n [5, 11, 12, -2],\n [-8, 0, -11, -11],\n [2, -10, 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" } ]
716
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -8, -11, -6],\n [0, -6, 2, 4],\n [0, 0, -1, 1],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
660
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -1, 7, 8],\n [3, -9, 0, 1],\n [6, -9, -9, -3],\n [-9, -11, -11, 12]]\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": "Determine the value of det(A) where A =\n[[-5, -3, -8, 6],\n [0, 10, -9, 5],\n [0, 0, -5, -11],\n [0, 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" } ]
500
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -2, -12, -8],\n [0, 1, -5, -8],\n [0, 0, -9, -4],\n [0, 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" } ]
946
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -5, -8, 12],\n [5, -4, 0, 1],\n [-11, -3, 6, -6],\n [-5, -10, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
246
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -12, 7, -8],\n [0, -9, 8, 7],\n [0, 0, -10, -8],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
730
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -1, -1, -2],\n [12, -5, -4, -1],\n [4, 9, 6, 11],\n [8, -12, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 4, 1, -4],\n [4, 12, 0, 4],\n [1, 0, 4, 2],\n [-4, 4, 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" } ]
332
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 6, -1, 0],\n [6, -3, 4, -3],\n [-1, 4, 1, 4],\n [0, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -3, 7, -10],\n [8, -2, 1, 8],\n [-12, 8, 2, 0],\n [-8, 7, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
248
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 7, 0, -8],\n [0, -10, -4, 8],\n [3, -10, 6, 7],\n [-7, -1, -8, 8]]\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[[-4, 6, 8, -1],\n [6, 9, -4, -2],\n [8, -4, 9, -4],\n [-1, -2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
367
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 7, -9, -10],\n [0, -9, -2, 6],\n [0, 0, 10, -10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -3, -2, -12],\n [10, -2, -6, -12],\n [-5, 12, -4, 1],\n [4, -3, -1, -12]]\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" } ]
118
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 2, 4, 2],\n [2, -1, 7, -8],\n [4, 7, -4, -8],\n [2, -8, -8, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
767
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -9, 2, 0],\n [0, -10, -10, 8],\n [0, 0, 8, 4],\n [0, 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" } ]
0
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, -12, -9, -6],\n [-12, 1, 2, -10],\n [-9, 2, 5, -6],\n [-6, -10, -6, -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" } ]
244
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 0, 5, 0],\n [0, 7, 7, 0],\n [0, 0, -1, -12],\n [0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
230
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 5, -4, 9],\n [0, 6, -12, 2],\n [0, 0, -12, -3],\n [0, 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" } ]
840
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 0, 8, -3],\n [0, 5, -2, -10],\n [8, -2, 1, -2],\n [-3, -10, -2, -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" } ]
31
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -8, 7, 6],\n [-8, -4, -10, 2],\n [7, -10, -2, -4],\n [6, 2, -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" } ]
116
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 5, 7, 1],\n [0, 7, 1, 9],\n [0, 0, -8, -5],\n [0, 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" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -7, 5, 6],\n [3, -4, -10, -11],\n [0, -5, 6, 3],\n [12, 2, 12, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
418
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, -7, -4],\n [2, -10, 2, 1],\n [-7, 2, 6, -8],\n [-4, 1, -8, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
701
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -3, 2, 10],\n [-3, -10, 0, 4],\n [2, 0, 3, 2],\n [10, 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" } ]
654
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -11, -4, -11],\n [0, 12, 12, -2],\n [0, 0, 10, 2],\n [0, 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" } ]
640
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 6, 10, 4],\n [0, 9, 5, 2],\n [0, 0, 5, 10],\n [0, 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" } ]
865
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -3, 1, -7],\n [-7, -10, 5, 7],\n [-5, 0, -9, -11],\n [-12, -4, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
792
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 4, -8, 2],\n [4, 11, 2, 0],\n [-8, 2, -7, 2],\n [2, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
372
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 10, -12, -5],\n [12, 6, 8, 2],\n [-7, 2, 1, -10],\n [-10, 6, -8, -12]]\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" } ]
104
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 6, 7, 12],\n [0, -5, 7, -7],\n [0, 0, -8, 7],\n [0, 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" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -11, 2, -11],\n [8, -2, 3, 11],\n [12, 5, 0, 9],\n [-10, 7, 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" } ]
646
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 2, -1, 2],\n [2, 0, -7, 6],\n [-1, -7, -11, -4],\n [2, 6, -4, 11]]\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" } ]
388
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 0, 10, -9],\n [0, 2, 7, 9],\n [0, 0, 5, 6],\n [0, 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" } ]
120
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -12, -7, -1],\n [-11, 11, 4, 1],\n [7, 3, -8, 9],\n [-12, -12, 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" } ]
854
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -10, 2, -10],\n [6, 10, 1, -2],\n [-1, 6, -4, 12],\n [-8, -10, -9, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 6, -3, -3],\n [-7, 9, -2, -12],\n [-9, -6, -6, -5],\n [-1, 4, -2, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
950
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -4, 1, 6],\n [0, -6, 5, -2],\n [0, 0, -6, 1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
676
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, 6, 4],\n [-2, 3, -2, 4],\n [6, -2, -7, -1],\n [4, 4, -1, 4]]\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[[4, -11, -6, 4],\n [0, -1, 4, 9],\n [0, 0, -4, -7],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -4, 0, 7],\n [0, -8, 12, -2],\n [0, 0, 4, -8],\n [0, 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" } ]
920
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -9, -7, 8],\n [0, 7, 5, 10],\n [0, 0, -4, -4],\n [0, 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" } ]
804
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 6, -12, 4],\n [0, -8, 10, 11],\n [0, 0, 4, -1],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
792
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 5, -12, -5],\n [0, 10, -8, 0],\n [0, 0, -6, -7],\n [0, 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" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 2, 4, -3],\n [2, 11, -3, -6],\n [4, -3, -9, -8],\n [-3, -6, -8, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, 5, 8],\n [0, -7, 11, -12],\n [0, 0, -1, 1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
986
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -10, -6, 2],\n [-10, 0, -1, -6],\n [-6, -1, -1, 8],\n [2, -6, 8, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
977
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 0, 7, -8],\n [5, -4, 11, 6],\n [10, -7, -11, 0],\n [8, -6, -11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
734
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 12, -8, -2],\n [0, -8, -10, 2],\n [0, 0, -3, 1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 12, -2, 2],\n [1, -6, 3, 7],\n [-8, 5, -8, -7],\n [-7, 10, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
369
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -9, 10, 2],\n [0, -9, 10, -4],\n [0, 0, -1, 12],\n [0, 0, 0, 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" } ]
540
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 1, -8, 1],\n [1, 4, -2, 6],\n [-8, -2, -5, 10],\n [1, 6, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
88
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -5, 12, -1],\n [-1, 0, -6, 8],\n [11, 8, -3, 7],\n [-3, -8, 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" } ]
968
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -3, -2, -2],\n [-3, -3, -6, 2],\n [-2, -6, 8, 8],\n [-2, 2, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 4, 8, -2],\n [0, 1, 1, 10],\n [0, 0, 3, 2],\n [0, 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" } ]
324
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -5, 0, 11],\n [0, -1, 9, 10],\n [0, 0, -2, 5],\n [0, 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" } ]
48
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, -12, -6],\n [0, -1, 4, -7],\n [0, 0, -4, 9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 10, 2, 7],\n [6, 4, -1, -8],\n [9, 11, 8, -9],\n [-10, -11, -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" } ]
489
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 8, -8, 6],\n [0, 1, 8, 7],\n [0, 0, 11, -9],\n [0, 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" } ]
208
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, 1, -6],\n [4, 10, 5, 1],\n [1, 5, 3, -2],\n [-6, 1, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
617
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 6, -3, 0],\n [6, 7, -8, -12],\n [-3, -8, -12, 0],\n [0, -12, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
423
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -5, -4, -4],\n [-5, -7, -2, 8],\n [-4, -2, 3, -4],\n [-4, 8, -4, -11]]? 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": "What is the determinant of the matrix:\n[[1, -9, 1, 2],\n [0, 5, 9, -11],\n [0, 0, -12, -7],\n [0, 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" } ]
240
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 7, -5, 8],\n [0, 4, 5, 3],\n [0, 0, -12, -7],\n [0, 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" } ]
192
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 12, 12, -1],\n [-9, -9, 2, -11],\n [8, 4, -8, -12],\n [9, 11, 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" } ]
568
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -11, 0, -8],\n [2, -4, 7, 0],\n [2, 6, -11, 0],\n [-3, 10, -11, 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" } ]
432
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -9, 1, -9],\n [6, -10, -11, 8],\n [7, 11, -4, 6],\n [4, -2, 5, 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" } ]
626
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 4, 2, -4],\n [4, -2, 2, -2],\n [2, 2, -11, -4],\n [-4, -2, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -9, -10, 8],\n [-9, -6, -6, 2],\n [-10, -6, 3, 11],\n [8, 2, 11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
927
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, -2, 4],\n [6, 5, 2, -4],\n [-2, 2, 7, -4],\n [4, -4, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
986
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 8, 0, 0],\n [0, -9, 7, 10],\n [0, 0, 2, -10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 1, -9, -2],\n [-7, 4, 5, -6],\n [10, -1, -2, 5],\n [-5, 5, -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" } ]
763
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 4, 5, -8],\n [4, 6, 2, -6],\n [5, 2, 8, -2],\n [-8, -6, -2, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
438
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 1, -9, 9],\n [8, 7, 12, 3],\n [-12, -9, 6, 11],\n [-9, 0, -11, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
742
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -2, -10, 4],\n [-4, -3, -2, -12],\n [12, 3, 8, 11],\n [-10, -10, 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" } ]
446
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 2, -2, -1],\n [2, 1, 0, 4],\n [-2, 0, 8, -2],\n [-1, 4, -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" } ]
140
MATH