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[ { "content": "What is the determinant of the matrix:\n[[9, -10, -2, 4],\n [-10, -4, -4, -6],\n [-2, -4, 5, 0],\n [4, -6, 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" } ]
916
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 11, 0, 11],\n [0, 2, -2, 12],\n [0, 0, -8, -3],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
888
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, 9, 7],\n [-11, -8, -9, -2],\n [-11, -8, 11, 1],\n [-1, -9, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
517
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 6, -2, -8],\n [0, 10, -10, -4],\n [0, 0, 3, 10],\n [0, 0, 0, -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" } ]
40
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -8, 6, 4],\n [-8, -4, 4, 8],\n [6, 4, -12, -6],\n [4, 8, -6, -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" } ]
0
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, -1, -12],\n [2, 9, 8, 1],\n [-1, 8, 1, 2],\n [-12, 1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
860
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, 0, -2],\n [3, -3, -2, -6],\n [0, -2, 6, -7],\n [-2, -6, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
594
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 9, -6, -4],\n [0, -2, -4, -8],\n [0, 0, -12, -8],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -9, 3, -8],\n [-12, -3, 6, 4],\n [-2, -3, 8, -3],\n [9, 12, 8, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
93
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -10, -3, 1],\n [0, 4, -9, 9],\n [0, 0, -12, -1],\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" } ]
480
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 9, 9, -8],\n [-7, -4, 3, 10],\n [-11, 3, -4, -2],\n [11, -5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
470
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 3, -6, -5],\n [0, 1, 12, 12],\n [0, 0, -1, -2],\n [0, 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" } ]
972
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 9, 9, -8],\n [9, 3, -4, -7],\n [-12, 11, -12, -5],\n [0, -1, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
335
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -2, 10, 5],\n [-2, -1, -2, 4],\n [10, -2, 6, 4],\n [5, 4, 4, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
938
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 8, 6, 5],\n [0, -8, 3, -5],\n [0, 0, -4, 5],\n [0, 0, 0, 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" } ]
408
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 0, 0, -5],\n [0, -8, -8, -10],\n [0, 0, 9, 3],\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" } ]
576
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -1, 4, -2],\n [-1, 7, -4, 7],\n [4, -4, -5, 9],\n [-2, 7, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
394
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 1, -3, 0],\n [1, -4, -8, -10],\n [-3, -8, 5, -4],\n [0, -10, -4, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 8, 1, -3],\n [8, -8, -8, 0],\n [1, -8, -3, 0],\n [-3, 0, 0, 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" } ]
192
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -6, -4, 2],\n [-6, -4, 0, 1],\n [-4, 0, 0, -4],\n [2, 1, -4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 9, 1, 10],\n [0, -5, 0, -11],\n [12, 6, 3, -7],\n [2, -7, 9, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
649
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -7, -8, 5],\n [0, -6, -2, 1],\n [0, 0, 9, -2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -12, -9, -11],\n [0, 3, 6, -7],\n [0, 0, -1, 2],\n [0, 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" } ]
784
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -2, 1, -4],\n [-2, -11, -4, 6],\n [1, -4, 6, 4],\n [-4, 6, 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" } ]
297
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 4, 0, -6],\n [4, 9, -4, -6],\n [0, -4, -11, -6],\n [-6, -6, -6, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
472
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 8, -4, 4],\n [8, -10, 4, 0],\n [-4, 4, 6, 1],\n [4, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
642
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 1, -10, 1],\n [-10, -10, -6, -7],\n [10, 2, 3, 7],\n [2, 4, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 10, 2, -5],\n [5, 12, -6, -2],\n [-1, -1, 11, -11],\n [-11, 11, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
755
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 3, -1, 5],\n [-8, 11, -12, 12],\n [10, -12, -10, -12],\n [-10, 7, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
724
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -12, 10, -5],\n [-3, -9, 11, 0],\n [-1, -7, -7, 12],\n [-7, 11, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
536
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 5, 10, -4],\n [5, -7, -2, 8],\n [10, -2, -6, 2],\n [-4, 8, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
910
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -8, 0, 0],\n [-8, 9, 1, 2],\n [0, 1, -5, 2],\n [0, 2, 2, -11]]\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[[8, -1, -4, -4],\n [-1, 4, -6, -1],\n [-4, -6, 12, -9],\n [-4, -1, -9, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
633
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -5, 1, -11],\n [-3, -3, -4, 8],\n [8, -12, -5, 1],\n [12, -5, -12, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
748
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -9, -8, 11],\n [6, -1, 11, 0],\n [12, -2, 8, -10],\n [6, 8, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -4, -7, 1],\n [-4, -10, -10, 8],\n [-7, -10, -11, -2],\n [1, 8, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
876
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -12, -8, -1],\n [5, 9, 8, 5],\n [-9, -4, 9, 12],\n [4, 8, 12, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
452
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -9, 1, 10],\n [0, -12, -1, 12],\n [0, 0, 7, 2],\n [0, 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" } ]
688
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -6, 9, 5],\n [0, 6, 0, -12],\n [0, 0, 10, 8],\n [0, 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" } ]
920
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -9, 10, -12],\n [0, 4, 6, -6],\n [0, 0, 6, 8],\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" } ]
96
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -2, 8, 2],\n [0, 1, -1, 10],\n [0, 0, 6, 0],\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" } ]
108
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 1, -1, -3],\n [0, 7, 5, -4],\n [0, 0, 6, 12],\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" } ]
512
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 6, 11, 3],\n [-4, -11, 8, 11],\n [-6, -12, 0, -4],\n [-10, 11, 5, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -4, -8, 12],\n [0, -9, -11, -1],\n [0, 0, 12, -1],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
752
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -6, -6, -2],\n [0, -12, 12, -3],\n [9, -9, -7, 8],\n [-12, 2, -12, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
556
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 8, 7, -2],\n [8, -9, -7, -3],\n [7, -7, -8, 0],\n [-2, -3, 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" } ]
388
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -10, -7, -3],\n [-10, -5, 2, 4],\n [-7, 2, 1, -2],\n [-3, 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" } ]
560
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 3, 9, 4],\n [0, -1, -2, 6],\n [0, 0, 2, -7],\n [0, 0, 0, -5]]\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[[5, 8, 12, -5],\n [0, 9, 8, -5],\n [0, 0, 6, 4],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
650
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 4, 2, -4],\n [4, -5, 7, 4],\n [2, 7, 3, 5],\n [-4, 4, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 8, 6, 6],\n [-4, -5, 2, -5],\n [-1, -11, 4, 10],\n [-6, -3, 8, -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" } ]
924
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -6, -12, 0],\n [0, 1, -8, 5],\n [0, 0, 9, -2],\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" } ]
964
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -7, 6, -12],\n [2, -3, -7, 10],\n [7, -1, -5, 4],\n [6, 3, -12, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 0, -6, 11],\n [10, 12, 1, -1],\n [3, -12, 7, -2],\n [-5, -6, 11, -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" } ]
500
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -4, 11, -5],\n [5, -10, -5, 2],\n [-12, -1, -4, 12],\n [4, -6, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
542
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -5, -2, -8],\n [-5, -5, 2, 2],\n [-2, 2, 12, 0],\n [-8, 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" } ]
576
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -6, -8, -10],\n [-6, -1, 4, 0],\n [-8, 4, -8, 0],\n [-10, 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" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 4, -2, -2],\n [4, 3, -2, -6],\n [-2, -2, 1, -3],\n [-2, -6, -3, 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" } ]
920
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, 8, -2],\n [10, 6, 9, 6],\n [8, 9, 12, -1],\n [-2, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
758
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, 2, 4],\n [2, -10, -9, 5],\n [2, -9, 6, -6],\n [4, 5, -6, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
811
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -6, 5, 0],\n [-6, 2, 6, -1],\n [5, 6, -10, 11],\n [0, -1, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
803
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 11, 4, -10],\n [-7, -9, -1, -9],\n [-8, -2, -6, 12],\n [10, 6, -9, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
998
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 4, -12, -9],\n [-9, 8, 10, -4],\n [1, -4, 10, 5],\n [-7, 10, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -2, 7, 4],\n [-2, -7, 0, -1],\n [7, 0, 12, -2],\n [4, -1, -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" } ]
674
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -1, 6, 2],\n [6, -9, 1, -10],\n [12, 8, 10, 3],\n [11, -9, 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" } ]
962
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -4, -8, -8],\n [-4, 3, -2, 10],\n [-8, -2, 1, -2],\n [-8, 10, -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" } ]
461
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 10, -1, 5],\n [0, -5, -4, -3],\n [0, 0, 5, 6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
750
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 7, -3, 0],\n [6, 4, -4, 6],\n [-7, -8, -6, 10],\n [5, -8, 7, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 6, 5, 8],\n [0, 12, -9, -10],\n [0, 0, 2, -5],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 8, 12, -10],\n [0, 5, 3, 1],\n [0, 0, 3, 6],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -8, 3, -12],\n [0, -8, -7, -5],\n [0, 0, 10, 7],\n [0, 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" } ]
80
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 11, -4, -3],\n [3, 5, -6, 7],\n [-7, -1, 8, 12],\n [-7, -4, 5, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
202
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -1, 5, -11],\n [0, 8, 5, 12],\n [0, 0, -2, -1],\n [0, 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" } ]
320
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -2, -8, -10],\n [-2, 4, 2, 11],\n [2, -7, -8, -8],\n [-7, -9, -3, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
688
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -6, 7, 9],\n [-2, -6, 10, -5],\n [7, 7, -11, 4],\n [-1, 1, 12, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
841
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 0, -4, 4],\n [0, 4, -6, -3],\n [-4, -6, -12, 4],\n [4, -3, 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" } ]
696
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 4, 5, 10],\n [0, -2, -6, 2],\n [0, 0, 6, -3],\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" } ]
76
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, -1, -11],\n [0, 11, 11, -4],\n [0, 0, -3, 10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
178
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, -7, 2, 4],\n [-7, 6, -1, 3],\n [2, -1, 9, 9],\n [4, 3, 9, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
660
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -9, 2, -9],\n [0, 12, -8, 2],\n [0, 0, 6, 12],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -2, 5, -8],\n [-5, 0, -7, -2],\n [8, 5, 9, 12],\n [-2, -4, 11, -11]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -6, 8, 9],\n [-1, -12, -9, -1],\n [10, 1, 4, 12],\n [-4, 4, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
683
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -6, -11, -3],\n [0, 1, -10, 7],\n [0, 0, 2, 12],\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" } ]
176
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 7, 8, -10],\n [0, 5, -9, -5],\n [0, 0, 12, -5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 8, -5, 5],\n [0, -4, -7, 1],\n [0, 0, -12, 9],\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" } ]
992
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -5, -3, -10],\n [1, 12, -2, -9],\n [-12, -12, 11, 3],\n [1, -7, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
155
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -6, -12, -9],\n [0, -12, 1, 6],\n [0, 0, 7, -8],\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" } ]
236
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 12, -5, -11],\n [12, -12, 6, 5],\n [12, -2, 1, 3],\n [-3, -10, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
926
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 4, 10, 1],\n [4, 8, 0, 7],\n [10, 0, 4, -7],\n [1, 7, -7, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -4, 7, -5],\n [-4, 11, -6, 6],\n [7, -6, 9, -2],\n [-5, 6, -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" } ]
202
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -5, 8, 2],\n [0, 11, -6, -5],\n [0, 0, -3, 2],\n [0, 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" } ]
584
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 7, -1, 1],\n [0, 5, 1, -10],\n [0, 0, 1, -9],\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" } ]
955
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, -4, -5],\n [2, -12, 6, -2],\n [-4, 6, -3, 2],\n [-5, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
176
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 4, 0, -4],\n [4, 9, -10, -12],\n [0, -10, -3, -6],\n [-4, -12, -6, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
866
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 10, -2, 9],\n [-9, 4, 0, -10],\n [1, 1, 4, 10],\n [-10, 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" } ]
810
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 0, 8, 2],\n [0, -9, -6, 10],\n [8, -6, 0, 3],\n [2, 10, 3, 7]]? 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[[-3, -8, 1, -9],\n [6, 0, 11, -12],\n [-7, -7, -2, -2],\n [10, 7, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
609
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 4, 0, -5],\n [4, -3, 2, -2],\n [0, 2, -5, -1],\n [-5, -2, -1, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
245
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -1, -12, 3],\n [0, -11, -5, 10],\n [0, 0, 9, -8],\n [0, 0, 0, 8]]\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[[-6, 2, 12, 2],\n [2, -6, 2, 7],\n [12, 2, 8, 4],\n [2, 7, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
808
MATH