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[ { "content": "Determine the value of det(A) where A =\n[[10, 0, 5, 11],\n [-6, -10, 6, 4],\n [7, 12, -8, 4],\n [9, 5, -1, -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" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -5, 9, -3],\n [0, 8, -11, -1],\n [0, 0, -12, -11],\n [0, 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" } ]
968
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 6, 5, 1],\n [6, -3, 10, 11],\n [5, 10, 8, 0],\n [1, 11, 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" } ]
596
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 10, 12, -8],\n [0, -8, -3, -5],\n [0, 0, -7, -1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 9, 4, 8],\n [0, -8, 9, 6],\n [0, 0, -11, 6],\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" } ]
112
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 12, 8, 12],\n [0, 11, -8, 10],\n [10, -4, 7, -10],\n [-9, 8, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
405
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -4, -10, -8],\n [0, -3, 5, 5],\n [0, 0, 3, -1],\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" } ]
28
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -11, 0, 6],\n [-10, 6, 9, 11],\n [7, 8, 4, -12],\n [-4, 3, -4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
177
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -5, 10, -5],\n [0, 7, -7, -8],\n [0, 0, -5, -11],\n [0, 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" } ]
50
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 1, 3, 9],\n [0, -2, -6, -10],\n [0, 0, -9, 0],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 2, 8, -12],\n [0, -12, -11, 9],\n [0, 0, -12, -1],\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" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -9, -10, -9],\n [0, 4, -7, -9],\n [0, 0, -1, 7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -2, -1, 5],\n [-4, -12, -6, -10],\n [9, -12, -8, 7],\n [1, 12, 4, -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" } ]
400
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 5, -7, 0],\n [-6, 8, 7, 5],\n [6, -9, 1, -9],\n [1, 3, 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" } ]
495
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -11, -2, -7],\n [0, -11, -12, -8],\n [0, 0, -9, 1],\n [0, 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" } ]
535
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -11, 9, -6],\n [-11, -3, 6, -4],\n [9, 6, 7, 4],\n [-6, -4, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 6, 8, -6],\n [6, 4, 4, -6],\n [8, 4, 9, -8],\n [-6, -6, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -7, -6, -7],\n [0, -3, -11, -4],\n [0, 0, -5, 2],\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" } ]
895
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, 2, 6],\n [-2, 6, -9, 3],\n [2, -9, 1, -1],\n [6, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
310
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 11, 12, -12],\n [0, 7, -8, -2],\n [0, 0, 3, 7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -3, -12, -1],\n [-1, -6, 8, 0],\n [6, 9, 10, 1],\n [6, -11, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
278
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -11, 2, 0],\n [0, -7, 2, 12],\n [0, 0, 6, 7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
984
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -12, 2, 8],\n [9, 1, 10, -4],\n [-12, -12, 4, -9],\n [-4, 5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
602
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 8, -9, -12],\n [-11, -3, 5, 3],\n [-7, -8, -5, 11],\n [6, -5, -4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
508
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 5, -11, -3],\n [0, -2, 11, -8],\n [0, 0, -11, 5],\n [0, 0, 0, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -5, 12, 8],\n [2, -7, 5, 10],\n [9, -11, 0, 9],\n [8, -5, 9, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
706
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -4, -2, 0],\n [-4, 3, -2, -4],\n [-2, -2, 4, -8],\n [0, -4, -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" } ]
192
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 2, 3, -9],\n [0, -7, 2, 7],\n [0, 0, -4, -4],\n [0, 0, 0, -11]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, -9, -2],\n [7, -3, 4, -9],\n [-9, 3, 1, -11],\n [-4, -5, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -11, -3, 0],\n [0, -2, 10, 7],\n [0, 0, 3, -6],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 8, 11, 12],\n [0, -2, 1, -7],\n [0, 0, -11, 6],\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" } ]
822
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -7, -6, 7],\n [0, 5, 3, 5],\n [0, 0, -8, 6],\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" } ]
800
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 3, 6, -3],\n [0, 11, -10, 7],\n [0, 0, 11, -10],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
338
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 12, 9, 9],\n [0, 3, -8, 11],\n [0, 0, 9, 5],\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" } ]
271
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -4, 4, -5],\n [-4, 0, -2, 4],\n [4, -2, 8, -4],\n [-5, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
556
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -9, -4, -3],\n [6, -8, -12, -10],\n [-9, 3, -6, 3],\n [2, 8, -4, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 3, -6, 2],\n [0, 5, -8, -11],\n [0, 0, 9, -10],\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" } ]
720
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 7, 8, 11],\n [-11, -3, 3, 3],\n [-10, 8, -12, -5],\n [6, 3, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
787
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 8, 4, 1],\n [8, -9, 2, 6],\n [4, 2, -8, 2],\n [1, 6, 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" } ]
308
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 2, -1, -9],\n [0, -2, -3, 11],\n [0, 0, -6, -8],\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" } ]
960
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -4, 6, -3],\n [-4, -1, 11, 8],\n [6, 11, 10, 3],\n [-3, 8, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
275
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -10, -8, -8],\n [12, 7, -1, 11],\n [-3, -4, -9, 0],\n [7, -2, 1, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
970
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -1, 1],\n [0, -3, -3, -7],\n [-1, -3, -1, -2],\n [1, -7, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
147
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -8, -6, 9],\n [-5, -8, -4, 9],\n [-4, -8, 10, -1],\n [4, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 4, 2, 6],\n [4, -6, -1, -2],\n [2, -1, 2, 4],\n [6, -2, 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" } ]
253
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 11, 5, 6],\n [0, 5, 10, -3],\n [0, 0, 3, 11],\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" } ]
900
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, -7, 12],\n [0, -2, 0, -12],\n [0, 0, 1, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, -8, -6],\n [0, 12, 0, 2],\n [0, 0, -6, 0],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 5, -8, -3],\n [6, 11, -4, 2],\n [-10, -11, -2, -10],\n [3, -1, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
550
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 3, -2, 9],\n [0, -6, -10, 1],\n [0, 0, 6, -4],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 1, 3, 1],\n [-12, 6, 10, 9],\n [-6, -11, 6, 11],\n [-12, 4, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
492
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -2, -5, 3],\n [-10, -11, 4, 1],\n [1, -11, 3, 2],\n [-11, -6, 7, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
654
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 8, -7, 3],\n [-4, 9, 3, 10],\n [-11, 8, -12, 1],\n [9, 9, 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" } ]
15
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 7, 12, 2],\n [2, -5, 4, -1],\n [-2, 12, -1, 8],\n [-7, 2, 3, -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" } ]
520
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -6, -6, 2],\n [-6, -5, 0, -4],\n [-6, 0, 5, 5],\n [2, -4, 5, 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" } ]
96
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 8, 0, 12],\n [-1, -2, -2, 0],\n [10, -12, 2, -7],\n [5, 9, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -4, 9, 7],\n [-4, -2, 4, 0],\n [9, 4, -11, -8],\n [7, 0, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
282
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 0, 6, -10],\n [12, 6, 2, 3],\n [-4, -1, 0, -8],\n [5, 11, -4, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
458
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 6, 9, 12],\n [-1, -2, 11, -3],\n [-6, -12, -2, -3],\n [11, 1, 9, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
656
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 0, 0, -1],\n [0, -10, -6, -2],\n [0, -6, 5, 4],\n [-1, -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" } ]
926
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 4, 7, 12],\n [8, -2, -2, -6],\n [-8, 0, 2, 7],\n [-11, -4, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
992
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -6, 10, -2],\n [0, 7, 0, 0],\n [0, 0, -1, 6],\n [0, 0, 0, -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" } ]
916
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 2, 0, -9],\n [2, 0, 10, 6],\n [0, 10, -7, 5],\n [-9, 6, 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" } ]
72
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -10, -2, -1],\n [-10, -7, 2, -9],\n [-2, 2, -4, 3],\n [-1, -9, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, 0, 0],\n [1, 7, -8, 0],\n [0, -8, 0, -1],\n [0, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
807
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 4, -2, -4],\n [4, 5, 3, -6],\n [-2, 3, 12, -10],\n [-4, -6, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
314
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -11, 6, -8],\n [6, 6, 11, 4],\n [-9, -8, -3, -1],\n [-6, -10, 2, 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" } ]
52
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 2, -2, 11],\n [2, -7, 1, 0],\n [-2, 1, 1, 6],\n [11, 0, 6, -11]]\nRound to the nearest integer, then take the result modulo 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[[-3, 11, 4, 2],\n [11, 2, 4, 6],\n [4, 4, -1, 0],\n [2, 6, 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" } ]
902
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -3, 9, -12],\n [1, -1, -1, -4],\n [10, 10, 5, -9],\n [-1, -7, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 2, 0, 9],\n [2, -8, -6, -8],\n [0, -6, 7, 6],\n [9, -8, 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" } ]
852
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, 12, -5],\n [0, 10, -12, 11],\n [0, 0, -1, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 7, -4, -4],\n [7, 10, 0, -2],\n [-4, 0, 4, 1],\n [-4, -2, 1, -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" } ]
553
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -4, 2, 6],\n [-4, -9, 8, -3],\n [2, 8, -6, 2],\n [6, -3, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
264
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 7, 6, -12],\n [-6, -4, -3, 3],\n [9, 4, -12, 12],\n [-6, 6, -7, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -10, -4, -9],\n [6, -11, 7, -10],\n [-2, 4, -11, -12],\n [3, -11, 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" } ]
639
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 10, -10, -4],\n [0, 3, -7, -4],\n [0, 0, -8, 4],\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" } ]
864
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 12, -4, -10],\n [0, 6, 2, -8],\n [0, 0, 9, -6],\n [0, 0, 0, 12]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -11, -7, -1],\n [0, -10, -7, 5],\n [0, 0, 9, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -10, 10, -11],\n [3, 12, 5, -1],\n [12, 3, 8, -9],\n [11, 9, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
211
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 6, 2, -2],\n [6, 9, 2, 0],\n [2, 2, -2, -8],\n [-2, 0, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -4, 2, -7],\n [0, -4, 2, 6],\n [0, 0, 9, -6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -4, -8, -6],\n [-4, -5, 5, 4],\n [-8, 5, 12, 6],\n [-6, 4, 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" } ]
252
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, -6, -12],\n [0, -6, 0, -6],\n [0, 0, 1, 10],\n [0, 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" } ]
784
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 12, -4, -2],\n [3, -7, 3, -10],\n [-10, -12, -12, 4],\n [-9, 11, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
428
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 0, -6, 2],\n [0, -6, 2, 4],\n [-6, 2, -6, 4],\n [2, 4, 4, 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" } ]
888
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 4, -5, 7],\n [4, 11, -1, 2],\n [-5, -1, -1, 2],\n [7, 2, 2, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -10, 12, 2],\n [4, -6, -6, -5],\n [-8, -11, -2, -5],\n [9, 1, -11, -2]]\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[[5, 0, -4, 7],\n [0, -11, -2, 0],\n [-4, -2, 9, -2],\n [7, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
374
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -6, -2, -9],\n [-5, -2, 7, 8],\n [7, -8, 7, 9],\n [-10, 5, -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" } ]
453
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 0, 5, -4],\n [0, 6, 0, 9],\n [5, 0, 10, 1],\n [-4, 9, 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" } ]
243
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 10, -12, 8],\n [0, -8, -2, -1],\n [2, -7, 4, 4],\n [12, -4, -11, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
657
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -12, -1, 3],\n [0, 3, -2, 1],\n [-8, -9, 0, 12],\n [0, -9, -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" } ]
596
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -8, -7, -1],\n [9, 8, -12, 11],\n [6, -6, 0, -9],\n [-8, 2, 4, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
182
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -6, -4],\n [2, 9, -4, 4],\n [-6, -4, -7, -1],\n [-4, 4, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
379
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 7, 12, -4],\n [-9, 6, 6, 3],\n [-4, 8, -6, 4],\n [1, 8, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
826
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, -2, 12],\n [0, -10, 7, -3],\n [-2, 7, -8, 1],\n [12, -3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
614
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 0, 12, -4],\n [0, -4, 2, -7],\n [0, 0, 8, -6],\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" } ]
352
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -4, -3, -11],\n [-2, 11, -7, 2],\n [6, 9, 7, 3],\n [0, -4, -6, 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" } ]
802
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, 0, -4],\n [8, 3, 2, -1],\n [0, 2, -11, 0],\n [-4, -1, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
56
MATH