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[ { "content": "Determine the value of det(A) where A =\n[[-2, -12, 2, 1],\n [6, 6, 5, -4],\n [10, -9, -6, -11],\n [-5, -6, -11, -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" } ]
9
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 2, -9, 2],\n [2, -9, -8, 2],\n [-9, -8, 9, 4],\n [2, 2, 4, -4]]\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[[-10, -12, 2, -3],\n [-3, 8, 6, 11],\n [-7, -1, -10, -9],\n [10, 1, 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" } ]
469
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 2, -5, 12],\n [0, 8, 7, -1],\n [0, 0, -4, 7],\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" } ]
776
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 1, -6, 0],\n [0, -2, 3, -10],\n [0, 0, -8, 7],\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" } ]
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -6, 6, 10],\n [1, -11, -11, -7],\n [-10, 9, -11, 4],\n [-6, 7, 9, -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" } ]
470
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -11, -5, -11],\n [-9, 8, 3, -12],\n [-8, 3, 10, 7],\n [12, -4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
860
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 9, -4, -8],\n [0, -2, 1, 1],\n [0, 0, 3, 6],\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" } ]
270
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, -9, 2],\n [0, -1, 10, 5],\n [0, 0, 11, -7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
340
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 10, -6, -4],\n [7, 5, 3, 3],\n [2, -12, 10, 12],\n [-1, -9, -11, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
318
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 4, 2, 0],\n [4, 3, 10, -2],\n [2, 10, -5, 9],\n [0, -2, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, 2, 11],\n [-2, 3, -9, -2],\n [-11, 6, -2, -10],\n [-3, -2, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
161
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 10, -5, 12],\n [-3, 2, 10, -9],\n [-5, -8, -11, -8],\n [-4, 7, -6, -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" } ]
796
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 3, 3, -11],\n [0, -2, -10, 6],\n [0, 0, -7, 7],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
294
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 0, 0, 6],\n [0, -8, 10, -3],\n [0, 10, -9, 2],\n [6, -3, 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" } ]
449
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -4, -1, 0],\n [-4, -12, 0, 0],\n [-1, 0, 10, -7],\n [0, 0, -7, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
308
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -10, -5, 3],\n [0, -2, 5, 6],\n [0, 0, -5, -6],\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" } ]
370
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 2, 8, -7],\n [0, 8, -4, -1],\n [0, 0, 5, 8],\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" } ]
320
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -8, -6, 8],\n [-8, -11, 8, 5],\n [-6, 8, -9, -2],\n [8, 5, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -7, -1, -2],\n [-11, -8, -12, 7],\n [-12, -11, -5, -12],\n [6, 1, 4, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
383
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 1, 3, 7],\n [0, 8, 1, -2],\n [0, 0, -4, 8],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
312
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 7, -7, 9],\n [0, 10, -12, 1],\n [0, 0, -4, 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" } ]
320
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 11, 4],\n [7, -8, 5, 0],\n [-9, 10, -3, 0],\n [8, -3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, 6, -4],\n [2, 8, -2, -4],\n [1, 2, -9, -10],\n [-8, 8, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
340
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 12, -8, 12],\n [0, -3, 0, 8],\n [0, 0, 3, -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" } ]
9
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -7, -12, -5],\n [0, 1, 7, 8],\n [0, 0, 4, 11],\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" } ]
776
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -1, 7, 0],\n [-1, 12, 6, 1],\n [7, 6, -4, -8],\n [0, 1, -8, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 0, -7, 7],\n [0, -6, 9, 9],\n [0, 0, -11, 2],\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" } ]
940
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -12, 11, 12],\n [4, -11, 9, -5],\n [-7, -1, 3, 10],\n [12, 9, 1, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
263
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 4, -10, -1],\n [4, -11, -6, -10],\n [-10, -6, 2, 8],\n [-1, -10, 8, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
74
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -9, 10, -6],\n [12, 8, -5, -2],\n [-5, 10, 9, -12],\n [8, -5, 9, -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" } ]
95
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -1, -8, 0],\n [-1, 10, -1, 10],\n [-8, -1, 1, -6],\n [0, 10, -6, -11]]? Round to the nearest integer, then express your answer modulo 1000.\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[[12, -10, -4, 0],\n [-10, -4, 0, -6],\n [-4, 0, -12, 2],\n [0, -6, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -7, -9, -1],\n [0, -4, 0, 7],\n [0, 0, -6, -5],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 0, 1, -9],\n [11, -12, -8, -11],\n [-1, 3, 6, -9],\n [3, 5, 2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
411
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -3, 9, -3],\n [-9, 10, -10, -10],\n [-1, 0, -9, 4],\n [4, -12, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
89
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -2, -9, 2],\n [-2, -1, 2, 8],\n [-9, 2, -2, 6],\n [2, 8, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
499
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 10, 12, 0],\n [-7, 0, -5, -1],\n [-5, 3, -8, 10],\n [1, -6, -3, 5]]\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, 2, 0, -2],\n [2, -2, 8, 6],\n [0, 8, -2, 6],\n [-2, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
272
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, -4, -10, 3],\n [12, 2, 0, -1],\n [-2, 12, 0, -7],\n [-3, -9, -5, -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" } ]
460
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 5, -3, 1],\n [5, -7, -2, -4],\n [-3, -2, -3, -1],\n [1, -4, -1, -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" } ]
480
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, 9, 2],\n [0, 11, -2, 1],\n [9, -2, -10, 2],\n [2, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
741
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -7, -6, 3],\n [-7, -12, 6, -4],\n [-6, 6, 5, 4],\n [3, -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" } ]
709
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -2, -4, 12],\n [-2, -7, -6, -6],\n [-4, -6, 10, 1],\n [12, -6, 1, -5]]\nRound to the nearest integer, then take the result modulo 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[[-1, -11, 12, 1],\n [11, 2, 6, -12],\n [-5, -5, 2, -3],\n [-6, 4, 9, 9]]\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[[-7, -11, -7, -4],\n [0, -6, -9, -9],\n [0, 0, 6, 3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
268
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 7, 5, -11],\n [-1, 3, -1, -2],\n [3, -1, -7, -5],\n [12, -4, -7, 4]]? Round to the nearest integer, then express your answer modulo 1000.\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[[3, 11, -5, -5],\n [0, 4, -4, -8],\n [0, 0, -3, -11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
396
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 3, 2, -4],\n [0, 9, 4, 8],\n [0, 0, 2, 12],\n [0, 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" } ]
386
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 12, 6, 2],\n [12, -10, 5, 6],\n [6, 5, -1, 0],\n [2, 6, 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" } ]
675
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -2, -2, -9],\n [-3, 0, 7, 11],\n [-8, 1, -5, -3],\n [11, -12, -10, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
687
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, -10, -3],\n [0, 10, -6, -9],\n [0, 0, 6, 4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, -11, -6],\n [0, 8, -2, 10],\n [0, 0, 5, 9],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 7, -7, -11],\n [0, -4, -4, 1],\n [0, 0, -5, 12],\n [0, 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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -6, 2, -1],\n [-8, 10, -6, -2],\n [12, 7, -2, -11],\n [-5, 10, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
886
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, 9, 1],\n [0, 7, 3, 0],\n [0, 0, 12, 7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -3, -8, -3],\n [0, 9, -10, -10],\n [8, 1, -8, -3],\n [7, -10, -7, -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" } ]
867
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -7, -12, -5],\n [0, -1, 4, -4],\n [0, 0, 12, 1],\n [0, 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" } ]
160
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 6, 0, 6],\n [6, -12, -4, -1],\n [0, -4, -3, -4],\n [6, -1, -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" } ]
309
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 11, -12, -10],\n [7, -6, -8, 7],\n [6, 5, 8, -11],\n [-10, 4, 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" } ]
92
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -9, 4, -7],\n [-8, 5, 9, -1],\n [5, -5, -2, 9],\n [-7, 1, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
956
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -8, -4, 6],\n [-8, 9, 4, -4],\n [-4, 4, -10, -2],\n [6, -4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
250
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -4, 7, 8],\n [0, -10, -2, -2],\n [0, 0, 5, -4],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 6, 12, 0],\n [0, 8, 1, 8],\n [0, 0, -11, -11],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
608
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -8, 0, 0],\n [-8, 2, 0, 5],\n [0, 0, -12, 0],\n [0, 5, 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" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -2, -5, 12],\n [6, -11, 6, 3],\n [4, 6, 6, 1],\n [-1, 2, 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" } ]
915
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, 9, 12],\n [3, 5, 9, -8],\n [-6, 1, -9, -12],\n [12, -9, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 10, -9, 4],\n [10, -10, -3, 6],\n [-9, -3, 12, 0],\n [4, 6, 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" } ]
824
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 4, -5, 6],\n [-11, -12, -1, -4],\n [-4, 11, 12, 10],\n [2, 3, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
532
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -5, -3, -6],\n [2, 8, 2, 9],\n [6, 7, 12, -6],\n [2, 10, -10, -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" } ]
416
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 10, 6, 5],\n [0, -8, -7, 12],\n [0, 0, -2, 12],\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" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 1, -1, -4],\n [-6, 9, -2, -10],\n [-6, 0, -7, 11],\n [-4, -7, -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" } ]
690
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -9, 9, -1],\n [0, -12, 12, -3],\n [0, 0, -8, -1],\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" } ]
272
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 7, 2, 9],\n [7, 12, 4, 8],\n [2, 4, 2, 0],\n [9, 8, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
898
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 11, -5, -11],\n [-5, 12, 6, 9],\n [9, -10, -5, 12],\n [-8, -8, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
751
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -6, 0, -3],\n [0, 9, 4, -7],\n [0, 0, 2, -1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
568
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -12, 0, 6],\n [0, -5, -6, -4],\n [0, 0, -4, -8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
440
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 5, 4, -7],\n [-10, -10, 8, -1],\n [-10, 3, 10, -2],\n [-10, 3, 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" } ]
420
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -3, -9, 3],\n [0, -11, 8, -5],\n [0, 0, 2, 4],\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" } ]
264
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 5, 4, -11],\n [0, -6, 12, -6],\n [0, 0, 12, 1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 3, -2, -12],\n [-10, 10, 5, -8],\n [-12, -7, 0, -7],\n [-1, -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" } ]
789
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 7, -12, -7],\n [0, 1, -4, 7],\n [0, 0, 5, 2],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 8, 2, 9],\n [0, 10, 6, 2],\n [0, 0, 2, 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" } ]
320
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 12, -8, -5],\n [9, -11, 7, -4],\n [-2, -10, 11, -4],\n [-7, -4, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
286
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -6, 2, -4],\n [-6, -11, 6, -9],\n [2, 6, -7, -2],\n [-4, -9, -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" } ]
514
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 8, -6, -12],\n [0, 2, 8, 3],\n [0, 0, -6, -10],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -11, 6, 1],\n [1, -12, -3, -1],\n [-3, 3, -3, 11],\n [-7, -4, -7, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
792
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -1, -2, 9],\n [-2, 5, 11, -5],\n [11, -8, -2, 8],\n [3, 12, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
737
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 1, -6, 5],\n [1, 4, -4, 8],\n [-6, -4, -7, 0],\n [5, 8, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
655
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 2, -6, -2],\n [2, -11, 4, -2],\n [-6, 4, -3, 0],\n [-2, -2, 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" } ]
978
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -12, -4, -5],\n [-9, 7, 3, -8],\n [2, -7, 4, -6],\n [4, -5, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
837
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 9, 9, 9],\n [0, 7, -2, -3],\n [0, 0, -5, 3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 2, -2, 6],\n [2, -4, 8, 3],\n [-2, 8, 0, 5],\n [6, 3, 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" } ]
852
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, 3, -2],\n [9, 5, -11, -7],\n [1, 0, -8, 12],\n [1, 12, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 10, -9, -12],\n [9, -3, -6, -4],\n [-1, 12, 2, -11],\n [-3, -9, -6, -5]]\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": "What is the determinant of the matrix:\n[[5, 2, -7, 8],\n [0, 5, -8, -11],\n [0, 0, -3, -11],\n [0, 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" } ]
475
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, -7, 0],\n [0, 11, 7, -5],\n [0, 0, -7, -9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
149
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -7, -3, 12],\n [0, 1, 9, 0],\n [0, 0, 11, -4],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
660
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 9, 10, 1],\n [0, 4, 8, 4],\n [0, 0, 11, 0],\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" } ]
40
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 7, 9, 9],\n [0, 5, -3, -4],\n [0, 0, -1, 0],\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" } ]
880
MATH