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[ { "content": "Compute |A| for the matrix A =\n[[-11, 3, -6, -6],\n [3, -10, 6, 2],\n [-6, 6, -6, 2],\n [-6, 2, 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" } ]
184
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -1, -2, -4],\n [0, 10, 4, 7],\n [0, 0, -1, -12],\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" } ]
460
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, -2, 0],\n [0, 4, -9, 2],\n [-2, -9, 4, 6],\n [0, 2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
576
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -6, 2, 0],\n [-6, -3, -2, -2],\n [2, -2, 10, 6],\n [0, -2, 6, 8]]\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[[-9, -2, 6, -4],\n [0, -5, -12, -5],\n [0, 0, -10, -7],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -6, 11, 6],\n [5, -8, -4, -4],\n [-11, 11, -4, 8],\n [-6, -2, -10, -5]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -7, -4, 1],\n [-9, -10, 11, -10],\n [-4, 5, -5, -6],\n [-4, -4, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
170
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 2, 3, -1],\n [0, -3, 8, 8],\n [0, 0, -2, 10],\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" } ]
96
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -1, 6, 6],\n [-1, 9, -2, 7],\n [6, -2, 1, -4],\n [6, 7, -4, 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" } ]
125
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -3, 0, -1],\n [-3, -4, 1, 0],\n [0, 1, -3, 2],\n [-1, 0, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
437
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 2, -4, 8],\n [0, 2, 4, 7],\n [0, 0, 11, 0],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
110
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -4, -10],\n [2, -5, -4, 8],\n [-4, -4, -5, 10],\n [-10, 8, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
918
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -12, -5, 5],\n [-5, -8, 11, -12],\n [-10, 6, 5, 12],\n [-6, -2, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
616
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, -10, -1, 0],\n [-10, -4, -1, 5],\n [-1, -1, -8, -4],\n [0, 5, -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" } ]
567
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 9, 5, -10],\n [11, -2, 4, 0],\n [-11, -6, -11, 8],\n [2, 2, -10, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 11, 0, 8],\n [-10, 9, -3, 6],\n [4, -7, -5, 4],\n [-6, 1, -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" } ]
122
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 4, 3, 0],\n [4, -7, 5, -2],\n [3, 5, 9, 1],\n [0, -2, 1, 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" } ]
509
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 12, 1, -7],\n [11, -9, -4, -7],\n [-7, -12, -12, 2],\n [-10, -11, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
308
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, 5, -2],\n [2, 4, 8, 2],\n [5, 8, 0, -4],\n [-2, 2, -4, 6]]\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, 0, -11],\n [-11, -9, 8, 9],\n [-2, 12, 9, 11],\n [5, 7, 12, -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" } ]
707
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 8, -8, 6],\n [8, -5, -11, 5],\n [7, -3, -5, -1],\n [2, 10, 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" } ]
750
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 11, 9, -6],\n [0, -4, 1, 9],\n [0, 0, -11, -2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
648
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 4, -3, -4],\n [-6, -12, -7, -5],\n [7, 0, 6, 3],\n [-12, 0, -4, 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" } ]
192
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 3, 3, 10],\n [3, 11, 8, -2],\n [3, 8, -10, -6],\n [10, -2, -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" } ]
389
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -10, 1, 0],\n [0, 9, -2, 12],\n [0, 0, -5, 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" } ]
900
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -3, 9, 6],\n [-10, -4, 2, -9],\n [4, 0, -1, 12],\n [12, 0, -1, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
182
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 8, -12, 0],\n [0, -9, -12, 8],\n [0, 0, 12, 9],\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" } ]
112
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -2, 8, -8],\n [-2, -5, 0, 6],\n [8, 0, 7, -2],\n [-8, 6, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 8, 1, -12],\n [0, 4, 11, 8],\n [0, 0, -3, 9],\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" } ]
48
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -8, -10, -9],\n [-9, -11, 10, -10],\n [-8, 8, -8, -12],\n [2, 0, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -6, 0, 4],\n [-6, -2, 2, -2],\n [0, 2, 7, -4],\n [4, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 11, -6, -2],\n [11, 4, 8, -4],\n [-6, 8, 4, -8],\n [-2, -4, -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" } ]
428
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 0, 6, 2],\n [0, 3, -6, 1],\n [6, -6, 4, -1],\n [2, 1, -1, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
408
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, 1, 4],\n [-1, 6, -4, 1],\n [1, -4, 12, -2],\n [4, 1, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
285
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -7, 3, 7],\n [-5, -4, -6, -3],\n [4, -4, 0, 0],\n [-2, 9, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
484
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -7, 0, -6],\n [-7, 1, 3, 10],\n [0, 3, -9, -4],\n [-6, 10, -4, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
115
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -9, -9, 5],\n [-7, -7, 10, -1],\n [-9, 3, 9, -9],\n [10, 12, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
780
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 4, -5, 7],\n [3, -11, -1, 12],\n [-1, 10, 6, 3],\n [-11, 2, -11, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
821
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 5, -11, -11],\n [12, 9, 2, 12],\n [-2, 0, 1, 8],\n [1, 8, 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" } ]
187
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 10, 5, 1],\n [10, 7, 2, -2],\n [5, 2, -11, -2],\n [1, -2, -2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -8, -3, -5],\n [-9, -11, 3, -12],\n [8, -12, -5, -12],\n [-9, 9, 8, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
555
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, -6, 2],\n [0, 8, 5, -2],\n [0, 0, -9, -3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
864
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 2, 3, 9],\n [0, 10, -6, 4],\n [0, 0, -9, -10],\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" } ]
440
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -10, 6, 7],\n [0, -11, 8, -10],\n [-11, -12, -3, 4],\n [12, -6, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -7, -12, -9],\n [0, -11, -1, -8],\n [0, 0, 1, 3],\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" } ]
900
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 0, 6],\n [-1, 12, -10, 11],\n [-6, -11, -9, -9],\n [9, -10, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
223
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 2, 9, 4],\n [2, 4, -1, 2],\n [9, -1, 9, 2],\n [4, 2, 2, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
452
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -6, -2, -2],\n [-6, 3, -6, 0],\n [-2, -6, 5, -8],\n [-2, 0, -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" } ]
712
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 10, -11, 2],\n [0, 11, 9, 3],\n [0, 0, -11, 9],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -2, -1, -2],\n [-5, 2, -5, 4],\n [2, 7, 9, -4],\n [8, -2, 5, -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" } ]
378
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -6, 5, 4],\n [7, 10, -2, 6],\n [-10, 6, 5, 1],\n [4, 3, 7, -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" } ]
5
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 0, 12, -1],\n [0, -3, 5, -3],\n [0, 0, -1, 4],\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" } ]
874
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -7, 11, -1],\n [-11, -4, -5, -8],\n [9, 6, -4, 10],\n [1, 2, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
192
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -7, 6, -12],\n [-10, 8, 0, 0],\n [-11, -5, 7, 9],\n [-12, 6, -10, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
256
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 12, 7, 8],\n [0, -8, 5, 8],\n [0, 0, 12, -8],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
576
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -2, 10, -2],\n [-2, 4, -2, 8],\n [10, -2, 4, -3],\n [-2, 8, -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" } ]
668
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 8, 0, 9],\n [-10, -1, -6, -6],\n [0, 1, 4, 4],\n [-5, 0, -6, -3]]? 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": "Compute |A| for the matrix A =\n[[-2, -9, 7, -2],\n [0, -11, 0, 11],\n [0, 0, -12, -4],\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" } ]
152
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -4, -11, -1],\n [0, 3, 0, -9],\n [0, 0, -5, -2],\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" } ]
680
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -4, -1, 3],\n [-6, -8, -9, 0],\n [2, -1, -5, 0],\n [-5, -7, 4, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
456
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 7, 5, -12],\n [0, 3, 1, 8],\n [4, 12, 7, 4],\n [11, 0, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
922
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 11, 5, -10],\n [0, -4, -5, -5],\n [0, 0, -2, 12],\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" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -2, 3, -7],\n [0, 6, -10, -12],\n [0, 0, -4, -5],\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" } ]
8
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -6, -2, -2],\n [0, 6, 5, -6],\n [0, 0, -12, -7],\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" } ]
272
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 0, 8, -8],\n [0, 4, -1, 8],\n [8, -1, -3, 6],\n [-8, 8, 6, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
394
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -1, -4, 1],\n [-1, 6, 2, -1],\n [-4, 2, -10, 4],\n [1, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
310
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 2, 0, 4],\n [2, 10, 6, 8],\n [0, 6, -7, -8],\n [4, 8, -8, 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" } ]
512
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 8, 6, 9],\n [3, -12, 7, 0],\n [12, -9, -7, 9],\n [10, -12, -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" } ]
708
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 0, 12, 2],\n [0, -9, 5, -4],\n [0, 0, -3, -8],\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" } ]
624
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 1, 7, 6],\n [0, -3, 12, 1],\n [0, 0, -10, 12],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -10, -5, -10],\n [0, -1, 3, 1],\n [0, 0, 7, 3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 6, 6, -2],\n [6, -9, -2, 10],\n [6, -2, -8, -1],\n [-2, 10, -1, -11]]\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[[1, -11, 9, 12],\n [0, 1, -9, -7],\n [0, 0, -10, -1],\n [0, 0, 0, 3]]\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[[1, -11, 6, -6],\n [6, -7, 6, -9],\n [6, 9, 12, 5],\n [8, -9, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
440
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -2, -5, 2],\n [-2, -4, 1, 1],\n [-5, 1, -10, 5],\n [2, 1, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
577
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -2, -10, 9],\n [0, -4, 8, 2],\n [0, 0, -1, 9],\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" } ]
808
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 0, 4, -8],\n [0, -8, -4, 0],\n [4, -4, 0, 4],\n [-8, 0, 4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -2, 3, 9],\n [-7, -8, 8, 11],\n [0, -5, -12, 5],\n [-3, 4, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
370
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 10, 9, -2],\n [0, 11, 0, -7],\n [0, 0, -4, -4],\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" } ]
816
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, 6, 6],\n [-1, -4, 4, 4],\n [6, 4, 9, 6],\n [6, 4, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
475
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -5, 1, -6],\n [3, 12, -2, 6],\n [-6, 3, -11, -12],\n [7, -12, 3, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
198
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -6, 4, 8],\n [-12, 9, -3, 4],\n [-6, 3, -7, 9],\n [-9, 9, -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" } ]
399
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 2, 7, -5],\n [-5, 0, 7, -2],\n [8, -2, 3, 11],\n [-11, 6, -11, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
530
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 10, 8, 3],\n [9, -9, 11, -5],\n [7, -7, -5, -11],\n [-5, 5, -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" } ]
350
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 9, -12, 7],\n [0, 1, -5, 6],\n [10, -8, 9, -10],\n [-8, 8, 7, 3]]? 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[[-8, 6, -2, -2],\n [6, -7, 6, 3],\n [-2, 6, 0, -2],\n [-2, 3, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -9, -1, 10],\n [8, -5, -6, 12],\n [6, -9, 7, 2],\n [-10, -3, 8, -4]]\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, -4, 2, 4],\n [-4, 3, 4, 6],\n [2, 4, 6, -4],\n [4, 6, -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" } ]
236
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 1, 11, 5],\n [1, 5, 4, -8],\n [11, 4, 4, -2],\n [5, -8, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
409
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 2, -11, 2],\n [2, -7, -6, -6],\n [-11, -6, 2, 0],\n [2, -6, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
214
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -9, -11, 9],\n [0, -4, -7, -8],\n [0, 0, -2, -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" } ]
216
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 10, -2, -2],\n [10, -8, -8, 2],\n [-2, -8, -11, 4],\n [-2, 2, 4, -2]]\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[[-7, 8, -1, 6],\n [0, -7, -11, -3],\n [0, 0, 3, 4],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
588
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -4, -11, -2],\n [0, 8, -4, -12],\n [0, 0, 10, -2],\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" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 6, -4, 3],\n [6, 3, 6, 3],\n [-4, 6, -6, -6],\n [3, 3, -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" } ]
54
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 6, -3, -10],\n [6, -12, 1, 5],\n [3, 1, 8, 0],\n [3, -9, -7, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
602
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -3, -11, -10],\n [0, -6, 8, -7],\n [0, 0, -8, 3],\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" } ]
576
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -5, 1, 11],\n [12, 5, -11, 5],\n [3, -5, -5, -10],\n [3, -8, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
126
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, 10, -5],\n [-2, -11, -1, 0],\n [10, -1, -10, 6],\n [-5, 0, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
683
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -8, -2, 4],\n [-8, 6, 8, -4],\n [-2, 8, 6, 2],\n [4, -4, 2, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
248
MATH