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[ { "content": "What is the determinant of the matrix:\n[[6, 10, 0, 8],\n [10, -8, -3, 0],\n [0, -3, -10, 0],\n [8, 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" } ]
438
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 7, 0, 10],\n [7, 12, -4, 10],\n [0, -4, -9, 6],\n [10, 10, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
474
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -2, 0, 9],\n [-6, -9, 8, 9],\n [-11, 0, -4, -2],\n [-7, -1, 8, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
228
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -5, 4, 2],\n [-5, -5, -2, -1],\n [4, -2, -9, 5],\n [2, -1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
837
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 2, 1, -5],\n [1, -3, 4, -1],\n [-7, 9, 6, -12],\n [1, -1, 9, 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" } ]
918
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -10, -11, 0],\n [-3, 1, -6, -3],\n [-7, -4, -12, -9],\n [-5, -8, 9, 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, 9, 11],\n [0, 7, 10, 10],\n [0, 0, -3, 1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
496
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -5, -2, 10],\n [-11, 3, 9, 11],\n [6, 10, 12, 11],\n [6, -6, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
787
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 6, -6, 1],\n [6, -2, -7, -1],\n [-6, -7, -9, 4],\n [1, -1, 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" } ]
191
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -2, 2, -10],\n [9, 11, -11, -7],\n [7, 0, 12, 10],\n [-1, -6, -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" } ]
240
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -5, 8, -9],\n [0, 5, 12, 8],\n [0, 0, 8, -3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 8, -4, 12],\n [0, -11, -4, 1],\n [0, 0, 7, -10],\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" } ]
380
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 2, -9, -6],\n [2, 7, 1, -4],\n [-9, 1, 0, -6],\n [-6, -4, -6, 4]]\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[[-12, -10, 0, 2],\n [-10, -9, 2, -2],\n [0, 2, 11, -7],\n [2, -2, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
332
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 7, -1, 10],\n [2, 0, -7, 11],\n [11, 1, -12, -3],\n [-7, 7, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
613
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 12, -5, -3],\n [0, 9, 2, -9],\n [0, 0, -8, 8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 0, 1, 5],\n [-7, 10, -11, -10],\n [5, -6, -12, -9],\n [-7, -5, -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" } ]
321
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 4, -9, 11],\n [9, 5, 0, -5],\n [-1, -1, -3, 1],\n [4, 11, 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" } ]
37
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 4, 8, -8],\n [-1, 1, 0, -2],\n [8, 3, -7, -8],\n [2, 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" } ]
486
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -6, 8, 2],\n [-6, -2, 6, -2],\n [8, 6, -9, 1],\n [2, -2, 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" } ]
86
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -4, -6, -4],\n [-4, 6, 0, -3],\n [-6, 0, 9, -2],\n [-4, -3, -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" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 8, 10, -9],\n [6, -11, -9, 11],\n [-11, -7, 10, -1],\n [10, 3, 9, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
582
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 8, 2, -10],\n [8, -12, 4, -10],\n [2, 4, 11, 0],\n [-10, -10, 0, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
104
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 9, -1, -1],\n [0, -8, -3, 8],\n [0, 0, -4, -1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
192
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -1, -7, 0],\n [0, -1, 12, -1],\n [0, 0, 8, -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" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 6, -6, -2],\n [6, -2, -11, 0],\n [-6, -11, 3, -6],\n [-2, 0, -6, 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" } ]
860
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -3, 8, -1],\n [-1, 11, 0, 3],\n [-9, -10, -7, -6],\n [-1, 5, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
770
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 6, 6, 8],\n [6, 2, -2, -10],\n [6, -2, -11, 2],\n [8, -10, 2, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 0, -12, 8],\n [-8, 3, 4, 5],\n [-12, 7, -9, -11],\n [5, 3, 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" } ]
792
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 8, 10, 2],\n [0, -7, 5, -10],\n [0, 0, 10, 7],\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" } ]
550
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -5, 9, 0],\n [6, 8, 4, -5],\n [5, -1, 7, -6],\n [10, 9, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
270
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -4, 0, -5],\n [-4, -10, -8, 10],\n [0, -8, -11, -10],\n [-5, 10, -10, -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" } ]
946
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 2, 0, -6],\n [2, -12, 6, -8],\n [0, 6, 11, 2],\n [-6, -8, 2, 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" } ]
568
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -12, -2, -1],\n [-1, 8, -4, 2],\n [7, -12, -12, 2],\n [8, -12, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
516
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -8, 4, 2],\n [-8, -5, 4, 1],\n [4, 4, -7, 0],\n [2, 1, 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" } ]
14
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 10, 9, -8],\n [0, -4, 8, 6],\n [0, 0, 5, -1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
940
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -4, -12, -1],\n [6, 10, 7, 2],\n [-11, -7, 7, -6],\n [-5, 2, 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" } ]
473
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -8, 1, -5],\n [-8, -10, 6, -2],\n [1, 6, -12, 0],\n [-5, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
636
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -1, -8, 10],\n [-1, 10, 10, 4],\n [-8, 10, 9, 2],\n [10, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
367
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 0, -11, 9],\n [-7, -1, 0, -6],\n [-3, -10, -8, -3],\n [10, 7, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
965
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -3, 10, 6],\n [-8, -3, 12, 9],\n [-11, -5, -7, -12],\n [1, 8, 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" } ]
731
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 6, 10, 2],\n [2, 2, -4, -2],\n [11, -7, 12, -12],\n [5, 3, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
448
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 0, 0, -2],\n [0, 9, 1, -4],\n [0, 1, 3, -2],\n [-2, -4, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
272
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 7, -5, -3],\n [-9, 0, 1, -7],\n [-8, -5, -10, -1],\n [1, 4, 3, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -2, -2, 4],\n [-2, -1, 8, -5],\n [-2, 8, -1, 2],\n [4, -5, 2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
507
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, -2, -3],\n [0, 11, -8, 10],\n [0, 0, -3, -8],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
911
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 3, 9, 2],\n [3, 11, -6, 10],\n [9, -6, 0, 2],\n [2, 10, 2, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -2, 10, 0],\n [0, 5, 5, 12],\n [0, 0, 3, -6],\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" } ]
265
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -11, -7, 2],\n [-11, -5, -2, -4],\n [-7, -2, 7, 1],\n [2, -4, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
114
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 10, 9, -11],\n [3, -8, -10, -8],\n [-11, 4, 2, 2],\n [4, 0, 5, -3]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 4, 1, -8],\n [4, 9, 0, 6],\n [1, 0, -1, -4],\n [-8, 6, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
382
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 2, 2, 2],\n [2, 11, 9, 4],\n [2, 9, 11, 2],\n [2, 4, 2, 4]]\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[[-2, -8, -7, 5],\n [0, 12, 0, -2],\n [0, 0, 7, 9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
512
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -6, -12, 5],\n [0, 10, 11, -2],\n [0, 0, 11, -8],\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" } ]
400
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 9, -9, -4],\n [0, -2, 8, -7],\n [0, 0, 6, 3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 8, 7, 12],\n [4, 7, -2, -1],\n [-12, -6, -9, 9],\n [-1, 1, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
806
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -8, 6, -5],\n [0, -7, -5, 9],\n [0, 0, -3, -8],\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" } ]
210
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -8, 3, 8],\n [-8, -3, 3, -6],\n [3, 3, 2, -5],\n [8, -6, -5, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
497
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -8, 1, -2],\n [-8, 10, 0, 2],\n [1, 0, 1, 0],\n [-2, 2, 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" } ]
284
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -2, -9, 1],\n [0, -2, -12, -12],\n [0, 0, 3, -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" } ]
892
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 2, 8, 10],\n [2, 12, 10, 8],\n [8, 10, 1, -10],\n [10, 8, -10, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
752
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -3, -1, -8],\n [-3, -8, -12, -5],\n [-1, -12, -9, -10],\n [-8, -5, -10, 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" } ]
188
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -3, -3, 0],\n [-3, -7, -4, -4],\n [-3, -4, 7, 6],\n [0, -4, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
316
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 5, -12, 3],\n [0, 11, -6, -3],\n [0, 0, -3, -4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
416
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 9, -5, -7],\n [0, 10, 8, 10],\n [0, 0, 1, 12],\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" } ]
950
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -1, 8, 11],\n [0, 10, 2, -8],\n [0, 0, -2, 8],\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" } ]
520
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -2, -4, 0],\n [-2, -2, 4, -4],\n [-4, 4, -12, 0],\n [0, -4, 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" } ]
24
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 9, -2, 5],\n [9, 11, 2, 0],\n [-2, 2, 7, -4],\n [5, 0, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
765
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 0, 6, 4],\n [0, -12, -2, 2],\n [6, -2, -6, 2],\n [4, 2, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
116
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -11, 3, -6],\n [-4, -5, 6, 10],\n [-4, -9, 12, 11],\n [8, -9, 9, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
539
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 7, -10, 0],\n [12, 8, 2, 11],\n [1, 8, -12, -10],\n [10, -9, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
974
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, -3, 7],\n [-7, 0, 3, 3],\n [-11, -11, 11, -12],\n [-5, -7, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 3, -12, 10],\n [11, -4, 6, -12],\n [1, -9, -5, -9],\n [2, 5, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
157
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 2, 5, 5],\n [5, -6, 0, 10],\n [-5, -1, -7, -9],\n [-12, -8, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
620
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -4, 11, -3],\n [0, -11, -8, 3],\n [0, 0, 8, 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" } ]
208
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -11, -11, -1],\n [-8, 11, 5, -7],\n [-12, 1, -9, -10],\n [-2, 0, 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" } ]
964
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -8, -7, 1],\n [0, 12, -10, -3],\n [0, 0, 5, 11],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 10, -8, 4],\n [10, 2, -2, -8],\n [-8, -2, 8, 8],\n [4, -8, 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" } ]
408
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -6, 2, -12],\n [0, 3, 3, 3],\n [0, 0, 6, -2],\n [0, 0, 0, 2]]\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[[-9, -10, -8, -8],\n [0, -11, 1, 1],\n [0, 0, 5, 9],\n [0, 0, 0, 6]]\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[[10, 12, 1, 10],\n [0, 1, 12, -9],\n [0, 0, -10, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 10, 8, -5],\n [8, 6, 12, 8],\n [-10, 0, -1, 9],\n [4, 4, -2, -5]]? Round to the nearest integer, then express your answer 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[[9, -10, -6, 6],\n [-10, 1, 3, 0],\n [-6, 3, 1, 8],\n [6, 0, 8, -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" } ]
656
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 11, 2, -11],\n [-1, -4, 6, 12],\n [-2, -5, 5, -3],\n [-8, -8, 6, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -3, 2, -10],\n [-3, 4, -4, -4],\n [2, -4, -7, -4],\n [-10, -4, -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" } ]
572
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -8, -6, -4],\n [-8, 12, 0, 0],\n [-6, 0, -9, 0],\n [-4, 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" } ]
520
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -9, -2, -12],\n [-9, 10, 6, 8],\n [-2, 6, 2, 10],\n [-12, 8, 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" } ]
824
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 5, 3, -5],\n [-5, 6, 6, -11],\n [-7, 10, 3, 12],\n [-8, -6, -2, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
518
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 6, -1, -12],\n [0, -7, 2, 12],\n [0, 0, 11, -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" } ]
78
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -10, 5, 7],\n [-6, -1, -7, -12],\n [-4, 1, 11, 4],\n [8, -5, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
698
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -4, 8, 5],\n [-7, 9, 11, 11],\n [2, -11, 11, -6],\n [-8, -6, 8, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
318
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, -5, 9],\n [-9, 1, -12, -12],\n [-1, -10, 12, -4],\n [-6, -6, 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" } ]
1
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -4, 0, 4],\n [-4, 7, 4, 5],\n [0, 4, -1, -6],\n [4, 5, -6, -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" } ]
214
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 5, 5, 11],\n [-8, -8, -3, -3],\n [-7, -7, 7, -9],\n [-2, -1, -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" } ]
836
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -3, 12, 3],\n [0, 3, 0, 2],\n [0, 0, 9, -8],\n [0, 0, 0, 2]]\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[[7, 1, -9, -1],\n [0, -11, -9, -1],\n [0, 0, 9, 4],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
842
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 0, 10, -8],\n [11, -10, 2, 1],\n [-8, 11, -3, 8],\n [11, -6, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
693
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -6, 4, -10],\n [-6, 0, -2, -6],\n [4, -2, -3, 0],\n [-10, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
284
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -10, -12, 4],\n [-12, 8, 12, -10],\n [-11, 10, 9, 8],\n [5, -10, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 3, 0, -4],\n [3, 8, 6, -2],\n [0, 6, 5, 4],\n [-4, -2, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH