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[ { "content": "What is the determinant of the matrix:\n[[3, 0, 7, -8],\n [6, -5, 3, 9],\n [-6, -1, 3, 0],\n [3, 10, -10, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
413
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -10, 5, 1],\n [11, 9, -6, -11],\n [-4, 5, -4, -4],\n [6, -8, 1, -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" } ]
771
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -2, 8, -6],\n [-2, -11, 1, 6],\n [8, 1, 6, -8],\n [-6, 6, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
468
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -9, -8, 1],\n [-9, 9, 5, 0],\n [-8, 5, 7, 2],\n [1, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 11, 7, 6],\n [-6, -7, -6, -8],\n [-6, -9, -1, 3],\n [6, -11, 1, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -5, -2, 6],\n [0, -6, 6, 12],\n [0, 0, 12, -9],\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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 3, 1, -10],\n [0, -7, -9, 4],\n [0, 0, 8, 6],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 1, -10, -5],\n [0, -5, -6, 10],\n [0, 0, 11, 6],\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" } ]
220
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, -2, -11, 12],\n [-7, 1, 8, 4],\n [8, -2, -1, -12],\n [7, 7, -7, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
891
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -8, -10, -10],\n [-8, -6, 0, 2],\n [8, -3, -5, -3],\n [9, -10, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
750
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -12, 3, -8],\n [0, 6, -9, 4],\n [0, 0, 10, 3],\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" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 8, 2, -7],\n [0, -3, -2, 1],\n [0, 0, 12, 4],\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" } ]
168
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 4, 1, 0],\n [0, 7, 0, -2],\n [0, 0, -7, -4],\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" } ]
706
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -5, 10, 9],\n [0, 5, -10, 9],\n [0, 0, -2, -9],\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" } ]
30
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -7, -6, 8],\n [0, 2, 1, 5],\n [0, 0, 10, -3],\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" } ]
720
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 9, -7, 8],\n [-3, -10, -6, 0],\n [11, -8, -3, 3],\n [3, -11, 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" } ]
708
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -4, 5, -4],\n [-4, 9, -6, -2],\n [5, -6, -2, 2],\n [-4, -2, 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" } ]
498
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 10, 9, -4],\n [10, 8, -5, 9],\n [9, -3, -9, 5],\n [-7, 2, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
53
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 5, 8, 12],\n [0, 7, 6, -11],\n [0, 0, 9, 10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
488
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -9, 4, -4],\n [0, -8, -10, 5],\n [0, 0, 1, 8],\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" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -2, -6, -5],\n [-2, -6, 2, 2],\n [-6, 2, 10, -6],\n [-5, 2, -6, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 10, 7, 4],\n [11, -4, -12, 5],\n [-1, 1, 11, -6],\n [-3, -3, -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" } ]
648
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 8, 12, -4],\n [7, -4, 10, 2],\n [5, 6, 11, 2],\n [-3, 11, 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" } ]
796
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 6, 9, 4],\n [-3, -12, 8, 0],\n [4, 7, -12, -7],\n [-3, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
798
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 7, -8, -1],\n [7, 5, -10, 1],\n [-8, -10, 1, -10],\n [-1, 1, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
352
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 1, 5, -6],\n [1, -6, -6, 2],\n [5, -6, -7, 0],\n [-6, 2, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
564
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -10, 10, -7],\n [5, 8, -1, 8],\n [12, -1, 11, 10],\n [-12, 10, 11, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
501
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 1, 3, 6],\n [1, -5, 4, 10],\n [3, 4, 5, -3],\n [6, 10, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
301
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -1, -6, 4],\n [10, 3, -5, -12],\n [-3, 4, -5, 7],\n [9, -7, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
375
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 0, 2, 0],\n [0, 12, 2, -1],\n [2, 2, -7, 2],\n [0, -1, 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" } ]
438
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 12, -10, -4],\n [0, -4, 6, 5],\n [0, 0, -6, -11],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
488
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -1, -2, -2],\n [-1, 6, -2, 8],\n [-2, -2, 8, 5],\n [-2, 8, 5, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
377
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 7, -10, 5],\n [-1, -2, 8, 8],\n [10, 1, 2, 3],\n [2, -12, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
736
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -8, 5, -4],\n [-10, -8, 1, -7],\n [-10, 1, -2, 1],\n [4, -1, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
942
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 12, -3, -7],\n [8, -6, 5, 9],\n [0, 7, -6, 3],\n [-6, -11, -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" } ]
196
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 8, -3, 1],\n [8, 11, -8, 4],\n [-3, -8, -2, 0],\n [1, 4, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
521
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -5, 4, -2],\n [8, 7, 1, -10],\n [8, 8, -5, 8],\n [-9, -6, -7, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 6, -10, 2],\n [6, 4, 5, 10],\n [-10, 5, -11, 2],\n [2, 10, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -6, 11, -5],\n [0, -12, -8, 9],\n [0, 0, -10, -12],\n [0, 0, 0, -7]]\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[[-6, 6, -9, 7],\n [4, -8, 10, 3],\n [10, -4, 5, 0],\n [-6, 2, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
876
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 4, 12, 7],\n [0, -7, -1, 8],\n [0, 0, 3, -4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
488
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -4, 11, 5],\n [0, -6, 2, 7],\n [0, 0, -9, 3],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
406
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, 4, 11, -1],\n [0, -9, -4, -1],\n [0, 0, 5, -12],\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" } ]
555
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 2, -11, 2],\n [0, 11, 4, 5],\n [0, 0, 8, 10],\n [0, 0, 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" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -8, -7, -6],\n [-11, 5, 9, -11],\n [5, -4, 2, 7],\n [-3, 3, -8, 7]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, 11, -5],\n [0, 10, 1, -4],\n [0, 0, -11, -6],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
440
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 3, 5, 11],\n [0, 4, -5, 9],\n [0, 0, 9, 5],\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" } ]
324
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 8, 0, 2],\n [2, 12, -8, 11],\n [-12, -8, -5, -4],\n [3, -9, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
967
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -4, -3, -12],\n [0, -6, -5, -9],\n [0, 0, -8, 10],\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" } ]
976
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -8, 7, 9],\n [6, 5, -10, -8],\n [1, -1, 8, 10],\n [11, 2, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
974
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -2, -12, 7],\n [0, -8, 9, 10],\n [0, 0, 12, 2],\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" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -5, 0, -1],\n [-5, -11, 2, -4],\n [0, 2, -7, 4],\n [-1, -4, 4, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
653
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 6, -9, -6],\n [0, -1, -7, 8],\n [0, 0, 7, 9],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 1, -4, 0],\n [0, -5, -4, 5],\n [0, 0, -11, -9],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
980
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -10, -8, -9],\n [-10, -8, -6, 0],\n [-8, -6, 4, -4],\n [-9, 0, -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" } ]
916
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -5, 0, -4],\n [-5, 9, 0, -1],\n [0, 0, 0, 6],\n [-4, -1, 6, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -2, 0, -11],\n [-12, 0, -10, -11],\n [12, -4, 4, 1],\n [-6, -5, 1, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
402
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 10, 11, 10],\n [0, 10, -2, 9],\n [0, 0, -6, 12],\n [0, 0, 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" } ]
800
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -2, 5, -5],\n [0, -8, -2, -11],\n [0, 0, -9, 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" } ]
760
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -10, 2, -12],\n [0, -6, -1, -7],\n [0, 0, -4, 11],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
408
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, -5, -1],\n [-2, -8, 4, 4],\n [-5, 4, 6, -6],\n [-1, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
328
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 8, 2, -11],\n [-5, 5, -7, -10],\n [-6, 10, 11, -8],\n [-7, -11, -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" } ]
705
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -8, -4, 8],\n [-8, -12, -2, -4],\n [-4, -2, 4, -6],\n [8, -4, -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" } ]
968
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 2, 2, -4],\n [2, 10, -2, 0],\n [2, -2, -6, -3],\n [-4, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 3, 2, 8],\n [0, 6, 4, -3],\n [0, 0, -6, -3],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
772
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -2, 4, -11],\n [0, -10, -2, -11],\n [0, 0, 12, 7],\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" } ]
200
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -3, 11, -11],\n [0, 5, -6, 2],\n [0, 0, -10, 8],\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": "What is the determinant of the matrix:\n[[12, -8, 6, -1],\n [0, -1, -4, -8],\n [0, 0, -9, -7],\n [0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -7, -2, 0],\n [10, -4, -8, -8],\n [0, 5, -9, -7],\n [12, -2, 7, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
878
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 9, -3, 7],\n [-4, 8, 9, 4],\n [10, -9, -11, -12],\n [-9, -1, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
915
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 11, -1, 0],\n [0, 5, -9, -6],\n [0, 0, 2, 0],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -8, 0, -1],\n [-8, -3, -2, -2],\n [0, -2, -5, -4],\n [-1, -2, -4, 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" } ]
559
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, 2, -7],\n [8, -8, -10, 1],\n [7, 1, 6, -1],\n [2, -10, -7, -12]]\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[[12, 6, 0, -6],\n [6, -5, -4, 8],\n [0, -4, 11, -7],\n [-6, 8, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
364
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -8, -12, -11],\n [5, 9, 6, 9],\n [-9, -7, 5, 1],\n [-4, -6, -8, 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" } ]
452
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 0, 2, 4],\n [0, 2, -6, -2],\n [2, -6, 0, 8],\n [4, -2, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -4, 5, 3],\n [0, 4, -12, -8],\n [0, 0, 5, -1],\n [0, 0, 0, 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" } ]
200
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, 1, -11],\n [0, -8, 6, -10],\n [0, 0, -4, 6],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -6, -4, -9],\n [0, -7, -2, -2],\n [0, 0, -6, 8],\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" } ]
210
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 5, 3, 6],\n [0, 11, -5, 8],\n [0, 0, -11, -7],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
82
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -5, 4, -1],\n [-5, -10, 6, 1],\n [4, 6, -11, 2],\n [-1, 1, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
862
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 8, 2, -9],\n [8, -9, 4, -2],\n [2, 4, 9, -8],\n [-9, -2, -8, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
159
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 8, -7, -4],\n [8, -8, -2, -2],\n [-7, -2, 8, 1],\n [-4, -2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
396
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -7, 5, -4],\n [10, 7, 2, -10],\n [6, -9, -4, -11],\n [-2, -7, -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" } ]
605
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 1, -2, -12],\n [-1, 4, 2, 3],\n [-9, -4, 3, -2],\n [-12, -9, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
327
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 1, 10, 6],\n [0, 11, -2, -4],\n [0, 0, -12, -6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -9, -8, -8],\n [0, -12, -5, 9],\n [0, 0, 9, -8],\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" } ]
28
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 9, 5, 8],\n [-6, 10, 2, 7],\n [-8, -11, -5, -10],\n [12, 10, 9, -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" } ]
63
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -5, 10, -11],\n [0, 12, -11, -4],\n [3, -1, -4, -12],\n [3, 2, 7, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
479
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 11, -4, 12],\n [0, -5, 2, 6],\n [0, 0, 8, 11],\n [0, 0, 0, -2]]\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[[8, -2, 0, -3],\n [6, -3, -7, -2],\n [8, -7, -10, 7],\n [-4, -2, 6, 2]]\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[[-4, 0, 8, 1],\n [0, 6, 6, 9],\n [8, 6, 7, -2],\n [1, 9, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
270
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 6, 2, -12],\n [8, -10, 10, -5],\n [12, 12, -7, -6],\n [8, 3, -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" } ]
623
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 4, -2, 4],\n [4, -1, 1, -4],\n [-2, 1, 10, -3],\n [4, -4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
684
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -5, -4, 0],\n [0, 4, 11, 0],\n [0, 0, -12, -4],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 4, -10, 10],\n [0, 1, 5, 8],\n [0, 0, -1, 10],\n [0, 0, 0, 2]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -10, -4, -4],\n [-10, -5, 2, 8],\n [-4, 2, 5, 8],\n [-4, 8, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
868
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -9, -5, 2],\n [0, 5, 2, -7],\n [0, 0, 12, 7],\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" } ]
60
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 4, -1, 2],\n [4, -5, -3, 0],\n [-1, -3, -5, 4],\n [2, 0, 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" } ]
604
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -3, -7, -10],\n [0, 5, 3, -10],\n [6, 9, -3, -12],\n [-1, -4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH