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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -3, -4, 6],\n [0, 7, 2, 7],\n [0, 0, -7, 4],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 10, -3, 6],\n [10, -8, -6, -2],\n [-3, -6, -4, -2],\n [6, -2, -2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -2, -4, 12],\n [10, 3, -6, -9],\n [-4, -1, -11, -10],\n [-6, 1, 2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
876
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 0, 2, -8],\n [0, 4, 0, -1],\n [2, 0, -11, 0],\n [-8, -1, 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" } ]
536
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -2, 2],\n [2, 5, 0, -2],\n [-2, 0, 10, -1],\n [2, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
966
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, -1, 2],\n [-4, 4, -7, -12],\n [-1, -7, -9, -2],\n [2, -12, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
938
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -6, -4, -2],\n [-6, 12, 2, -5],\n [-4, 2, 11, 2],\n [-2, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
673
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -1, -10, 1],\n [0, -11, 10, -5],\n [0, 0, 8, -11],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -4, 4, 8],\n [-9, -2, 2, 10],\n [-12, 3, 12, -5],\n [-12, 11, -3, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
564
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 4, 3, 2],\n [11, 8, 12, 0],\n [4, -2, -1, -5],\n [3, -2, -5, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 6, -9, 11],\n [0, -2, -8, -8],\n [0, 0, -3, -7],\n [0, 0, 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" } ]
604
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 2, -12, -3],\n [6, -11, -9, -4],\n [12, -4, 0, 10],\n [-7, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
618
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -4, -12, -12],\n [-7, -1, 7, 7],\n [3, 5, -11, 12],\n [5, 5, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -9, -1, 7],\n [0, -11, -4, 4],\n [0, 0, -7, -11],\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" } ]
470
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 9, -4, 8],\n [7, -1, 0, 10],\n [7, -10, 7, 8],\n [-8, 2, 6, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 2, 1, 7],\n [0, 9, -3, 11],\n [0, 0, -1, 0],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
505
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -2, -3, 9],\n [-2, -3, -1, 0],\n [-3, -1, 6, 7],\n [9, 0, 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" } ]
50
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 0, -5, -11],\n [0, 10, -3, 6],\n [-5, -3, -7, 2],\n [-11, 6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
499
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 4, 0, -2],\n [4, 9, 8, 6],\n [0, 8, -2, -2],\n [-2, 6, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
786
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -7, -5, -10],\n [0, 11, -8, -4],\n [0, 0, 11, -3],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
96
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -2, -4, -3],\n [-2, -8, 4, 6],\n [-4, 4, 8, 1],\n [-3, 6, 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" } ]
28
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 0, -4, -4],\n [0, -4, -8, 4],\n [-4, -8, 8, 0],\n [-4, 4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -4, -6, -5],\n [7, -4, 9, -9],\n [7, -9, -11, 10],\n [11, 6, -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" } ]
555
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -8, -5, 8],\n [-8, 3, 10, -2],\n [-5, 10, -4, -8],\n [8, -2, -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" } ]
442
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 0, -2, -6],\n [0, -10, 2, -4],\n [-2, 2, 1, -4],\n [-6, -4, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 12, -6, -3],\n [-10, -10, -11, -11],\n [-7, -12, 12, -11],\n [0, -9, 9, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
711
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, 11, 1],\n [0, 10, 12, 3],\n [0, 0, -5, 7],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -12, 11, -11],\n [0, -12, -11, -6],\n [0, 0, 1, 5],\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" } ]
108
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 8, 10, -1],\n [0, 5, -7, 4],\n [0, 0, -10, -2],\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" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 2, -2, 6],\n [-6, 12, 3, -1],\n [-2, 5, 4, -5],\n [-9, -11, 9, -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" } ]
82
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 7, 2, -2],\n [7, 3, -4, 8],\n [2, -4, -4, 10],\n [-2, 8, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
516
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, -5, -8],\n [-5, 3, 10, -1],\n [5, 11, 6, 1],\n [-6, 9, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 2, 3, 8],\n [2, -8, 7, -6],\n [3, 7, 7, -3],\n [8, -6, -3, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
223
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -9, 8, -9],\n [7, 8, 9, -4],\n [-6, 7, -8, -11],\n [0, 3, -4, -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" } ]
720
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 2, 8, 6],\n [2, -12, 2, -5],\n [8, 2, 10, -6],\n [6, -5, -6, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
656
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 7, -3, -4],\n [7, -9, 2, 8],\n [-3, 2, 4, -6],\n [-4, 8, -6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
947
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 5, 7, 12],\n [0, -11, -3, 5],\n [0, 0, 1, 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" } ]
934
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, -11, 6],\n [0, 12, 9, -11],\n [0, 0, 11, -4],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 5, -7, -3],\n [5, -7, -8, 0],\n [-7, -8, 12, 4],\n [-3, 0, 4, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
790
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 11, -8, 5],\n [11, 7, 2, 0],\n [-8, 2, -4, 0],\n [5, 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" } ]
100
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 9, -5, -5],\n [-5, -10, -2, 5],\n [-1, -1, 4, -9],\n [12, -1, -3, -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" } ]
848
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 1, 10, 8],\n [-10, -3, -9, 2],\n [-5, 7, -5, 3],\n [11, 11, -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" } ]
203
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 1, 8, 11],\n [0, 12, 6, -8],\n [0, 0, -8, -3],\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" } ]
728
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 7, -9, -5],\n [10, -12, 6, -11],\n [12, 7, 11, -10],\n [6, 8, 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" } ]
245
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -2, -6, 1],\n [-2, 12, 8, -6],\n [-6, 8, -4, 8],\n [1, -6, 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" } ]
368
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 7, -2, -4],\n [7, 8, -1, -4],\n [-2, -1, -5, -1],\n [-4, -4, -1, -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" } ]
944
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 1, 0, -2],\n [1, -11, 7, 6],\n [0, 7, -2, -6],\n [-2, 6, -6, 0]]\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[[-9, -3, -4, -9],\n [0, -11, 0, 9],\n [0, 0, 10, 8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
110
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 11, -7, -4],\n [-12, 7, -7, -3],\n [-4, -10, 10, -12],\n [-6, 2, 5, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
684
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -12, 1, 3],\n [7, -11, 5, -1],\n [-11, 7, -2, 5],\n [-4, -5, -12, 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" } ]
353
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 2, 2, 10],\n [0, 7, 12, 0],\n [0, 0, -10, -11],\n [0, 0, 0, 10]]\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[[-10, 3, 3, 8],\n [-10, 0, 11, 9],\n [4, 8, -5, -3],\n [0, 12, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
686
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 12, 6, 11],\n [0, 12, -12, -12],\n [0, 0, -12, 5],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 7, -4, 4],\n [0, 6, 11, -9],\n [0, 0, -8, -9],\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" } ]
992
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 11, -5, 2],\n [0, -2, 10, -2],\n [0, 0, 12, -12],\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" } ]
72
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 4, -2, -2],\n [4, 4, -2, 2],\n [-2, -2, -1, -7],\n [-2, 2, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 7, 4, 5],\n [0, -12, 5, 8],\n [0, 0, 5, -5],\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" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -8, 5, 0],\n [0, 6, 3, -4],\n [0, 0, -8, -2],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 1, 11],\n [4, -10, 6, 6],\n [-8, 1, 6, -4],\n [6, 0, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
628
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 1, -12, 4],\n [0, -6, -6, 12],\n [0, 0, 4, 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" } ]
192
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 12, 7, -11],\n [8, -2, 2, 8],\n [4, -7, 11, 12],\n [-3, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
808
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 8, -10, -9],\n [0, 12, -8, 7],\n [0, 0, 6, 3],\n [0, 0, 0, -3]]\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[[3, -7, 12, 7],\n [0, 6, -10, -2],\n [0, 0, 6, 2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
136
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -4, -6, -2],\n [-4, 7, -2, 1],\n [-6, -2, 10, -8],\n [-2, 1, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
650
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -4, -10, 10],\n [-4, -9, -3, 7],\n [-10, -3, -9, -6],\n [10, 7, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
131
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -10, -5, 12],\n [0, 6, -7, -11],\n [0, 0, 8, -3],\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" } ]
288
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -11, -1, -12],\n [0, 12, 12, 1],\n [0, 0, -2, -9],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 0, -2, -6],\n [0, 1, -5, 7],\n [-2, -5, -8, -1],\n [-6, 7, -1, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
888
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -4, 4, 4],\n [-4, 0, 8, -4],\n [4, 8, -5, -2],\n [4, -4, -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" } ]
56
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -12, 7, -12],\n [-7, 9, 12, 4],\n [-5, 8, 5, -7],\n [-9, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
291
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -6, -7, -4],\n [-6, -3, 8, 0],\n [-7, 8, -3, 0],\n [-4, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 6, -9, 2],\n [0, -11, 4, -5],\n [0, 0, 1, -3],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
264
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 11, -5, -9],\n [0, -1, 8, -6],\n [0, 0, -10, -3],\n [0, 0, 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" } ]
720
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 12, 0, 6],\n [0, 2, 7, -4],\n [0, 0, -9, 3],\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" } ]
540
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -2, 12, -3],\n [0, 6, 12, -11],\n [0, 0, 7, -12],\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" } ]
992
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -8, 12, 0],\n [0, -7, 5, -3],\n [0, 0, 3, 6],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
189
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -7, 11, 8],\n [0, -10, 1, -3],\n [0, 0, -5, -8],\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" } ]
900
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 11, -6, -5],\n [-4, 0, 12, 6],\n [-9, -9, -10, -1],\n [-4, 12, 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" } ]
648
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -12, 7, -11],\n [-1, -5, 5, 12],\n [-2, -11, 11, 0],\n [-9, 12, 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" } ]
770
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, 1, 0],\n [-10, -12, -8, -6],\n [11, -12, 4, -8],\n [-6, 0, -2, -2]]\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": "What is the determinant of the matrix:\n[[10, 4, 2, 2],\n [4, -9, -4, -4],\n [2, -4, 7, -1],\n [2, -4, -1, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
64
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 3, -2, 0],\n [3, -7, -6, -6],\n [-2, -6, -12, 6],\n [0, -6, 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" } ]
112
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -8, -6, 2],\n [-8, -5, -2, -6],\n [-6, -2, 10, -1],\n [2, -6, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
504
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -8, 3, -9],\n [0, 3, 5, 6],\n [0, 0, 11, 11],\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" } ]
376
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 9, -1, 5],\n [9, 6, -6, -4],\n [-1, -6, 1, 5],\n [5, -4, 5, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -6, 7, -4],\n [0, 12, 10, 7],\n [0, 0, -8, 12],\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" } ]
912
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 2, -6, -10],\n [2, -7, -4, 2],\n [-6, -4, 9, 0],\n [-10, 2, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
235
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 4, -5, -4],\n [0, 4, 8, 5],\n [0, 0, 9, -6],\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" } ]
704
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 5, -4, -8],\n [-5, 6, 9, 10],\n [2, 7, -6, -10],\n [-3, 1, 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" } ]
428
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 8, -2, 2],\n [-10, 1, -5, 9],\n [0, -4, -4, 12],\n [4, -8, 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" } ]
696
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -2, -7, -12],\n [0, 8, 3, -9],\n [0, 0, -1, 4],\n [0, 0, 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" } ]
568
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -8, -9, 7],\n [0, 6, -2, 1],\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" } ]
650
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -5, 1, -8],\n [0, 8, -10, 5],\n [0, 0, 4, -4],\n [0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 3, 9, -4],\n [0, -1, -1, -10],\n [0, 0, 4, 4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 10, 7, 0],\n [-7, -5, 8, 9],\n [-11, -6, 9, 12],\n [11, -10, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
969
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -9, 0, 1],\n [0, 3, 3, 8],\n [0, 0, 1, -8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
330
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -10, -1, 6],\n [8, 5, 0, 9],\n [-2, 11, 3, 10],\n [7, -3, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
357
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -9, -12, -12],\n [0, 3, -6, 7],\n [0, 0, 7, 11],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 10, 9, -2],\n [0, -9, -8, 8],\n [0, 0, 1, 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" } ]
135
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -2, 2, -6],\n [-2, 12, 8, -7],\n [2, 8, -10, 8],\n [-6, -7, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
456
MATH