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[ { "content": "What is the determinant of the matrix:\n[[-4, 7, 8, -6],\n [7, -6, -10, -2],\n [8, -10, -1, -5],\n [-6, -2, -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" } ]
580
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 8, 0, 2],\n [8, -12, -1, 5],\n [0, -1, -4, 0],\n [2, 5, 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" } ]
898
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -1, 4, -7],\n [7, -2, 10, -7],\n [-7, -4, -3, 6],\n [-11, -5, -12, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
927
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 10, 1, -8],\n [3, 8, 4, -12],\n [0, -10, -8, 6],\n [7, 0, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
538
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, -3, -1, 11],\n [0, 1, -9, 4],\n [0, 0, -6, 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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -9, 10, -2],\n [0, 7, 1, -4],\n [0, 0, 6, 7],\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" } ]
780
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 7, -9, 9],\n [0, -8, -4, 12],\n [0, 0, -7, -11],\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" } ]
48
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -5, -9, 5],\n [0, 3, 2, 10],\n [-1, -6, 3, -10],\n [-8, -1, 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" } ]
832
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -3, -8, 4],\n [-3, 10, 5, 0],\n [-8, 5, -11, -2],\n [4, 0, -2, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
268
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -10, 1, 8],\n [7, 2, 1, -7],\n [-3, -7, 5, 0],\n [-9, -3, -5, 4]]? 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": "Determine the value of det(A) where A =\n[[-8, -3, 4, -2],\n [-3, 11, 10, -2],\n [4, 10, 1, -8],\n [-2, -2, -8, -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" } ]
638
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -7, -3, -9],\n [11, -5, -5, 10],\n [9, 4, -12, 1],\n [-8, 3, -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" } ]
970
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 5, 2, -1],\n [-10, -9, -7, -11],\n [-2, -3, 10, -3],\n [8, 5, -4, -11]]\nRound to the nearest integer, then take the result modulo 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[[1, -7, -9, 12],\n [-3, 2, -11, 4],\n [-12, -5, -6, 8],\n [3, 5, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
64
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 3, -12, 1],\n [-8, 5, 5, -10],\n [0, -10, -10, 3],\n [-9, 6, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
117
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 3, 4, -4],\n [0, 2, -2, -5],\n [0, 0, -9, 2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
542
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -12, 6, -4],\n [2, 2, 4, 1],\n [9, 12, 12, 3],\n [-6, 11, 11, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
746
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -10, 5, 4],\n [11, 11, 4, 1],\n [3, -11, 6, -9],\n [-10, 1, -4, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 1, 0, 4],\n [0, -10, 3, -4],\n [0, 0, 11, 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" } ]
220
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -6, 2, -5],\n [0, -5, -3, 1],\n [0, 0, 3, -3],\n [0, 0, 0, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 5, -12, -7],\n [0, -3, -5, 6],\n [0, 0, 7, 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" } ]
105
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -10, 4, 10],\n [0, 7, 6, -2],\n [0, 0, 11, 1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
773
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -3, -8, -5],\n [-11, -9, 6, -12],\n [-11, 7, -5, -3],\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" } ]
357
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 10, -2, 3],\n [-12, -6, -11, 6],\n [7, -8, 1, -2],\n [-12, 6, 2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
212
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -11, 7, 1],\n [0, 9, -7, -7],\n [0, 0, -11, 0],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
228
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 0, -1, 1],\n [0, 10, -7, -8],\n [0, 0, -2, 7],\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" } ]
280
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -3, 0, 6],\n [-3, -7, 8, -1],\n [0, 8, -9, -5],\n [6, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
851
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, -6, 1, -8],\n [-6, 5, -6, 0],\n [1, -6, 7, 6],\n [-8, 0, 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" } ]
748
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -5, -4, 4],\n [0, -10, -1, -10],\n [0, 0, -7, 5],\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" } ]
200
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 5, -5, 8],\n [0, -5, -11, 9],\n [0, 0, 11, 1],\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" } ]
50
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, 5, 11],\n [0, 9, 0, 10],\n [0, 0, 5, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -8, 11, -5],\n [0, 5, 11, -3],\n [0, 0, 1, 11],\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" } ]
940
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, 0, -11],\n [0, -1, -4, -1],\n [0, 0, 2, -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" } ]
32
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 5, 0, -4],\n [5, 8, 10, 6],\n [0, 10, -1, 0],\n [-4, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 8, 6, 1],\n [-9, 3, -4, -12],\n [12, 10, 9, 0],\n [-12, 6, 3, 7]]\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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 7, -12, -12],\n [9, 11, 1, 1],\n [-7, -5, -2, 10],\n [10, -9, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
334
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 4, 10, -2],\n [4, 0, 8, 7],\n [10, 8, -3, -10],\n [-2, 7, -10, -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" } ]
376
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -6, 1, 7],\n [0, 6, 9, -12],\n [0, 0, 2, 5],\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" } ]
396
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -3, -11, -7],\n [-8, -4, -11, -8],\n [-7, 2, -7, 1],\n [9, -8, -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" } ]
826
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 9, 7, 9],\n [-8, -3, -5, 5],\n [-4, -3, 4, -7],\n [-6, 5, -10, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
446
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, 0, -4],\n [-12, 0, -7, -3],\n [-5, 2, 0, -10],\n [11, -11, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
738
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 7, 9, -10],\n [9, -1, 10, -7],\n [4, -8, -9, -9],\n [-9, 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" } ]
410
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 6, 5, -5],\n [0, -7, -2, 2],\n [0, 0, 6, 2],\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" } ]
924
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 9, -12, 0],\n [0, 5, 12, 8],\n [0, 0, -9, -4],\n [0, 0, 0, -10]]\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, -9, -2, 11],\n [0, 11, -2, -6],\n [0, 0, 1, -6],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
924
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, -4, -2],\n [0, -5, 2, 2],\n [-4, 2, -9, 6],\n [-2, 2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
500
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 6, 4, -2],\n [6, 1, 2, 4],\n [4, 2, -10, 8],\n [-2, 4, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
584
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 1, -2, 12],\n [1, -2, 3, -7],\n [-4, 0, -1, -2],\n [-3, 10, 12, 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" } ]
13
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 10, 4, -9],\n [10, 2, 6, 2],\n [4, 6, -7, -5],\n [-9, 2, -5, -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" } ]
246
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 0, 8, 4],\n [0, -1, -7, 10],\n [0, 0, 12, -3],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 10, -11, 9],\n [4, -6, 7, -1],\n [11, 9, 12, 1],\n [4, 7, 2, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -11, -4, -3],\n [3, 9, -11, 2],\n [-1, -5, 4, -9],\n [12, 1, -3, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
128
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -1, 4, 0],\n [-1, -8, -10, 4],\n [4, -10, -3, -3],\n [0, 4, -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" } ]
714
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 9, -2, 7],\n [0, -5, 12, -7],\n [0, 0, -7, 2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
580
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 12, 11, 2],\n [-12, -5, 4, -5],\n [-8, 10, -5, 1],\n [11, -12, 4, 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" } ]
775
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 0, -1, -4],\n [0, 11, -6, 9],\n [-1, -6, 10, 3],\n [-4, 9, 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" } ]
832
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -7, 1, 11],\n [0, 12, 3, 12],\n [0, 0, -11, -2],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
424
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 4, 0, 1],\n [4, -10, 4, -5],\n [0, 4, -7, 10],\n [1, -5, 10, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
134
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 4, -4, -11],\n [0, -10, 1, 1],\n [0, 0, 2, -5],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 3, 7, 7],\n [6, 4, -10, 6],\n [-12, 5, -8, -12],\n [-11, -12, 11, 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" } ]
632
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 0, 2, 7],\n [-3, 9, -6, 8],\n [-5, 3, 1, -1],\n [2, -7, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
176
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 10, -3, 3],\n [0, 3, -6, -11],\n [0, 0, -12, 1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
424
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 11, 4, 10],\n [11, -12, 4, -10],\n [4, 4, 0, 2],\n [10, -10, 2, -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" } ]
780
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 1, 10, -10],\n [0, -8, -6, -11],\n [0, 0, 10, 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" } ]
800
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -12, -8, -5],\n [-12, -10, 6, -2],\n [-8, 6, -8, 8],\n [-5, -2, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -2, 4, -4],\n [-2, 5, -7, 9],\n [4, -7, -10, 5],\n [-4, 9, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
167
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 6, -9, -11],\n [0, 9, -8, -5],\n [0, 0, 6, -4],\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" } ]
184
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 11, -10, 9],\n [2, -7, 10, 2],\n [9, 2, 6, 1],\n [-5, 1, 7, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
835
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 3, -12, -2],\n [0, 7, 6, 5],\n [0, 0, -4, -11],\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" } ]
104
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 2, 2, 0],\n [2, 10, -1, -2],\n [2, -1, -3, -4],\n [0, -2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
508
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -3, 12, 7],\n [0, -7, -5, -12],\n [0, 0, 11, 4],\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" } ]
692
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -5, 2, -11],\n [2, -2, -11, 7],\n [2, 0, -8, -9],\n [-7, -3, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
219
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -10, -3, -10],\n [-10, -12, 3, 4],\n [-3, 3, -9, -5],\n [-10, 4, -5, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
948
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 6, -4, 1],\n [0, -9, 12, 2],\n [0, 0, -10, -1],\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" } ]
640
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -12, -1, 2],\n [-9, -6, 11, -11],\n [8, 5, 8, -10],\n [-5, -1, 5, -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" } ]
718
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -8, -4, 9],\n [0, 11, 7, 8],\n [0, 0, 2, 9],\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" } ]
956
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -4, -2, 2],\n [-4, 4, 0, 6],\n [-2, 0, -2, 4],\n [2, 6, 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" } ]
8
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 6, -7, 7],\n [6, -5, 8, 0],\n [-7, 8, 12, 3],\n [7, 0, 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" } ]
788
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 3, -3, 6],\n [0, -10, -2, 12],\n [0, 0, 2, -3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 9, -7, -7],\n [-9, -3, -12, 12],\n [-3, -6, 2, -10],\n [7, -10, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -7, -8, 4],\n [8, -5, -4, -4],\n [-8, 6, 10, -6],\n [2, -7, 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" } ]
192
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, -10, 10, -12],\n [0, -5, -6, -4],\n [0, 0, -11, 11],\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" } ]
525
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 9, -7, -3],\n [0, 3, -9, 3],\n [0, 0, 8, 7],\n [0, 0, 0, 2]]\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[[-11, 5, 0, -8],\n [5, 8, -2, 8],\n [0, -2, -8, -6],\n [-8, 8, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 5, 2, 11],\n [12, -9, -3, -11],\n [10, 5, 12, -8],\n [7, 9, 4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
293
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -2, -6, -5],\n [-2, 3, -6, -6],\n [-6, -6, -2, 1],\n [-5, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
470
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 1, -7, 2],\n [1, -9, -2, 8],\n [-7, -2, 7, 0],\n [2, 8, 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" } ]
772
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -2, -2, -3],\n [-2, -8, -9, 2],\n [-2, -9, -9, -6],\n [-3, 2, -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" } ]
679
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 6, 0, 11],\n [9, -7, 8, -12],\n [-11, -1, -6, 7],\n [-7, -3, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
434
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -2, -5, 6],\n [0, -5, 6, 1],\n [0, 0, 8, -7],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 2, -6, 7],\n [2, 10, -6, 1],\n [-6, -6, 6, 4],\n [7, 1, 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" } ]
766
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 11, -6, 10],\n [-4, 4, -5, 8],\n [-6, -8, 7, -3],\n [4, 5, -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" } ]
402
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, -3, 2],\n [-9, 1, 8, -3],\n [-12, -4, 6, 0],\n [-9, 4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
746
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -1, 3, -2],\n [-7, 11, -8, 3],\n [-11, 9, 11, -7],\n [0, 0, -2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
995
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -7, -9, 8],\n [0, 3, 8, -11],\n [0, 0, -9, 5],\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" } ]
785
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 0, 6, 6],\n [0, -3, -1, 4],\n [6, -1, 1, -8],\n [6, 4, -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" } ]
160
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -12, 2, -6],\n [-12, 0, -2, 1],\n [2, -2, -3, -8],\n [-6, 1, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
590
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -10, -9, 3],\n [0, -3, -10, -2],\n [0, 0, 6, -11],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
486
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 6, 2, -7],\n [2, 12, 4, 6],\n [-8, 6, -3, 2],\n [10, -1, -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" } ]
710
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -1, -12, -2],\n [0, 7, 12, 4],\n [0, 0, -4, -10],\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" } ]
24
MATH