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[ { "content": "What is the determinant of the matrix:\n[[-12, 8, 10, 9],\n [8, -7, -2, 0],\n [10, -2, 5, -1],\n [9, 0, -1, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
887
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -10, 4, 0],\n [-10, 9, -8, -11],\n [4, -8, 2, 8],\n [0, -11, 8, -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" } ]
232
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -7, -1, -12],\n [0, -11, 8, -5],\n [0, 0, -7, 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" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -2, 5, 9],\n [-2, 0, 0, -4],\n [5, 0, -8, -4],\n [9, -4, -4, -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" } ]
8
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -2, -6, -12],\n [0, 9, 11, 4],\n [0, 0, -1, 1],\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" } ]
288
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 12, 5, -10],\n [0, 2, 12, -11],\n [0, 0, 12, 3],\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" } ]
728
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -8, 8, 10],\n [-7, -3, -3, -7],\n [-3, 3, 0, 9],\n [10, 7, -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" } ]
685
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -3, 4, 3],\n [0, 5, -10, 6],\n [0, 0, -4, -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" } ]
160
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, -6, -6],\n [0, -5, -6, -1],\n [0, 0, -8, -12],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 2, -11, -2],\n [2, 4, 0, -4],\n [-11, 0, -4, 7],\n [-2, -4, 7, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
512
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 4, -2, 5],\n [4, 7, -2, 8],\n [-2, -2, 6, 2],\n [5, 8, 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" } ]
282
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 4, 12],\n [0, -5, 7, 9],\n [0, 0, -4, 7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -5, 2, 11],\n [0, 2, 1, -9],\n [0, 0, -12, -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" } ]
864
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -2, 2, 2],\n [-2, -7, 1, -8],\n [2, 1, 8, 0],\n [2, -8, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 8, 12, -5],\n [-9, -7, -9, -6],\n [-7, -5, -9, 1],\n [9, -12, 7, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
554
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -8, -9, 1],\n [1, 11, 6, -7],\n [-8, 5, -10, 8],\n [-1, -9, 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" } ]
480
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -11, -10, -1],\n [12, 11, -12, -2],\n [-5, -10, -4, -3],\n [5, 3, 12, 0]]? Round to the nearest integer, then express your answer 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[[2, 9, -11, 9],\n [5, 12, 1, -4],\n [12, 8, -6, 8],\n [0, 6, -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" } ]
554
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, -11, 1],\n [0, 8, 9, 9],\n [0, 0, -8, 6],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 4, 6, 11],\n [0, -2, -8, 8],\n [0, 0, 12, -5],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -5, 10, -8],\n [0, -10, 10, -5],\n [0, 0, 12, 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" } ]
200
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 7, 8, 1],\n [7, 2, 6, 4],\n [8, 6, 9, 2],\n [1, 4, 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" } ]
533
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -3, -4, 8],\n [-4, -7, 8, 9],\n [-7, 6, 5, 2],\n [-3, -4, 11, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
194
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 7, -2, -6],\n [0, -3, 7, -12],\n [0, 0, -7, -3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
155
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 7, 3, 0],\n [-5, -3, 2, 11],\n [6, -8, 6, -7],\n [6, -10, -9, 12]]\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[[2, -6, 8, 10],\n [12, 5, 11, -12],\n [-2, -1, -7, -3],\n [10, -4, 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" } ]
844
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -9, -6, -2],\n [-9, -4, -4, 1],\n [-6, -4, -2, -10],\n [-2, 1, -10, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -10, 7, -9],\n [0, -11, -2, 5],\n [0, 0, -7, -3],\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" } ]
152
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -4, 9, 7],\n [2, 10, -5, 3],\n [4, -10, 7, -7],\n [-4, -2, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
348
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -9, -5, 6],\n [-5, -8, 11, 2],\n [-3, 2, 6, 12],\n [-1, 6, 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" } ]
903
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 12, -9, -3],\n [7, -4, -3, 9],\n [7, 3, -2, 11],\n [-12, -8, -11, -9]]? 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": "What is the determinant of the matrix:\n[[7, 2, -5, -6],\n [2, 7, -6, 2],\n [-5, -6, -12, -4],\n [-6, 2, -4, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
46
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 2, -5, -11],\n [-5, 3, -1, -2],\n [11, 9, 3, -11],\n [11, 1, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
926
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -6, -6, 12],\n [-8, 12, -1, -9],\n [-4, 2, 12, -11],\n [-5, 7, 6, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
378
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -2, -3, 8],\n [-8, 11, 6, -5],\n [-12, -7, -12, -5],\n [-3, -4, -1, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 10, 1, -7],\n [0, -1, -4, 10],\n [0, 0, -2, 2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -11, -1, -6],\n [-11, -12, 8, -2],\n [-1, 8, 5, 0],\n [-6, -2, 0, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
317
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -4, 4, -2],\n [0, -7, 7, 9],\n [0, 0, -5, 6],\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" } ]
740
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 3, -10, 5],\n [-10, 8, 7, 9],\n [-3, -7, -4, 1],\n [8, -7, 12, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
866
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -7, 0, -7],\n [3, 10, -12, -4],\n [1, -2, -9, 2],\n [6, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
512
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 4, -11, -7],\n [0, -6, 10, -11],\n [0, 0, 7, 5],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -12, -9, -8],\n [0, -8, -3, -2],\n [0, 0, 1, 4],\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" } ]
840
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -9, 1, 12],\n [-6, 8, 8, 10],\n [-6, 9, 4, -12],\n [11, -2, -11, -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" } ]
756
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 9, 12, 4],\n [0, -2, -9, 4],\n [0, 0, 11, -5],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
790
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -4, -9, 8],\n [12, 3, 4, -1],\n [-2, -11, -2, 4],\n [-1, 12, 3, -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" } ]
177
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 6, -4, -5],\n [6, -9, -2, -1],\n [-4, -2, -12, -2],\n [-5, -1, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
248
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 2, 0, -8],\n [2, 7, -2, 0],\n [0, -2, 8, 6],\n [-8, 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" } ]
980
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -2, -1, -2],\n [-2, 7, 4, -1],\n [-1, 4, -3, 2],\n [-2, -1, 2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
435
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -3, -11, 6],\n [-3, -9, 5, -10],\n [-11, 5, -9, 8],\n [6, -10, 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" } ]
772
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -9, -1, 8],\n [-7, 4, -9, -4],\n [5, 11, -7, -1],\n [10, 5, 9, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
327
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 10, 9, -7],\n [0, 10, -11, -5],\n [0, 0, -10, 9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 6, -3, -4],\n [-5, 0, -5, 3],\n [-8, 11, 9, 6],\n [5, -1, -9, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
852
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 11, 0, -11],\n [0, 4, 4, 12],\n [0, 0, 12, 5],\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" } ]
280
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -6, 0, -7],\n [-11, 5, 10, -12],\n [-2, 8, -4, -11],\n [1, 8, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -6, -5, -5],\n [-7, -4, 7, -8],\n [11, 1, 4, 12],\n [1, 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" } ]
949
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -1, 6, 8],\n [-1, 7, 4, 0],\n [6, 4, -5, -2],\n [8, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 8, -2, -2],\n [0, 11, -5, 1],\n [2, 12, 4, -7],\n [4, 6, 6, 3]]\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[[-8, -8, -3, -4],\n [-8, 6, -4, -3],\n [-3, -4, -11, 0],\n [-4, -3, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
451
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 5, -8, -3],\n [10, 7, -7, -3],\n [-10, 2, -9, 1],\n [1, -2, 4, -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" } ]
619
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -10, -8, 0],\n [-10, 3, -4, -2],\n [-8, -4, 10, -4],\n [0, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 5, -1, 9],\n [5, 1, -4, 5],\n [-1, -4, 2, 6],\n [9, 5, 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" } ]
501
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -2, 12, 1],\n [0, 3, 7, 3],\n [0, 0, 10, 5],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
620
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -11, 5, 1],\n [-3, 0, -12, -11],\n [1, -12, 1, -6],\n [0, -1, -1, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -4, 8, 3],\n [-4, 10, -8, -3],\n [8, -8, 9, 8],\n [3, -3, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
536
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -6, -6, -3],\n [-6, -12, 6, -3],\n [-6, 6, 5, -7],\n [-3, -3, -7, -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" } ]
238
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -8, -3, 10],\n [-8, 4, -1, 0],\n [-3, -1, -6, 6],\n [10, 0, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
290
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 8, 1, 1],\n [0, -7, 6, -9],\n [0, 0, 5, 4],\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" } ]
800
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -1, 1, 9],\n [1, -6, 9, -7],\n [9, -6, -5, 12],\n [-11, 1, -11, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
375
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 4, -5, -4],\n [4, 9, 2, 5],\n [-5, 2, -7, -2],\n [-4, 5, -2, 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" } ]
952
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 0, 7, 6],\n [0, -4, 2, 0],\n [7, 2, 5, -2],\n [6, 0, -2, -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" } ]
80
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, -9, 2, 2],\n [-9, -9, 4, -8],\n [2, 4, -4, 6],\n [2, -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" } ]
712
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 12, 9, 6],\n [-11, -4, -2, -3],\n [-5, 11, -1, -8],\n [-4, 6, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -10, -2, -5],\n [5, 4, 6, 2],\n [-12, 0, 9, 4],\n [-1, -8, -8, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
778
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -3, 2, 0],\n [-3, 2, -1, -6],\n [2, -1, -4, 8],\n [0, -6, 8, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 1, -7, 0],\n [1, 1, 0, -4],\n [-7, 0, 10, 6],\n [0, -4, 6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
956
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 5, -2, -1],\n [5, -6, 9, 4],\n [-2, 9, 10, -6],\n [-1, 4, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
416
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 4, -3, -4],\n [4, 1, 0, -8],\n [-3, 0, -6, 9],\n [-4, -8, 9, 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" } ]
266
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 1, 4, 2],\n [1, -1, -4, 2],\n [4, -4, 2, -2],\n [2, 2, -2, 7]]\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[[-8, -1, 12, -3],\n [-6, -9, 8, -11],\n [0, 12, 2, 7],\n [12, 10, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
324
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, -8, -3],\n [-2, -2, 0, -6],\n [-8, 0, -12, 2],\n [-3, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 8, 9, -5],\n [-5, 11, 4, 4],\n [-4, 6, -12, 0],\n [-3, -11, -8, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
896
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -5, 6, 12],\n [-5, 4, 5, -2],\n [6, 5, 5, -4],\n [12, -2, -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" } ]
582
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -6, 2, -6],\n [-6, 1, -1, -8],\n [2, -1, -3, -2],\n [-6, -8, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -12, 11, -10],\n [0, 3, 12, -10],\n [0, 0, -7, -8],\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" } ]
677
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -5, 4, 12],\n [-5, 10, 8, -2],\n [-11, -9, -2, 8],\n [-9, 2, 6, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
122
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 6, 12, 2],\n [6, 3, 0, 6],\n [12, 0, -3, -6],\n [2, 6, -6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -8, -6, 0],\n [-8, 12, 7, 4],\n [-6, 7, -10, 5],\n [0, 4, 5, -8]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -1, 10, -6],\n [0, -2, 3, -3],\n [0, 0, -1, 11],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 6, -2, 4],\n [6, -4, 7, -10],\n [-2, 7, 10, -4],\n [4, -10, -4, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 4, -5, 8],\n [5, -9, -4, -1],\n [-9, 9, -6, -4],\n [2, 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" } ]
226
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -1, 4, 6],\n [0, -11, -4, 7],\n [0, 0, 3, -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" } ]
690
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -8, -3, 8],\n [-9, -5, 5, 2],\n [-8, 9, 8, -9],\n [3, 12, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
707
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 0, 5, -1],\n [12, -7, 6, 4],\n [6, 9, 4, -1],\n [7, 2, 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" } ]
619
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 10, 2, 8],\n [0, 8, 11, -3],\n [0, 0, 5, -10],\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" } ]
600
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -12, -3, 5],\n [0, -1, -6, -6],\n [0, 0, 10, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -8, -3, 5],\n [-11, 7, 2, 10],\n [5, 12, -5, 7],\n [-3, -1, -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" } ]
510
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -1, 0, 1],\n [0, 10, -4, 4],\n [0, 0, -2, -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" } ]
640
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -11, -7, 3],\n [11, 10, 8, 1],\n [3, 9, 1, -11],\n [5, 3, -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" } ]
364
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 8, -11, 3],\n [7, 1, 9, -12],\n [-7, 2, 6, 10],\n [7, 5, 12, -2]]\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": "Determine the value of det(A) where A =\n[[7, -10, 12, 11],\n [-8, -8, 3, 1],\n [-6, -10, 12, -12],\n [2, -3, 1, -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" } ]
324
MATH