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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 2, 2, -4],\n [2, -3, -6, 8],\n [2, -6, 9, -4],\n [-4, 8, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -6, 5, -5],\n [-8, 10, 6, 10],\n [5, -8, -4, 9],\n [4, -6, -11, -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" } ]
464
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 9, -8, 4],\n [10, -1, -1, -7],\n [10, -5, 3, 0],\n [-1, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
185
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -2, 7, -4],\n [12, -9, -10, -7],\n [10, 0, -5, 9],\n [7, 0, -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" } ]
978
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, -4, -7, -7],\n [0, -8, 7, 12],\n [0, 0, -5, 5],\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" } ]
120
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -9, -8, -6],\n [0, -4, 11, -9],\n [0, 0, 3, -3],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
972
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 10, -4, 8],\n [0, -4, -6, 9],\n [0, 0, 2, -9],\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" } ]
672
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -4, -10, 4],\n [-4, -10, -4, 2],\n [-10, -4, -11, -10],\n [4, 2, -10, 0]]\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": "Compute |A| for the matrix A =\n[[-1, -7, -10, -3],\n [0, 9, 5, 10],\n [0, 0, -11, 6],\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" } ]
10
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, -11, 8, 12],\n [3, -6, 9, -12],\n [6, 11, -6, -5],\n [4, -12, 8, -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" } ]
772
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 4, -1, 5],\n [4, -9, -3, 2],\n [-1, -3, -2, 4],\n [5, 2, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
934
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -3, 2, -4],\n [-3, 0, -2, 0],\n [2, -2, -5, -10],\n [-4, 0, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
238
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -7, 1, -12],\n [2, -3, 12, 1],\n [-4, -7, 0, 11],\n [7, -7, -6, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -9, 3, 10],\n [-5, -6, 7, -5],\n [-7, 3, 9, -2],\n [6, 12, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 3, -3, -6],\n [3, 11, 0, -1],\n [-3, 0, -10, -3],\n [-6, -1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -3, -1, 4],\n [-3, -5, -12, -2],\n [-1, -12, 0, -4],\n [4, -2, -4, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
799
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 11, -5, -8],\n [0, 1, 9, 9],\n [0, 0, 12, 8],\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" } ]
808
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 4, 12, 1],\n [2, 8, 7, 2],\n [4, 1, 5, -8],\n [8, -11, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
376
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 7, 4, 4],\n [7, 6, -2, 4],\n [4, -2, 10, -2],\n [4, 4, -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" } ]
422
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 11, -9, -12],\n [-12, -2, 7, 12],\n [12, 1, 10, -5],\n [2, 2, 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" } ]
549
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -10, 0, 7],\n [6, 5, 4, 9],\n [7, 2, -3, 4],\n [4, -5, -11, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
660
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -7, -12, -2],\n [0, 6, 12, -5],\n [0, 0, 1, 12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
664
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 11, 9, 0],\n [0, 1, 3, 9],\n [0, 0, 3, 9],\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" } ]
33
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 3, -1, 9],\n [-6, -12, -5, 8],\n [7, -6, -9, 9],\n [5, -9, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
924
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 6, -2, 2],\n [0, -3, -1, -8],\n [0, 0, -1, 8],\n [0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 2, 8, 2],\n [5, -9, -6, 3],\n [0, 2, -6, 9],\n [-2, 6, -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" } ]
592
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -9, -2, -5],\n [-7, 8, 3, -5],\n [-8, -10, -11, -10],\n [-9, 10, 5, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
635
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -4, -12, 2],\n [0, 8, 6, -5],\n [0, 0, -10, 12],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, -11, 2, 0],\n [-11, 6, 6, 0],\n [2, 6, 4, -4],\n [0, 0, -4, 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" } ]
128
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 8, 2, 11],\n [4, 2, -4, -3],\n [1, 12, 9, -6],\n [12, -6, 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" } ]
62
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -4, 12, 6],\n [0, 11, -12, -7],\n [0, 0, 10, 3],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, 11, 7],\n [0, -2, 5, -3],\n [-2, -1, 11, 11],\n [-10, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
826
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 10, 7],\n [0, 0, -2, 0],\n [10, -2, 9, 2],\n [7, 0, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
224
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 10, 0, -2],\n [10, -11, -8, -6],\n [0, -8, 6, -7],\n [-2, -6, -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" } ]
411
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 0, -3, -2],\n [-6, 7, -2, 4],\n [-8, 11, -5, -4],\n [9, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
244
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -3, 8, 9],\n [0, 12, 2, -2],\n [0, 0, 11, 3],\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" } ]
888
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 7, -1, 12],\n [-8, 0, 10, -3],\n [5, 4, -7, 1],\n [12, -7, 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" } ]
580
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -6, 10, 7],\n [0, 1, -7, -1],\n [0, 0, 9, -6],\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" } ]
676
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 4, -4, 6],\n [4, -1, -4, 8],\n [-4, -4, -1, -2],\n [6, 8, -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" } ]
607
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 3, 4, 4],\n [3, 2, 2, 5],\n [4, 2, -9, 8],\n [4, 5, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, 0, 2, 2],\n [0, 5, -4, -2],\n [2, -4, -11, 4],\n [2, -2, 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" } ]
970
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -7, 4, -12],\n [-7, -4, 1, 2],\n [4, 1, 8, -4],\n [-12, 2, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
328
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 8, -4, -1],\n [0, -11, 9, -7],\n [0, 0, -4, 3],\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" } ]
640
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 4, -6, -1],\n [4, -8, 8, -1],\n [-6, 8, 11, 2],\n [-1, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
767
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, 3, 5, 6],\n [3, -8, -3, 0],\n [5, -3, 1, -8],\n [6, 0, -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" } ]
987
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -11, -11, -12],\n [4, 2, 10, -11],\n [10, -4, -7, -5],\n [11, 2, -10, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
543
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -8, -7, -6],\n [-4, 11, 10, -8],\n [0, -12, 10, -10],\n [3, -10, -3, -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" } ]
636
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, -2, 1, -4],\n [-2, -12, 8, 4],\n [1, 8, -9, -3],\n [-4, 4, -3, 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" } ]
796
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -6, 3, 2],\n [-6, 12, 7, 10],\n [3, 7, 2, -2],\n [2, 10, -2, -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" } ]
485
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -9, 0, 11],\n [7, 3, -9, 11],\n [-8, 2, 4, -11],\n [9, -10, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
92
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -11, -9, -10],\n [0, 4, -5, -3],\n [0, 0, -1, -3],\n [0, 0, 0, -9]]\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[[2, -10, -3, -11],\n [0, -11, -2, -7],\n [0, 0, 11, -5],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
484
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -1, -6, 10],\n [0, -1, -10, -12],\n [0, 0, 12, 3],\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" } ]
736
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -10, 8, 11],\n [0, -10, -11, 5],\n [0, 0, -6, 10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -6, 6, 1],\n [-12, -6, 9, 2],\n [-10, 7, -6, -6],\n [6, -7, -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" } ]
645
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 10, 12, 0],\n [10, -3, -2, 12],\n [-1, 9, 7, 7],\n [11, 3, 10, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
214
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -9, 1, 9],\n [4, 11, 11, -6],\n [-3, 7, -6, 8],\n [-7, -10, -4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
821
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -2, -6, 0],\n [-2, -5, -4, -10],\n [-6, -4, 3, 2],\n [0, -10, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
816
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 7, 5, -6],\n [7, -12, -2, -1],\n [5, -2, 4, -3],\n [-6, -1, -3, 10]]? 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": "Compute |A| for the matrix A =\n[[-5, 6, 8, 5],\n [0, -9, 1, -8],\n [0, 0, 10, 3],\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" } ]
650
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -4, 7, 2],\n [-4, 4, 10, 1],\n [7, 10, -7, -7],\n [2, 1, -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" } ]
517
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -2, 9, 11],\n [-2, 0, 1, 10],\n [9, 1, 12, 6],\n [11, 10, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
969
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -6, -10, -10],\n [-7, 8, -5, -10],\n [-3, 9, 4, -11],\n [8, 12, 3, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
754
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 8, 10, -7],\n [0, -8, -10, 5],\n [0, 0, 11, -9],\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" } ]
392
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 1, 1, 10],\n [0, 1, -12, -12],\n [0, 0, -9, 7],\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" } ]
712
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 1, 7, -8],\n [0, -5, 1, 3],\n [0, 0, -5, 11],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
300
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 3, -8, 3],\n [3, 2, 0, 2],\n [-8, 0, -6, -2],\n [3, 2, -2, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
632
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 12, -1, 5],\n [-3, 11, 7, -2],\n [3, -7, 12, -11],\n [11, 8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
364
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -9, 0, 0],\n [-9, -7, 2, -8],\n [0, 2, 10, -4],\n [0, -8, -4, 3]]\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[[4, 12, 7, 6],\n [0, 10, -5, -9],\n [0, 0, 7, -4],\n [0, 0, 0, 12]]\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[[3, 5, 6, -5],\n [-2, -12, -7, -3],\n [6, -1, 5, -6],\n [1, -8, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -7, 10, 6],\n [0, -9, 9, -12],\n [0, 0, 10, -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" } ]
680
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, 8, 7],\n [11, -2, 7, 8],\n [7, 9, 3, 10],\n [10, -10, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
137
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 7, 2, 12],\n [0, 6, 5, 3],\n [0, 0, -11, 4],\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" } ]
680
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -6, -10, 11],\n [-5, 0, -2, -8],\n [-6, 4, 8, 8],\n [-3, -10, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
220
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -11, 12, -9],\n [-12, -1, -6, 10],\n [10, -6, -9, 6],\n [4, -2, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
432
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, -5, -1, -6],\n [-5, -11, 2, -2],\n [-1, 2, -6, 10],\n [-6, -2, 10, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
962
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -8, 3, 0],\n [-8, -4, -6, 2],\n [3, -6, 4, 0],\n [0, 2, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
316
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, -3, 5],\n [10, 8, -5, -6],\n [9, 4, 10, 11],\n [-2, -7, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
836
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, -10, 2],\n [0, 11, 10, 1],\n [0, 0, 1, 0],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -8, 0, -2],\n [-8, -11, -6, -2],\n [0, -6, 3, -5],\n [-2, -2, -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" } ]
911
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 0, 6, -6],\n [0, 2, 8, 2],\n [0, 0, 10, 5],\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" } ]
880
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 1, 9, 0],\n [-4, 8, -3, -12],\n [-2, -7, -5, -7],\n [11, 12, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
168
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, 2, -4, -7],\n [2, 10, -8, 6],\n [-4, -8, 8, -6],\n [-7, 6, -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" } ]
24
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -2, -2, -3],\n [0, -9, -12, -11],\n [0, 0, -3, 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" } ]
215
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 8, -1, -2],\n [-5, 2, -10, 5],\n [-6, -11, -7, 5],\n [-4, 10, -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" } ]
64
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, 4, -6],\n [0, -8, -6, 10],\n [0, 0, -1, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
448
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 3, 8],\n [-3, 0, 2, -3],\n [1, 10, 6, -3],\n [-7, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 1, -2, 8],\n [11, -9, 4, -8],\n [-8, -5, -11, -9],\n [-7, -6, -12, -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" } ]
782
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -5, -6, -2],\n [0, -4, 12, 7],\n [0, 0, -11, -9],\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" } ]
528
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 6, -10, 2],\n [0, -8, -1, -6],\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" } ]
48
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 6, -5, -1],\n [0, 3, -4, 5],\n [0, 0, 2, 12],\n [0, 0, 0, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
150
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 8, 4, -1],\n [0, -2, -10, 10],\n [0, 0, 6, -9],\n [0, 0, 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" } ]
748
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -7, 3, 4],\n [-1, 12, -8, -7],\n [-5, -4, -2, 1],\n [-12, -11, 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" } ]
700
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 6, -8, -6],\n [0, 7, -2, 0],\n [0, 0, 9, 9],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
952
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, -4, -4],\n [0, 10, 10, -6],\n [0, 0, 4, 9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 3, 1, 3],\n [0, -4, 11, -12],\n [0, 0, -11, 0],\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" } ]
176
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -12, 10, -7],\n [0, 11, 5, -6],\n [0, 0, 1, 5],\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" } ]
153
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -10, 7, 5],\n [0, 4, 3, -9],\n [0, 0, 4, 5],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
480
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, -6, -6],\n [0, 2, -4, -10],\n [0, 0, -8, 3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
256
MATH