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[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 4, 4, 4],\n [4, -11, 9, -4],\n [4, 9, -12, -6],\n [4, -4, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
732
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 5, -12, 11],\n [-6, -4, -6, 6],\n [-7, -6, 7, 2],\n [-9, -5, -9, 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" } ]
592
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -8, -8, -8],\n [-8, -4, -4, -7],\n [-8, -4, -7, -2],\n [-8, -7, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
743
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 2, 10, 11],\n [5, 10, -3, 6],\n [11, -10, 7, 4],\n [-12, 1, 0, 0]]\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" } ]
598
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 [0, 5, -9, -11],\n [0, 0, -7, 0],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, -12, 11, -3],\n [-2, -12, -5, -12],\n [11, -4, 7, 10],\n [11, 10, 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" } ]
706
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 7, 3, -10],\n [7, -8, -9, 1],\n [3, -9, -8, 3],\n [-10, 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" } ]
972
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 7, 9, 12],\n [-6, 7, -12, -11],\n [1, 1, -7, 6],\n [0, 12, -12, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
816
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, -6, 11],\n [8, -4, 8, 7],\n [11, -8, -1, 1],\n [-6, -9, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 1, -9, 1],\n [0, -10, 3, -3],\n [0, 0, 12, 0],\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" } ]
600
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 10, -3, -6],\n [10, -4, -1, 2],\n [-3, -1, -3, 4],\n [-6, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
420
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 4, 0, 8],\n [-11, 1, 6, -1],\n [2, 1, -11, -7],\n [-7, 3, 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" } ]
984
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -10, -9, -5],\n [0, -10, -9, -10],\n [0, 0, 2, 7],\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": "Compute |A| for the matrix A =\n[[-9, -10, 5, 6],\n [-10, 0, -4, -2],\n [5, -4, -11, 1],\n [6, -2, 1, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 10, -8, 6],\n [10, 9, -4, 0],\n [-8, -4, 9, -9],\n [6, 0, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
408
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -4, 9, 9],\n [-11, -2, -10, -1],\n [8, -12, -6, 2],\n [-12, 12, 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" } ]
336
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, 6, 6],\n [-2, -3, 6, 5],\n [6, 6, 7, -7],\n [6, 5, -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" } ]
176
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -9, -10, -1],\n [0, 6, 2, 5],\n [0, 0, -1, 2],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
330
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -12, 5, -5],\n [0, 8, 0, 3],\n [0, 0, -3, -9],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -4, 0, -4],\n [0, 4, 0, -9],\n [7, -4, -6, -10],\n [6, 1, -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" } ]
988
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, -4, -9],\n [0, -5, 9, -12],\n [0, 0, -9, -1],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
685
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 7, 1, 10],\n [10, 2, 8, -11],\n [9, 10, 5, 2],\n [11, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
427
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 7, 12, -5],\n [-6, -2, 11, -7],\n [3, -7, 11, 3],\n [6, -11, -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" } ]
622
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -5, -8, -3],\n [-5, -9, 11, -2],\n [-8, 11, -3, -2],\n [-3, -2, -2, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
810
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 0, 7, 0],\n [0, -7, -7, -5],\n [7, -7, -4, 1],\n [0, -5, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -11, -1, 0],\n [0, 12, 3, 2],\n [0, 0, 6, 3],\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" } ]
952
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -10, -10, -8],\n [-12, -7, -10, -1],\n [-7, -4, -12, 8],\n [11, -5, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
986
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, 0, 6, 0],\n [1, 1, -3, 0],\n [-11, 3, 5, -7],\n [10, -12, 12, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
412
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 2, -1, 1],\n [0, 6, 2, 10],\n [0, 0, 7, 3],\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" } ]
740
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -2, 6, 5],\n [-2, -12, 2, 4],\n [6, 2, 12, 0],\n [5, 4, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -9, 8, -10],\n [-5, 3, 2, -5],\n [-10, 8, 2, -6],\n [6, -5, -2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 1, 9, 7],\n [1, -12, 2, -3],\n [9, 2, -7, -6],\n [7, -3, -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" } ]
34
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 0, 2, 4],\n [0, -6, 1, 6],\n [2, 1, -10, -4],\n [4, 6, -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" } ]
781
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -6, -8, 5],\n [-6, 1, -6, -1],\n [-8, -6, 10, -8],\n [5, -1, -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" } ]
778
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 2, 2, -2],\n [2, -6, 6, -5],\n [2, 6, -12, 6],\n [-2, -5, 6, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
196
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 2, -2, 1],\n [2, 3, -2, -8],\n [-2, -2, 2, -4],\n [1, -8, -4, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
734
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 0, -1, 2],\n [0, 1, 3, 3],\n [0, 0, -11, 11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
132
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 5, 1, 11],\n [-10, -7, 10, -6],\n [9, 4, -9, 0],\n [-8, -12, -7, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
810
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 3, 7, -6],\n [0, -6, -11, -7],\n [0, 0, -3, -12],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 6, 2, -2],\n [6, -1, -8, -4],\n [2, -8, -8, 3],\n [-2, -4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
479
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 8, 4, 10],\n [0, -12, -8, -11],\n [0, 0, 9, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -6, 6, 6],\n [-10, -6, -12, 4],\n [-6, -5, 9, -2],\n [2, 10, 7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 7, 8, 11],\n [0, 1, 0, 11],\n [0, 0, 9, -9],\n [0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 3, -6, -1],\n [0, 6, -2, -11],\n [0, 0, -11, 2],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 9, 5, 0],\n [3, 12, 1, 12],\n [-10, -3, 2, 4],\n [11, -3, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
510
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 2, -8, 0],\n [2, -7, -2, 0],\n [-8, -2, -2, 4],\n [0, 0, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, 6, 0],\n [0, -12, -11, -2],\n [6, -11, 5, -5],\n [0, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 8, 12, 2],\n [8, 12, -12, 4],\n [7, 11, 1, 11],\n [-1, -1, -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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 3, 6, -8],\n [3, 2, 10, 8],\n [6, 10, 2, -6],\n [-8, 8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
816
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, 2, 6],\n [-4, -11, -2, 2],\n [2, -2, -11, 8],\n [6, 2, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
612
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 0, -12, -12],\n [0, -1, -9, -2],\n [7, 2, 10, -1],\n [-9, 10, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -8, -1, -4],\n [-8, 11, -7, -6],\n [-1, -7, 3, 2],\n [-4, -6, 2, 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" } ]
443
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -5, 7, 10],\n [4, 10, -7, 10],\n [-11, -3, 9, 5],\n [-3, 3, 11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
742
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 2, 7, 12],\n [0, 1, -7, -10],\n [0, 0, -10, -12],\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" } ]
990
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, 11, 8],\n [-12, 9, -11, -8],\n [1, -2, 12, -1],\n [1, 7, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
979
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -10, 1, 1],\n [5, -12, -12, -7],\n [6, 4, -8, -11],\n [7, -2, -1, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 2, -8, 0],\n [2, 0, 2, -10],\n [-8, 2, -4, -8],\n [0, -10, -8, 5]]\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[[7, -11, -6, 8],\n [0, 6, -9, 5],\n [0, 0, 8, 11],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -8, 2, 4],\n [0, -9, -4, -11],\n [0, 0, -12, -2],\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" } ]
940
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 0, -3, 0],\n [0, -11, 3, 4],\n [0, 0, -3, 3],\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" } ]
630
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -8, -3, -4],\n [0, -8, 5, -7],\n [0, 0, 12, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, 9, 2, 5],\n [-12, 3, 5, -12],\n [12, -6, 6, 4],\n [-1, -4, -5, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
256
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 1, -12, 9],\n [0, 8, 8, 0],\n [0, 0, -4, -7],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 5, -9, 5],\n [5, -11, -11, 12],\n [-7, -7, -4, 3],\n [-1, 1, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
522
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 8, -1, 5],\n [0, 8, -6, -6],\n [0, 0, 2, 9],\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" } ]
424
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, 0, -5],\n [-2, -5, 7, 0],\n [0, 7, -3, 7],\n [-5, 0, 7, 2]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -9, -11, -10],\n [0, -6, 1, -9],\n [0, 0, -7, 6],\n [0, 0, 0, -11]]\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[[-10, 5, -12, 7],\n [0, 5, 1, -12],\n [0, 0, -5, -4],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
750
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, -5, -10],\n [0, -9, 4, -8],\n [0, 0, 9, 12],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
872
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -11, -11, 7],\n [-9, 10, -6, 2],\n [7, -4, 8, 6],\n [9, -3, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
770
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 7, -9, -11],\n [0, -12, 0, -3],\n [0, 0, 2, 9],\n [0, 0, 0, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -2, 2, -3],\n [-2, 6, -6, 0],\n [2, -6, -4, 5],\n [-3, 0, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 10, 7, 10],\n [0, 3, -3, 6],\n [0, 0, 10, 11],\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" } ]
190
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 8, -1, -1],\n [8, -10, 2, -4],\n [-1, 2, 9, -2],\n [-1, -4, -2, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
906
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 7, 2, -6],\n [-9, 2, -4, 12],\n [-5, 5, 2, 7],\n [9, 5, 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" } ]
399
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -4, -4, 6],\n [-4, 6, -8, 6],\n [-4, -8, -3, -2],\n [6, 6, -2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -12, -8, -12],\n [8, 10, -2, 11],\n [0, 0, 3, 10],\n [6, -12, 5, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
948
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 10, -8, -6],\n [0, -4, 7, 2],\n [0, 0, -3, 7],\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" } ]
704
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 4, 3, 4],\n [4, 7, -1, 0],\n [3, -1, 8, 12],\n [4, 0, 12, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
636
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -8, 4, -1],\n [-8, -11, -8, 1],\n [4, -8, 6, 2],\n [-1, 1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
678
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -8, -5, -3],\n [0, -7, -10, 12],\n [0, 0, 5, 0],\n [0, 0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 8, 6, 6],\n [-6, -7, -11, 1],\n [-9, 8, -4, -7],\n [-3, 5, 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" } ]
134
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -11, -2, 2],\n [-11, 0, -2, 6],\n [-2, -2, -9, 6],\n [2, 6, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
672
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -8, -11, -9],\n [5, 12, -11, -6],\n [12, -5, 2, 12],\n [-7, -10, 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" } ]
70
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -12, 6, 10],\n [-4, 0, 12, 2],\n [10, -2, 5, 2],\n [9, -7, 6, -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" } ]
292
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 11, 9, -5],\n [-11, 12, 6, -7],\n [-12, 12, -6, 6],\n [-7, 10, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -4, -3, 10],\n [-9, -7, -3, -8],\n [-1, -8, -5, 9],\n [12, 9, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
838
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 2, 6, 1],\n [11, -4, -6, 2],\n [12, 9, -10, 6],\n [3, -8, -12, -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" } ]
750
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 5, -5, -8],\n [0, -6, 11, 12],\n [0, 0, 8, -1],\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" } ]
960
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, 5, 6],\n [1, -12, -8, 12],\n [-3, 5, 5, 9],\n [-10, -4, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
353
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 11, -1, -8],\n [7, -7, 2, -5],\n [10, -1, -7, -4],\n [-10, 9, 1, 3]]? 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": "What is the determinant of the matrix:\n[[-6, -11, -11, 4],\n [-3, 6, 11, -7],\n [-9, 11, -5, 6],\n [-11, -12, -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" } ]
962
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -2, 0, 6],\n [-2, 0, 2, 10],\n [0, 2, -1, 10],\n [6, 10, 10, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
488
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 11, 7, 7],\n [-5, 2, -2, -10],\n [9, 0, -3, 1],\n [-11, -10, 10, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
630
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 2, 12, -9],\n [1, -3, 4, -12],\n [-12, 2, 8, 0],\n [-2, -12, 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" } ]
344
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -2, -4, 0],\n [7, -1, -9, -6],\n [-12, 10, 8, 7],\n [2, -11, -11, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
286
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -1, 10, 2],\n [-12, -1, 3, 1],\n [4, 0, -10, 3],\n [-3, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 4, 4, 5],\n [4, 10, 10, 6],\n [4, 10, -8, 2],\n [5, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
652
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -11, -2, 3],\n [7, 10, 7, -2],\n [4, -6, 8, -1],\n [10, -9, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
367
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 5, -11, 0],\n [7, -2, 2, -2],\n [-1, 7, -1, -1],\n [6, 6, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
429
MATH