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[ { "content": "Compute |A| for the matrix A =\n[[-12, -4, -9, 11],\n [3, -3, -1, 10],\n [2, -4, -1, 4],\n [-8, -5, -7, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
411
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, -3, 8, 0],\n [0, 4, 11, 8],\n [0, 0, 1, -3],\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" } ]
192
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 8, 2, 10],\n [8, 7, 8, 3],\n [2, 8, 5, 0],\n [10, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
295
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 11, -7, -11],\n [0, -4, 9, 1],\n [0, 0, 7, -5],\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": "What is the determinant of the matrix:\n[[-9, -6, 6, 7],\n [-6, -6, 4, -1],\n [6, 4, -2, -10],\n [7, -1, -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" } ]
550
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -3, 12, -9],\n [0, 12, -5, 4],\n [0, 0, 6, -12],\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" } ]
720
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, -4, -11, 3],\n [0, -7, -1, -7],\n [0, 0, -3, -6],\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" } ]
386
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -3, 1, -6],\n [-11, -3, 5, -9],\n [-11, -5, -7, -2],\n [-7, -3, 1, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
878
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 4, 8, -5],\n [-3, 8, 1, 11],\n [-7, 6, -3, -11],\n [4, -10, -3, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
836
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 0, 7],\n [-7, -7, 1, -3],\n [-5, -7, -2, 12],\n [-6, 0, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
132
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 10, 6, 4],\n [5, 7, -1, -8],\n [1, 9, -6, 12],\n [-3, -2, -1, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
462
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 1, 6, 6],\n [11, -5, 1, -9],\n [-3, -3, 4, 6],\n [-9, 9, 7, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
180
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -6, -12, 9],\n [0, 5, -7, -9],\n [0, 0, 7, -7],\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" } ]
750
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -10, 5, 5],\n [0, 6, 0, 5],\n [0, 0, 1, -8],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
964
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 7, -8, -2],\n [1, 4, 9, 1],\n [-11, 11, -2, -4],\n [4, 5, -5, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
935
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 2, 6, 1],\n [0, 3, -1, -12],\n [10, -2, -6, 9],\n [4, 9, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 11, -12, -11],\n [-9, -4, 11, 12],\n [7, 12, -9, -12],\n [1, -1, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 4, -7, 7],\n [0, -3, -9, 3],\n [0, 0, -8, 7],\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" } ]
168
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, -2, -11],\n [0, 7, 10, -9],\n [0, 0, 12, -10],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
544
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -10, 10, 6],\n [0, 7, 5, -2],\n [0, 0, -7, -9],\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" } ]
147
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -8, 3, 8],\n [0, 3, -9, -3],\n [0, 0, 5, 5],\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" } ]
350
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -4, -7, -6],\n [-3, -7, -2, -3],\n [-11, 2, -2, -5],\n [-9, 10, -3, -3]]? 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[[-4, 2, 6, -5],\n [2, 0, -1, 2],\n [6, -1, 6, 8],\n [-5, 2, 8, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
789
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -6, 0, -2],\n [-6, -2, -4, -6],\n [0, -4, -4, 3],\n [-2, -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" } ]
556
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 5, 5, -10],\n [0, 11, 4, 2],\n [0, 0, 12, 10],\n [0, 0, 0, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
848
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -8, 11, 6],\n [2, 12, 9, 8],\n [12, 3, -2, 12],\n [-5, 7, 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" } ]
518
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -4, -2, 8],\n [-4, -12, -5, 6],\n [-2, -5, -5, 4],\n [8, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
290
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, -1, 5],\n [0, 3, 2, -4],\n [-1, 2, 10, -4],\n [5, -4, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, 1, 4],\n [-2, 11, 2, 4],\n [1, 2, -6, 2],\n [4, 4, 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" } ]
567
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -2, -2, 6],\n [-2, -8, 0, 2],\n [-2, 0, 3, -2],\n [6, 2, -2, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
500
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 3, -9, 0],\n [3, 10, 0, 4],\n [-9, 0, 2, 1],\n [0, 4, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
585
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -10, -2, -2],\n [-10, -4, -8, -4],\n [-2, -8, -6, 10],\n [-2, -4, 10, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -11, -5, -6],\n [0, 7, 10, 3],\n [0, 0, -11, 9],\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" } ]
462
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, -9, 5, -9],\n [0, -10, 10, -6],\n [0, 0, -10, -12],\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" } ]
0
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 6, 8, 12],\n [-10, -11, -3, 2],\n [-8, 7, 0, 4],\n [5, -1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
942
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 2, 8, 6],\n [2, 1, -7, 9],\n [8, -7, -5, 10],\n [6, 9, 10, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
91
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -9, -12, 0],\n [2, -9, 5, -1],\n [-10, 3, 11, -9],\n [-6, -2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
932
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -4, -8, 0],\n [-4, -4, 8, -6],\n [-8, 8, -4, 8],\n [0, -6, 8, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
688
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -7, -11, 3],\n [0, -10, 10, 2],\n [0, 0, 12, 8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, -3, -10, 10],\n [0, -9, -8, 3],\n [0, 0, 5, 10],\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" } ]
760
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -9, -3, 6],\n [-12, -7, 1, -1],\n [-5, 6, -9, 3],\n [-1, -11, 5, 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" } ]
429
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -3, 4, -1],\n [-3, -9, 0, -8],\n [4, 0, 11, 2],\n [-1, -8, 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" } ]
411
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -6, -11, 8],\n [0, 4, -10, 11],\n [0, 0, 6, -2],\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" } ]
144
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 12, 5, 0],\n [-8, 11, -4, 4],\n [6, 1, 2, -4],\n [9, -3, -2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
624
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 3, -4, -1],\n [4, 9, 11, -5],\n [3, -5, 11, 10],\n [-4, -7, 10, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
632
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 2, -9, 3],\n [2, 12, 8, -5],\n [-9, 8, -6, 0],\n [3, -5, 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" } ]
189
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 10, -11, 2],\n [0, -5, 4, 12],\n [0, 0, 11, 3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 1, 3, 1],\n [0, -12, -6, 0],\n [0, 0, -9, 3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
960
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -1, -3, -5],\n [0, 11, -8, 3],\n [0, 0, -7, -1],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
615
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 9, 2, -10],\n [0, 10, -6, 10],\n [0, 0, -8, 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" } ]
440
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -7, -5, 10],\n [0, -3, 2, 3],\n [0, 0, -7, 8],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
890
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -4, -2, -4],\n [-4, -2, -2, -4],\n [-2, -2, 2, 3],\n [-4, -4, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
166
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -8, 6, -8],\n [-10, 2, -1, 8],\n [8, 2, 2, -12],\n [1, 7, 9, -10]]\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": "What is the determinant of the matrix:\n[[3, -11, -8, -2],\n [5, 8, -11, 4],\n [4, -5, 9, 2],\n [6, -8, 4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 2, 2, 4],\n [2, -5, 4, 1],\n [2, 4, 2, -8],\n [4, 1, -8, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
282
MATH
[ { "content": "Determine the value of det(A) where A =\n[[2, -8, 8, 7],\n [5, -10, 1, 3],\n [-9, 7, 7, -6],\n [-11, -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" } ]
22
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 9, -10, -11],\n [0, 8, -3, -2],\n [0, 0, -4, 8],\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" } ]
608
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 6, -12, -10],\n [2, 8, -6, 8],\n [-5, -9, -1, -1],\n [-4, -1, 1, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
456
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, -5, -8],\n [4, -9, 5, -8],\n [-5, 5, -8, 3],\n [-8, -8, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
986
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -12, 1, 5],\n [-10, 1, 11, -2],\n [6, 11, -11, -10],\n [0, -7, 3, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 12, 1, 6],\n [-9, -2, 4, -8],\n [1, -1, 8, 0],\n [0, 0, -5, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
665
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 7, 8, 2],\n [0, 7, -4, -8],\n [0, 0, -10, 1],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
620
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 1, -12, -12],\n [0, -1, 10, 9],\n [0, 0, -12, 1],\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" } ]
616
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -2, -4, -3],\n [-2, -11, 4, -3],\n [-4, 4, 4, -4],\n [-3, -3, -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" } ]
492
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, 12, 8, -8],\n [0, -3, -5, 9],\n [0, 0, 12, 1],\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" } ]
84
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, -8, 9, 7],\n [0, -1, 0, 6],\n [0, 0, -11, 1],\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" } ]
780
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 8, 0, -10],\n [8, 6, 12, -5],\n [0, 12, 12, 7],\n [-10, -5, 7, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
242
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -9, 10, 6],\n [-9, -12, -5, -5],\n [10, -5, 7, -8],\n [6, -5, -8, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
532
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 4, 4, 12],\n [0, 2, -5, -4],\n [0, 0, -3, 9],\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" } ]
352
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 12, -4, 10],\n [3, -9, -1, -5],\n [1, 12, -11, 8],\n [7, 0, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
286
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 12, 0, 5],\n [-4, 10, 11, -6],\n [5, 6, 0, 10],\n [10, -11, -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" } ]
557
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -4, -3, 10],\n [-4, 6, 6, 5],\n [2, 5, 9, 4],\n [5, -9, -8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
814
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 2, -10, 3],\n [2, 0, 2, 0],\n [-10, 2, -9, 5],\n [3, 0, 5, 1]]\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": "Compute |A| for the matrix A =\n[[-9, 12, 2, -10],\n [0, -8, 2, -3],\n [0, 0, -10, 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" } ]
920
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 0, -8, 2],\n [0, -12, 6, 3],\n [-8, 6, -6, 6],\n [2, 3, 6, -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" } ]
472
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 2, -7, 1],\n [2, -4, 11, 0],\n [-7, 11, 10, 0],\n [1, 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" } ]
385
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, -7, -8],\n [0, -10, 9, -7],\n [0, 0, -2, 7],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
400
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 1, 7, -9],\n [1, 11, -6, 6],\n [7, -6, -4, -1],\n [-9, 6, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
694
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 7, 3, -10],\n [0, 4, 5, -6],\n [0, 0, 1, -12],\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" } ]
680
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, -4, -2],\n [-2, 6, -2, 10],\n [-4, -2, 4, 8],\n [-2, 10, 8, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -4, -11, 9],\n [-2, 2, 4, -4],\n [-3, 8, 1, -5],\n [1, 11, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, 3, 11],\n [0, -5, 0, -4],\n [0, 0, 10, 2],\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[[7, 2, -9, 0],\n [0, -4, -8, 7],\n [0, 0, -12, -2],\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" } ]
344
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -1, 0, 2],\n [-1, -8, 2, -1],\n [0, 2, 8, -1],\n [2, -1, -1, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
509
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 0, 2, -3],\n [0, -2, -1, -5],\n [2, -1, 9, -6],\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" } ]
960
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -11, -5, 8],\n [-3, 0, 5, 3],\n [-1, -3, -7, -3],\n [-3, -9, -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" } ]
677
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -3, 2, 0],\n [-3, 0, -1, 6],\n [2, -1, -8, -4],\n [0, 6, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
626
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 4, 2, 3],\n [4, 0, 0, 0],\n [2, 0, -10, -4],\n [3, 0, -4, 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" } ]
856
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -3, 2, -2],\n [-9, -4, -1, -4],\n [-1, -10, 12, -9],\n [-3, 9, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
862
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -9, -1, 5],\n [8, 10, -2, -7],\n [-6, -5, 3, 6],\n [-7, 2, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 5, -9, 6],\n [0, 9, -2, -6],\n [0, 0, -3, 0],\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" } ]
676
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, 0, 3, -5],\n [0, -6, 0, 0],\n [3, 0, -12, 4],\n [-5, 0, 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" } ]
290
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 5, -5, -4],\n [5, -11, -10, 2],\n [-5, -10, 5, 5],\n [-4, 2, 5, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
55
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, 2, -7, -4],\n [11, -7, 8, -8],\n [-7, 5, 7, -6],\n [3, -8, 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" } ]
634
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 8, -2, -11],\n [8, -2, -6, 8],\n [-2, -6, -8, 2],\n [-11, 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" } ]
200
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -5, 7, -1],\n [-1, -9, 2, 11],\n [-3, 2, 11, 1],\n [10, 1, 9, 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" } ]
674
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -10, -3, -3],\n [-10, -9, 6, 0],\n [-3, 6, -12, -12],\n [-3, 0, -12, 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" } ]
103
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -8, 9, -8],\n [6, -10, -3, -5],\n [3, 1, -10, -6],\n [-11, -2, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
371
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 5, 4, 6],\n [-10, -7, 12, -2],\n [-10, 7, -1, 7],\n [12, 11, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
704
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -1, 0, 5],\n [-1, -10, -3, -6],\n [0, -3, 3, 6],\n [5, -6, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
609
MATH