messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
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[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 0, -1, -2, 4, 3],\n [0, 1, 12, -9, -1, -5],\n [-1, 12, 10, 6, 2, -2],\n [-2, -9, 6, -4, 0, 10],\n [4, -1, 2, 0, 10, -8],\n [3, -5, -2, 10, -8, 7]]\n\nPresent the answer in LaTex fo... | 734 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -14, -12, -7, 12, -14],\n [0, 2, 3, -6, 10, -1],\n [0, 0, -15, 0, 2, 15],\n [0, 0, 0, -13, 9, -8],\n [0, 0, 0, 0, -8, 11],\n [0, 0, 0, 0, 0, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -1, -5, -5, 14, -8],\n [0, -11, -15, 11, -5, -13],\n [0, 0, 11, -11, -2, 6],\n [0, 0, 0, -3, 0, 6],\n [0, 0, 0, 0, -5, 15],\n [0, 0, 0, 0, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 550 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 8, 6, 3, 1, 8],\n [8, 3, -8, 1, 0, 3],\n [6, -8, 4, -2, -6, 8],\n [3, 1, -2, -6, 3, -4],\n [1, 0, -6, 3, 8, 0],\n [8, 3, 8, -4, 0, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\box... | 900 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -8, 14, 14, 10, -12],\n [-2, 15, 5, -8, 5, -4],\n [8, 14, 15, 11, 2, 15],\n [0, 11, 13, 8, 14, -2],\n [-14, 11, -5, 8, -6, 12],\n [15, -2, 7, -7, 5, -3]]\n\nPresent the answer in La... | 572 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 6, 8, 14, 7, 13],\n [9, 4, 11, 14, 13, 5],\n [5, 4, -6, -13, 13, 15],\n [2, -8, 13, -4, -3, 8],\n [-13, -3, 15, -4, 10, -7],\n [10, 7, -1, 5, -4, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed... | 678 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 0, -9, -4, -4, -4],\n [0, 4, 2, 4, -12, -6],\n [-9, 2, 12, 8, -5, 6],\n [-4, 4, 8, -9, -4, 4],\n [-4, -12, -5, -4, 1, -6],\n [-4, -6, 6, 4, -6, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 3, 1, 2, 4, -1],\n [0, 13, 8, -14, 15, 5],\n [0, 0, -12, -6, -2, -9],\n [0, 0, 0, 14, 13, 3],\n [0, 0, 0, 0, 2, -6],\n [0, 0, 0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 688 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 9, -15, -4, -7, 13],\n [0, -12, 10, -7, -4, 12],\n [0, 0, 10, -10, 14, -11],\n [0, 0, 0, -8, -3, 12],\n [0, 0, 0, 0, 1, 1],\n [0, 0, 0, 0, 0, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 920 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -4, -5, 11, 12, -10],\n [3, -5, -11, 1, 9, -9],\n [12, -4, 12, 2, -6, -13],\n [5, 6, 0, 13, 7, 14],\n [-4, 3, -15, -8, -11, 14],\n [8, -10, 14, -7, 9, 14]]\n\nPresent the answer in LaTex ... | 471 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 4, 11, -6, -14, -6],\n [4, -6, -6, -2, 2, -3],\n [11, -6, -2, 0, 0, -5],\n [-6, -2, 0, 0, 10, 2],\n [-14, 2, 0, 10, -9, 4],\n [-6, -3, -5, 2, 4, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 936 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -14, -2, 8, 9, -7],\n [0, -3, -5, 0, -3, -12],\n [0, 0, 1, 3, 6, -13],\n [0, 0, 0, -9, 7, 3],\n [0, 0, 0, 0, 9, -9],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{... | 626 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, 8, -4, 2, -3],\n [-9, -15, -4, 2, 3, 6],\n [14, 5, -1, -12, -4, 11],\n [3, 7, 0, 3, -1, -5],\n [-1, 7, 0, 11, -2, -8],\n [-12, 7, -12, 13, 1, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 700 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 6, -6, 9, -3, -15],\n [0, -11, 3, 5, -5, 8],\n [0, 0, -4, -5, 7, -8],\n [0, 0, 0, 12, 5, -7],\n [0, 0, 0, 0, 6, -8],\n [0, 0, 0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 416 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 6, 14, -10, -15, -10],\n [0, -12, -15, -1, 0, 12],\n [0, 0, 4, 8, -9, -4],\n [0, 0, 0, 3, 3, 15],\n [0, 0, 0, 0, 8, 9],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 792 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -9, 14, 8, -5, -14],\n [0, 1, 11, -15, 15, 3],\n [0, 0, 7, -8, -4, 5],\n [0, 0, 0, -3, -4, -15],\n [0, 0, 0, 0, -5, -14],\n [0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -10, 2, -2, -6, 7],\n [0, 2, 5, 10, 8, -10],\n [0, 0, -9, 12, -2, 0],\n [0, 0, 0, 10, 8, -10],\n [0, 0, 0, 0, -7, -14],\n [0, 0, 0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 680 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, 8, -6, -1, -2, -3],\n [8, 14, -2, 6, -8, 4],\n [-6, -2, 3, -4, 0, -2],\n [-1, 6, -4, -4, -15, -6],\n [-2, -8, 0, -15, 11, -6],\n [-3, 4, -2, -6, -6, 14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTe... | 842 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -1, -3, 14, 12, -11],\n [0, -4, 0, -13, -6, 10],\n [0, 0, -3, -14, 0, -15],\n [0, 0, 0, 4, 11, 0],\n [0, 0, 0, 0, 14, 9],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\... | 56 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 1, 10, 11, 6, 0],\n [0, -2, -6, 7, -10, -8],\n [0, 6, -7, -11, -1, 2],\n [4, 0, -2, 11, -3, -8],\n [4, -8, 10, -8, 8, -4],\n [4, -4, 7, 5, -7, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex form... | 840 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 12, 4, 10, -5, 15],\n [0, -6, -2, -13, -10, 10],\n [0, 0, -8, 8, 9, 0],\n [0, 0, 0, 3, -15, 1],\n [0, 0, 0, 0, 11, 13],\n [0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex forma... | 240 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, -8, -2, -4, 12],\n [-2, -1, 4, -2, 4, -4],\n [-8, 4, 14, 4, 3, -2],\n [-2, -2, 4, -2, 0, -2],\n [-4, 4, 3, 0, -4, -2],\n [12, -4, -2, -2, -2, 11]]\n\nPresent the answer in LaTex forma... | 622 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 12, -3, -7, -3, -13],\n [0, -6, -6, -14, 10, -13],\n [0, 0, -11, -9, 8, 10],\n [0, 0, 0, 7, 4, 8],\n [0, 0, 0, 0, -2, -2],\n [0, 0, 0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 560 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -8, 0, -5, 4, 2],\n [-8, 2, 0, 1, -4, 4],\n [0, 0, -10, -12, -7, 2],\n [-5, 1, -12, -11, 3, 2],\n [4, -4, -7, 3, 8, -12],\n [2, 4, 2, 2, -12, 0]]\n\nPresent the answer in LaTex format: \\... | 804 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, -2, -6, -9, 7, -5],\n [5, -4, -9, -6, -15, 7],\n [-4, -7, 9, -11, 9, 5],\n [8, -14, 11, -3, -4, -5],\n [15, 11, -10, 15, 3, 2],\n [-5, -12, -5, -13, -13, -5]]\n\nPresent the answe... | 723 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, 7, -6, 1, 1],\n [4, -11, 0, 10, 3, 6],\n [7, 0, 8, 13, -6, 6],\n [-6, 10, 13, 6, 9, -5],\n [1, 3, -6, 9, -6, 2],\n [1, 6, 6, -5, 2, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 806 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 6, -4, 10, 1, -6],\n [6, -1, 0, 2, -2, -6],\n [-4, 0, -3, -8, 0, 0],\n [10, 2, -8, 15, 6, -8],\n [1, -2, 0, 6, 7, 12],\n [-6, -6, 0, -8, 12, 0]]\n\nPresent the answer in LaTex form... | 488 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 4, -10, -1, -11, -2],\n [4, -8, 1, 6, -2, 6],\n [-10, 1, -7, 0, -6, 4],\n [-1, 6, 0, -8, 2, -4],\n [-11, -2, -6, 2, -12, 9],\n [-2, 6, 4, -4, 9, -8]]\n\nPresent the answer in LaTex... | 323 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 7, 11, -13, -9, -15],\n [0, -2, 15, 5, -6, 1],\n [0, 0, 2, 9, -11, -11],\n [0, 0, 0, -12, -9, 15],\n [0, 0, 0, 0, 9, 12],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format... | 328 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, -1, 12, -12, -12, 14],\n [0, 2, -3, 6, 11, -15],\n [0, 0, 13, -8, 7, -14],\n [0, 0, 0, 12, 14, 3],\n [0, 0, 0, 0, -10, -6],\n [0, 0, 0, 0, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex ... | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 0, 5, 12, -11, 6],\n [-15, -6, -4, -1, 10, -12],\n [-4, 9, 9, -6, 3, -13],\n [-5, 8, -12, 6, -8, 15],\n [13, 1, -6, 7, -2, -12],\n [-4, 13, -2, -14, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format... | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -7, -5, -4, 3, 3],\n [-7, 7, -6, -1, -2, 0],\n [-5, -6, 14, 9, 0, 2],\n [-4, -1, 9, -6, -3, 2],\n [3, -2, 0, -3, -1, 3],\n [3, 0, 2, 2, 3, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 797 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -15, 0, -15, -1, -11],\n [0, 6, -2, -1, -5, -3],\n [0, 0, 11, 9, 4, -11],\n [0, 0, 0, -6, -4, 11],\n [0, 0, 0, 0, -8, 3],\n [0, 0, 0, 0, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 280 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -9, 4, 6, -1, -5],\n [-9, -4, 13, -5, 9, -12],\n [4, 13, -13, 2, -8, 0],\n [6, -5, 2, 5, -8, 1],\n [-1, 9, -8, -8, 3, 10],\n [-5, -12, 0, 1, 10, -10]]\n\nPresent the answer in LaTex... | 943 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -5, 13, -7, 0, 11],\n [-11, 3, -6, 1, -9, -13],\n [-7, -15, -9, 5, -8, -14],\n [3, -11, -13, 13, -10, -14],\n [12, 13, 5, -14, -13, 13],\n [-4, 15, 5, 4, -14, 8]]\n\nPresent the answer in... | 446 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -4, 6, -4, 5, -2],\n [-4, 13, -2, 4, 0, -6],\n [6, -2, -4, 0, 2, 0],\n [-4, 4, 0, 1, 0, -2],\n [5, 0, 2, 0, -10, -4],\n [-2, -6, 0, -2, -4, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 216 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, 5, 5, -3, -10],\n [3, -13, 2, 6, 3, -5],\n [5, 2, -9, -12, 0, 2],\n [5, 6, -12, 4, 0, 1],\n [-3, 3, 0, 0, -12, -12],\n [-10, -5, 2, 1, -12, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 295 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -15, 11, 3, -10, 12],\n [13, -9, -1, 12, 1, -10],\n [7, 12, -2, -9, 10, 6],\n [1, -6, -10, 3, -5, -3],\n [8, 7, 13, 9, -11, -8],\n [3, 1, 14, 4, -8, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 434 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 4, 0, 0, 4, 9],\n [4, -9, 0, 0, -2, 4],\n [0, 0, 2, -10, 10, 2],\n [0, 0, -10, 3, 3, -8],\n [4, -2, 10, 3, 14, 6],\n [9, 4, 2, -8, 6, 14]]\n\nPresent the answer in LaTex format: \\... | 230 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -13, -9, -3, -4, -2],\n [0, 2, 14, -1, -8, -5],\n [0, 0, 11, -15, 13, -5],\n [0, 0, 0, 2, 3, -7],\n [0, 0, 0, 0, 1, 8],\n [0, 0, 0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 664 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -11, 6, -2, -4, 2],\n [-11, -7, 4, 4, 10, 8],\n [6, 4, 3, 8, 11, -2],\n [-2, 4, 8, 3, 10, -2],\n [-4, 10, 11, 10, 15, 4],\n [2, 8, -2, -2, 4, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 512 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, -4, 0, 4, -2, -2],\n [-4, 9, 0, 9, 6, -4],\n [0, 0, -3, -4, -3, 11],\n [4, 9, -4, 2, 6, 8],\n [-2, 6, -3, 6, 0, 0],\n [-2, -4, 11, 8, 0, 10]]\n\nPresent the answer in LaTex format: \\box... | 532 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, -2, 5, -11, 15, 3],\n [0, -7, -11, 11, -7, -9],\n [0, 0, -6, 1, 1, -10],\n [0, 0, 0, -12, -4, -3],\n [0, 0, 0, 0, -2, 11],\n [0, 0, 0, 0, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Y... | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 6, 8, 0, -2, -4],\n [6, -2, 3, 1, 2, 4],\n [8, 3, 13, 4, -6, -4],\n [0, 1, 4, -2, 0, 2],\n [-2, 2, -6, 0, -10, 8],\n [-4, 4, -4, 2, 8, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 576 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -2, 2, 0, 2, 12],\n [-2, 1, 2, 8, -2, 9],\n [2, 2, -2, -8, 2, -1],\n [0, 8, -8, -13, 2, 0],\n [2, -2, 2, 2, -2, 4],\n [12, 9, -1, 0, 4, -14]]\n\nPresent the answer in LaTex format: \\boxe... | 884 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 12, 9, -14, 1, 5],\n [14, -4, 11, -5, 8, 1],\n [15, -3, 13, -2, -3, -4],\n [1, 9, 10, -9, -11, -14],\n [0, -2, -6, 5, 5, -2],\n [-12, 11, -11, 14, 2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in La... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, -1, -4, 2, -4, 3],\n [-1, 8, -2, -8, -4, 8],\n [-4, -2, -3, 0, -9, 1],\n [2, -8, 0, 11, -6, -2],\n [-4, -4, -9, -6, -2, 6],\n [3, 8, 1, -2, 6, 13]]\n\nPresent the answer in LaTex ... | 691 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -5, 9, 1, 3, -3],\n [0, 3, -4, 10, -9, -13],\n [0, 0, -4, -11, -5, 8],\n [0, 0, 0, 14, -1, -1],\n [0, 0, 0, 0, 1, -15],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format... | 680 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, -3, 2, 4, -3, 6],\n [-3, -8, 5, 10, 6, 3],\n [2, 5, -15, -6, 4, -4],\n [4, 10, -6, 3, 0, 7],\n [-3, 6, 4, 0, -9, -2],\n [6, 3, -4, 7, -2, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format... | 236 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -4, 0, -4, -2, -1],\n [-4, 2, 0, 10, 0, 6],\n [0, 0, -6, 3, 0, 2],\n [-4, 10, 3, -9, 1, 4],\n [-2, 0, 0, 1, 2, -2],\n [-1, 6, 2, 4, -2, 13]]\n\nPresent the answer in LaTex format: \\boxe... | 584 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, -3, 4, 8, -2, 0],\n [-11, 15, -11, -6, 10, -3],\n [-10, 3, -2, 12, 1, 11],\n [-3, -5, 4, 0, -12, -11],\n [8, -3, -2, -12, -2, -11],\n [0, 15, -6, -6, 14, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in... | 994 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -10, 11, -4, -15, -10],\n [0, -14, 15, -15, 7, -1],\n [0, 0, -5, 14, 3, -1],\n [0, 0, 0, -4, -13, -8],\n [0, 0, 0, 0, -15, 15],\n [0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -8, 5, 4, 2, 2],\n [-8, -4, -12, -6, 10, -2],\n [5, -12, -10, 8, -2, -9],\n [4, -6, 8, 6, 10, -8],\n [2, 10, -2, 10, -15, 0],\n [2, -2, -9, -8, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 12 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -10, -11, 15, 8, -4],\n [0, -2, -7, 2, -4, -1],\n [0, 0, 14, -6, 12, 3],\n [0, 0, 0, 15, 2, 14],\n [0, 0, 0, 0, -3, 12],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex form... | 300 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 14, -12, -13, -15, -9],\n [0, -15, -6, 3, 9, 10],\n [0, 0, 9, -15, -1, -13],\n [0, 0, 0, 12, 12, -6],\n [0, 0, 0, 0, 3, -1],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Y... | 580 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, 12, 12, 9, -4],\n [12, -15, 3, 11, 1, -12],\n [12, 15, -6, -6, 2, -12],\n [15, 9, -2, -10, 0, -4],\n [-2, 5, -5, -6, 11, 11],\n [-8, -6, 14, 13, 1, -11]]\n\nPresent the answer in LaT... | 34 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, -6, -4, 3, 11],\n [14, 3, 5, -14, 12, -3],\n [-14, -12, -8, -13, -8, 4],\n [-6, -8, -8, 2, 1, -1],\n [15, -1, 1, 15, 5, 8],\n [-8, -5, 5, 12, 0, -3]]\n\nPresent the answer in La... | 120 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 11, -3, 6, -3, -8],\n [0, 3, 6, -4, 0, 5],\n [0, 0, -1, 14, -3, 3],\n [0, 0, 0, -7, 3, 0],\n [0, 0, 0, 0, -14, 0],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 112 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 8, 5, -11, -6, 5],\n [8, -8, -15, 8, 9, 1],\n [5, -15, 5, 3, -12, -10],\n [-11, 8, 3, 13, -12, 4],\n [-6, 9, -12, -12, -13, 5],\n [5, 1, -10, 4, 5, 4]]\n\nPresent the answer in LaT... | 692 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 0, 1, 0, 4, -14],\n [0, 4, -2, 10, -2, -7],\n [1, -2, 4, 6, 0, -4],\n [0, 10, 6, -15, 10, 5],\n [4, -2, 0, 10, -1, 7],\n [-14, -7, -4, 5, 7, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 739 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 9, 11, -15, 12, -11],\n [0, -3, -8, 0, -9, 14],\n [0, 0, -1, -12, 14, 6],\n [0, 0, 0, 9, 6, 0],\n [0, 0, 0, 0, -11, 14],\n [0, 0, 0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: ... | 880 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -2, 0, 2, -5, -10],\n [12, 14, -4, 8, -4, 15],\n [-6, 6, 5, -4, -8, -12],\n [2, 12, -1, 4, 8, 1],\n [12, 3, 14, 13, 4, 12],\n [4, -8, -7, -3, -2, -12]]\n\nPresent the answer in LaT... | 420 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -13, 3, 11, 13, 13],\n [6, -5, 12, 11, 11, -5],\n [-1, 2, 9, 4, -14, 14],\n [7, 1, -1, 10, 0, 10],\n [-3, 8, 13, -2, 9, 12],\n [13, 5, 0, -1, 0, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex f... | 842 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -12, 5, -10, -14, 7],\n [-10, -2, 7, 5, -9, -2],\n [-7, 5, -3, -6, -4, 6],\n [13, -1, 11, 15, 7, -5],\n [-6, -9, 5, 15, -13, -1],\n [-10, 9, 0, -12, -10, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answ... | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -1, 0, -4, 0, 6],\n [-1, -4, 4, -2, 13, 0],\n [0, 4, 15, -4, 4, 7],\n [-4, -2, -4, 5, 3, -2],\n [0, 13, 4, 3, -4, 1],\n [6, 0, 7, -2, 1, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 453 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -8, -9, -8, -15, -1],\n [-6, -5, -3, -3, -7, -14],\n [-7, -2, 6, -11, 4, -4],\n [-9, -1, -6, 11, -8, -15],\n [8, 13, 14, -9, -13, 9],\n [-13, -11, 3, -11, -8, -9]]\n\nPresent the a... | 58 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -6, -2, 2, 2, -7],\n [-6, 2, -7, 8, 4, 4],\n [-2, -7, 9, 2, 2, 0],\n [2, 8, 2, -3, -8, 2],\n [2, 4, 2, -8, 4, -7],\n [-7, 4, 0, 2, -7, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 972 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -12, -8, 0, -7, -15],\n [0, -3, 3, -7, -8, -10],\n [0, 0, -15, -13, 12, -8],\n [0, 0, 0, 7, -7, -3],\n [0, 0, 0, 0, 2, 14],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex fo... | 490 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -4, -2, -2, -2, 12],\n [-4, 2, -4, 1, -2, -2],\n [-2, -4, 9, 4, -4, -2],\n [-2, 1, 4, 12, -4, 1],\n [-2, -2, -4, -4, -3, -5],\n [12, -2, -2, 1, -5, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in... | 571 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 4, 7, 14, 8, -4],\n [4, -2, -4, -8, -4, -9],\n [7, -4, 15, -4, 2, -7],\n [14, -8, -4, 12, 4, -2],\n [8, -4, 2, 4, -2, 11],\n [-4, -9, -7, -2, 11, 11]]\n\nPresent the answer in LaTex for... | 248 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 1, 1, -12, -1, 11],\n [0, 10, 13, -3, -13, 14],\n [0, 0, 2, -12, 6, -8],\n [0, 0, 0, 4, 10, 12],\n [0, 0, 0, 0, 3, 14],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format... | 640 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -6, 4, -8, -2, -2],\n [-6, -14, 7, -8, 6, 6],\n [4, 7, -1, -9, 0, 1],\n [-8, -8, -9, -3, -2, -2],\n [-2, 6, 0, -2, -9, -3],\n [-2, 6, 1, -2, -3, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTe... | 252 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -10, -7, -1, -8, -9],\n [-10, -2, -3, -15, 1, -3],\n [4, -12, -10, 2, -1, 10],\n [5, -2, -1, -3, 5, 3],\n [9, 14, -7, 5, 4, -5],\n [5, -1, -7, -10, -9, 10]]\n\nPresent the answer in LaT... | 24 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -2, -14, 5, 6, 1],\n [0, 7, 0, -8, -13, -5],\n [0, 0, -8, 4, -5, -15],\n [0, 0, 0, -11, 3, 14],\n [0, 0, 0, 0, 7, -15],\n [0, 0, 0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: ... | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 3, -6, -15, -10, -5],\n [-2, -4, -1, 4, 8, 6],\n [4, -4, -10, -13, 14, 3],\n [-11, 14, 5, 9, 1, 7],\n [5, 12, -4, -5, 10, -1],\n [6, -1, 8, 13, 11, 13]]\n\nPresent the answer in LaT... | 570 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -2, 0, 0, -6, 0],\n [-2, 0, 4, 6, 2, 0],\n [0, 4, -14, 6, 8, 0],\n [0, 6, 6, 1, -10, 6],\n [-6, 2, 8, -10, -6, 3],\n [0, 0, 0, 6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 856 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 13, 0, -1, -4, 3],\n [4, 7, -4, -8, 5, -13],\n [-15, 10, 4, 8, -5, 10],\n [-6, 5, -4, -7, 15, -8],\n [-15, -13, -4, -9, 2, 11],\n [3, -3, 0, -1, 3, 7]]\n\nPresent the answer in LaT... | 276 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 12, 1, 2, -7, 8],\n [15, -1, -2, 5, 8, -9],\n [11, 8, -10, 5, 4, -15],\n [3, -11, 7, -14, 8, 10],\n [3, 9, -10, -3, 9, 10],\n [3, 4, -8, 2, 9, -5]]\n\nPresent the answer in LaTex fo... | 865 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 1, -2, 8, -3, 9],\n [1, 15, 6, 0, 1, 1],\n [-2, 6, -8, 2, 3, 0],\n [8, 0, 2, 0, -6, -4],\n [-3, 1, 3, -6, 3, 0],\n [9, 1, 0, -4, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 56 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[14, 2, -7, 7, 12, 14],\n [0, -7, 12, 4, 14, -10],\n [0, 0, -4, -12, -15, -1],\n [0, 0, 0, -2, -12, 2],\n [0, 0, 0, 0, -12, 5],\n [0, 0, 0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 632 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -11, 8, 0, 4, 11],\n [-11, -1, -4, -14, 2, 11],\n [2, 7, 12, 14, -1, 11],\n [-5, 2, -4, 8, -1, 14],\n [5, -6, 2, 6, 7, 2],\n [-5, -14, 3, 13, -13, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaT... | 488 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -3, 7, 11, -4, -13],\n [-11, -1, 2, 6, 11, -9],\n [-4, 11, 9, -11, -13, 9],\n [11, 2, -8, -12, 14, -2],\n [-9, 8, 3, -7, -9, -4],\n [-4, -9, -6, 11, -4, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answ... | 206 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 13, 8, 8, 14, -7],\n [0, 14, -13, 2, 10, -9],\n [0, 0, -9, -10, 2, 5],\n [0, 0, 0, -1, -5, 11],\n [0, 0, 0, 0, -6, -10],\n [0, 0, 0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \... | 512 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -4, 0, -7, 7, -6],\n [-10, -15, -2, -4, 3, 13],\n [-10, -3, -8, 7, 8, 4],\n [-3, 9, -9, -10, 13, -11],\n [10, -15, -6, -11, 1, 15],\n [-10, -7, -2, 4, -8, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in ... | 76 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -5, -4, 6, -9, 9],\n [0, -6, 3, -12, 14, 8],\n [-5, -5, -3, 3, 0, 2],\n [-7, -15, 9, 8, -9, -4],\n [15, 0, 6, -15, 6, 14],\n [5, 8, -12, 0, -3, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 116 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -9, -13, 12, 12, 8],\n [5, -15, 9, 7, -8, -6],\n [-10, -15, -4, -15, 12, 7],\n [-8, 8, -4, -8, 4, 4],\n [-3, -2, -4, 3, -13, 11],\n [-9, 9, -6, -3, -8, 7]]\n\nPresent the answer in ... | 676 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -6, 0, -8, 2, 1],\n [-6, -12, -5, 9, -6, 10],\n [0, -5, -1, 12, -10, 3],\n [-8, 9, 12, 5, -3, -8],\n [2, -6, -10, -3, 15, 6],\n [1, 10, 3, -8, 6, 12]]\n\nPresent the answer in LaTex form... | 422 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -15, -12, 11, 10, -8],\n [8, 1, 2, 6, 4, -10],\n [14, -10, -13, -6, 5, -13],\n [4, 8, 1, 1, -15, 0],\n [-7, 9, 12, 0, 6, 2],\n [-4, 5, 13, 10, -8, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 61 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 4, -8, 15, 8, -3],\n [4, -12, 0, 0, 12, -4],\n [-8, 0, 7, -7, -2, 0],\n [15, 0, -7, 13, 5, -5],\n [8, 12, -2, 5, -7, 12],\n [-3, -4, 0, -5, 12, 7]]\n\nPresent the answer in LaTex format: ... | 192 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, 1, 6, -13, 2],\n [-3, 0, -9, 10, 1, 13],\n [-9, -7, 12, 15, -13, 4],\n [-7, -7, -3, 12, -12, -2],\n [12, 5, -8, -15, 7, -9],\n [12, 3, 3, -14, -7, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: ... | 158 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 15, 2, 15, -1, 13],\n [-9, 15, 9, 15, 9, 11],\n [9, -10, -8, -5, -10, -9],\n [14, 0, 15, 3, 3, -2],\n [-10, -6, 3, -12, 14, -3],\n [1, 4, -5, 8, -9, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in L... | 974 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 0, -7, -4, -5, -6],\n [0, -15, 11, -6, -14, -4],\n [6, -8, -2, -5, -4, 12],\n [-3, -12, -12, -8, -2, -14],\n [8, 8, 7, 10, -6, 10],\n [10, 9, -4, 6, -14, 0]]\n\nPresent the answer in LaT... | 598 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 4, -5, 1, 5, -8],\n [0, 7, 0, 12, -9, 5],\n [0, 0, -3, 10, -14, -15],\n [0, 0, 0, 12, -5, -11],\n [0, 0, 0, 0, 12, -14],\n [0, 0, 0, 0, 0, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex form... | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -15, 6, 5, -4, -1],\n [4, 13, 14, 0, -14, 3],\n [12, -2, -9, -13, 0, 14],\n [7, -5, 13, -3, 8, -13],\n [11, 5, -8, 9, 9, 14],\n [-6, 13, -11, 14, -12, -14]]\n\nPresent the answer in LaTex... | 695 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -15, 1, -14, 12, -10],\n [4, 14, 15, -8, -1, 14],\n [14, -4, -15, -2, 15, -4],\n [15, -13, -8, 0, 0, -5],\n [1, -3, -12, -9, 11, -13],\n [-11, -2, 5, 7, 11, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answe... | 472 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 3, -3, 7, 12, -7],\n [0, -12, -13, 6, 6, -1],\n [0, 0, 13, 14, 12, 15],\n [0, 0, 0, 1, -14, 8],\n [0, 0, 0, 0, -8, -5],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\bo... | 528 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -3, 15, 11, -15, 10],\n [-4, -4, 10, -11, -8, -6],\n [5, -8, 9, 13, -4, -1],\n [15, -10, -11, -3, 12, -9],\n [-11, 3, -9, 11, 14, 8],\n [-12, 15, -3, 4, 14, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer ... | 766 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 6, 4, -5, 4, -2],\n [6, -12, 4, -2, 2, -2],\n [4, 4, -9, 6, -10, 1],\n [-5, -2, 6, -2, -6, 2],\n [4, 2, -10, -6, 0, -11],\n [-2, -2, 1, 2, -11, -10]]\n\nPresent the answer in LaTex... | 844 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, 10, 1, -3, -6, 1],\n [10, -12, -2, 1, 2, 9],\n [1, -2, 1, 2, 2, 10],\n [-3, 1, 2, 7, 0, 0],\n [-6, 2, 2, 0, 1, 4],\n [1, 9, 10, 0, 4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 232 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 2, 1, -15, -1, -8],\n [4, 7, 15, 0, -7, -1],\n [-10, 13, -1, 15, -8, 14],\n [13, -10, 4, 11, 1, 8],\n [-14, -1, -12, -9, 13, 1],\n [8, 1, 15, 7, 5, -1]]\n\nPresent the answer in La... | 861 | MATH |
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