messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -7, -7, 2, 8, -11],\n [14, 0, -14, 9, -12, 5],\n [7, 2, -11, -8, -4, -2],\n [11, 1, -4, 11, 8, -14],\n [-12, -5, -4, 3, -14, -6],\n [-6, -14, 10, 6, 3, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format... | 2 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, -4, 14, -9, 0, 8],\n [-4, -3, -8, 4, -5, -1],\n [14, -8, 7, -2, -2, -13],\n [-9, 4, -2, -12, -1, -5],\n [0, -5, -2, -1, 5, -8],\n [8, -1, -13, -5, -8, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 911 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -6, -8, -2, 3, -2],\n [-6, -1, 6, -8, -13, -1],\n [-8, 6, -4, -9, -2, -6],\n [-2, -8, -9, -13, -6, 0],\n [3, -13, -2, -6, -15, 2],\n [-2, -1, -6, 0, 2, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer... | 154 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -2, -11, 13, 3, -14],\n [0, 15, -10, -5, -4, 8],\n [0, 0, 13, -6, -2, -12],\n [0, 0, 0, -1, -7, 10],\n [0, 0, 0, 0, -4, -2],\n [0, 0, 0, 0, 0, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Y... | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 15, 15, 15, -8, -8],\n [0, 3, -11, 15, -9, 14],\n [0, 0, -2, 9, 5, -1],\n [0, 0, 0, 15, 4, 15],\n [0, 0, 0, 0, 13, 1],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\box... | 830 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 14, -11, -2, 10, 4],\n [0, 7, -2, 6, -14, 5],\n [0, 0, 2, -10, -7, -7],\n [0, 0, 0, -4, 9, 5],\n [0, 0, 0, 0, 6, 4],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\... | 64 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 0, -1, 13, -5, 4],\n [7, 1, 14, 12, 3, 6],\n [10, 1, -1, -3, 7, 2],\n [7, 0, 14, 4, 9, 5],\n [-15, 12, 11, 4, 11, -3],\n [-12, -4, -1, 4, -4, 3]]\n\nPresent the answer in LaTex fo... | 125 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 10, -1, 5, -11, -5],\n [0, -6, 12, 10, -3, 9],\n [0, 0, 4, -1, 2, -8],\n [0, 0, 0, -5, 11, -11],\n [0, 0, 0, 0, 10, -10],\n [0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \... | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -1, -1, -3, 0, 8],\n [-1, -3, -6, 6, 6, 2],\n [-1, -6, -9, 2, -10, 3],\n [-3, 6, 2, -5, -5, 2],\n [0, 6, -10, -5, 0, -4],\n [8, 2, 3, 2, -4, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex f... | 196 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, -5, 2, 6, 9, -11],\n [-11, 4, 1, -12, -7, -2],\n [-7, 7, -3, 0, 4, -3],\n [-7, 5, -4, -4, -6, 13],\n [-14, 9, 6, -11, -5, 10],\n [12, 8, -14, 5, -6, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTe... | 757 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -6, 10, -5, -7, -9],\n [0, -9, 0, 9, 3, 0],\n [0, 0, -2, -3, 13, -13],\n [0, 0, 0, -9, -14, -6],\n [0, 0, 0, 0, -10, 13],\n [0, 0, 0, 0, 0, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -11, -2, 2, -4, 6],\n [-11, 2, -4, -4, 2, 0],\n [-2, -4, -5, -6, 2, 2],\n [2, -4, -6, 14, 0, -3],\n [-4, 2, 2, 0, -9, 4],\n [6, 0, 2, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\... | 761 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -13, 11, 2, -13, 13],\n [-4, -14, 14, -8, 15, 12],\n [5, -2, 3, -5, 0, -2],\n [-8, 14, 8, 11, 4, -2],\n [9, -4, 1, 7, -4, 5],\n [-4, -4, -9, -6, 14, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 751 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 2, 11, 15, -13, -13],\n [-9, 6, 1, 12, 13, -10],\n [0, 12, -11, 6, 8, 1],\n [13, -5, 6, -4, -4, -12],\n [-7, -2, -4, -6, -8, 7],\n [-13, 11, -3, 0, 9, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaT... | 824 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 3, 6, 14, 2, -8],\n [0, 1, 8, -7, -6, -7],\n [0, 0, -6, 13, -8, -12],\n [0, 0, 0, -9, 9, -6],\n [0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: ... | 28 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 0, 4, -6, -2, -14],\n [0, -12, -4, -1, 6, -2],\n [4, -4, -6, -7, -4, 3],\n [-6, -1, -7, 15, 0, 3],\n [-2, 6, -4, 0, -10, 4],\n [-14, -2, 3, 3, 4, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in L... | 924 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 8, 0, 9, 0, 4],\n [8, -5, 2, -2, 4, -4],\n [0, 2, 13, 2, 4, 3],\n [9, -2, 2, 12, -8, -2],\n [0, 4, 4, -8, 0, 4],\n [4, -4, 3, -2, 4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 208 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 8, 13, 10, -7, 3],\n [0, -4, -5, 10, -15, -5],\n [0, 0, 11, -8, 9, 4],\n [0, 0, 0, -5, 13, 3],\n [0, 0, 0, 0, -10, 12],\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 forma... | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 9, -6, 6, -4, 2],\n [9, -14, -6, 2, 10, 2],\n [-6, -6, 14, -2, 0, 2],\n [6, 2, -2, -12, 10, -8],\n [-4, 10, 0, 10, 10, 6],\n [2, 2, 2, -8, 6, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex forma... | 120 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 1, 10, 9, 4, -10],\n [0, 3, -15, -10, 10, -11],\n [0, 0, -3, 4, 1, 10],\n [0, 0, 0, -3, 7, -15],\n [0, 0, 0, 0, 11, 8],\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 format... | 504 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 4, -4, 2, 0, 6],\n [4, -2, -6, 0, -9, -4],\n [-4, -6, -11, -3, -7, -7],\n [2, 0, -3, 11, -14, -7],\n [0, -9, -7, -14, 10, -2],\n [6, -4, -7, -7, -2, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 432 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 8, -11, -5, 6, 1],\n [0, 3, 4, 11, 7, 11],\n [0, 0, -11, 1, 3, -5],\n [0, 0, 0, -13, -1, 2],\n [0, 0, 0, 0, -11, -7],\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: \\box... | 58 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 10, 4, 10, -6, -10],\n [10, 15, 10, -6, -2, 2],\n [4, 10, 13, -5, 3, 5],\n [10, -6, -5, -8, 5, 6],\n [-6, -2, 3, 5, 14, -4],\n [-10, 2, 5, 6, -4, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 820 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -4, -5, 0, -10, 6],\n [-4, 12, 10, 4, -6, 0],\n [-5, 10, -8, 10, 7, -4],\n [0, 4, 10, -11, 8, 8],\n [-10, -6, 7, 8, 5, 11],\n [6, 0, -4, 8, 11, -6]]\n\nPresent the answer in LaTex ... | 848 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 12, 0, -10, 4, 8],\n [-6, -12, -10, 14, -4, -13],\n [12, -4, 7, 0, -4, -1],\n [6, 7, 15, 5, 5, 2],\n [0, -10, 1, 7, -13, 2],\n [-5, 7, 9, 1, -10, 8]]\n\nPresent the answer in LaTex... | 173 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, 3, -1, 0, -1],\n [-4, 10, 4, 6, -8, 9],\n [3, 4, 5, -2, -9, 2],\n [-1, 6, -2, 10, 2, -1],\n [0, -8, -9, 2, -1, -12],\n [-1, 9, 2, -1, -12, -3]]\n\nPresent the answer in LaTex format: ... | 402 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -10, -2, 2, -5, 4],\n [0, 5, -3, 0, 11, 8],\n [0, 0, 7, -2, 6, -13],\n [0, 0, 0, -6, -15, 2],\n [0, 0, 0, 0, -11, 10],\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 forma... | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, 9, 11, 6, -3],\n [0, 14, 6, -10, -15, -15],\n [0, 0, 2, 11, -4, -15],\n [0, 0, 0, 13, -3, -2],\n [0, 0, 0, 0, -12, -7],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex fo... | 472 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 10, -9, 12, -9, 4],\n [-15, -8, 10, -15, -4, 14],\n [1, 9, 13, 10, 15, -6],\n [12, 3, -7, -6, -5, -6],\n [14, 12, 14, 1, -9, -11],\n [12, 12, 4, 11, -4, -11]]\n\nPresent the answer... | 765 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, -15, -6, -9, 11, -4],\n [0, 14, 12, -7, -11, -11],\n [0, 0, 3, 10, 2, -8],\n [0, 0, 0, -13, 12, -2],\n [0, 0, 0, 0, -4, -5],\n [0, 0, 0, 0, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex forma... | 576 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 6, 4, 2, 2, -1],\n [6, 4, 2, -4, 8, -5],\n [4, 2, 3, 0, 4, 1],\n [2, -4, 0, 3, -10, 2],\n [2, 8, 4, -10, 0, 5],\n [-1, -5, 1, 2, 5, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\bo... | 444 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 3, -6, -8, 4, -11],\n [0, 5, 11, -14, -15, 15],\n [0, 0, 12, -11, 2, 7],\n [0, 0, 0, -7, 0, 4],\n [0, 0, 0, 0, -15, 9],\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 forma... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -2, 10, 0, 4, -3],\n [-2, 6, 4, -12, 4, -8],\n [10, 4, -8, -8, 8, -10],\n [0, -12, -8, 4, 4, -8],\n [4, 4, 8, 4, 3, 6],\n [-3, -8, -10, -8, 6, -15]]\n\nPresent the answer in LaTex format... | 56 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -8, 11, 1, 3, -1],\n [14, -15, 14, 2, -9, -9],\n [13, 0, -5, -11, 5, -2],\n [7, 10, 11, 15, 12, -6],\n [-11, 14, 8, 3, 2, 10],\n [-12, 15, 7, -7, 3, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 235 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 2, 0, 7, 10, 3],\n [8, -7, -5, -5, -2, -6],\n [-7, -11, 10, 11, -5, 12],\n [-7, -3, 13, 3, -8, 7],\n [-12, -4, 9, 15, -9, 8],\n [11, -8, 3, 7, -8, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 451 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[14, -13, -15, 6, -6, 1],\n [-15, 0, 7, -15, 11, 13],\n [-13, -11, 3, 15, 6, 15],\n [-2, -2, 9, 2, -9, 4],\n [13, -5, 6, -6, -4, -6],\n [-10, 15, -8, -9, -3, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 743 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 14, -11, 0, -5, 7],\n [9, -15, -6, 13, 1, 15],\n [5, 8, 7, -9, -13, 9],\n [-11, 11, 14, -4, -6, -13],\n [0, -10, 0, 8, -8, 4],\n [13, 15, 4, -7, 14, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer i... | 488 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -10, 6, 13, 12, -14],\n [-15, 7, -12, -7, -5, 8],\n [-10, 0, -6, -13, 8, 12],\n [-6, -4, 15, -15, 11, 9],\n [-6, 13, 9, -6, 8, 10],\n [-12, -7, 11, -7, -4, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex for... | 160 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -2, 0, -8, 2, -7],\n [-12, -2, 8, 4, 6, 8],\n [5, 6, 2, 4, -11, -15],\n [7, -10, 4, -12, 3, 12],\n [1, -10, -11, -10, 15, 10],\n [-15, 2, 15, -1, 0, 7]]\n\nPresent the answer in LaTex for... | 62 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, -15, -4, -9, -5, -3],\n [0, 6, -4, -10, -10, -9],\n [0, 0, -7, 5, 14, 12],\n [0, 0, 0, -1, -15, -2],\n [0, 0, 0, 0, -3, 5],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 534 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 10, -12, 5, 14, 12],\n [0, -4, -3, 14, 2, -3],\n [0, 0, 11, 12, 2, -11],\n [0, 0, 0, 7, -6, -2],\n [0, 0, 0, 0, -5, 14],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex forma... | 160 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 2, 0, -7, 2, -6],\n [0, -11, 11, -14, -7, 2],\n [0, 0, 11, -15, 15, -2],\n [0, 0, 0, 6, 11, 2],\n [0, 0, 0, 0, 11, -13],\n [0, 0, 0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 168 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, 0, -13, 13, -14],\n [5, 9, -2, -1, 12, 8],\n [-8, -15, 9, 8, -2, 11],\n [14, -2, 13, 3, -8, -7],\n [-1, -4, 2, 15, -15, -1],\n [15, -15, -15, 5, -14, -12]]\n\nPresent the answer in La... | 899 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -14, -9, 15, 9, 6],\n [0, -6, -3, -11, 10, 11],\n [0, 0, 13, -2, 2, 6],\n [0, 0, 0, 10, 4, 5],\n [0, 0, 0, 0, -14, -2],\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{Your a... | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, 0, -4, -2, 8, 2],\n [0, 2, 8, 0, -10, 5],\n [-4, 8, -7, 4, -4, -7],\n [-2, 0, 4, -14, 12, 4],\n [8, -10, -4, 12, -2, 0],\n [2, 5, -7, 4, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex forma... | 588 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -1, 1, 14, -12, 0],\n [-1, 8, -4, 10, -4, 10],\n [1, -4, 2, -2, 2, -10],\n [14, 10, -2, 1, 4, -2],\n [-12, -4, 2, 4, -15, 11],\n [0, 10, -10, -2, 11, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \... | 386 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 3, 14, 3, -7, 5],\n [-13, 11, 5, 12, -7, 3],\n [0, 14, 5, -14, -8, -2],\n [-10, -4, 8, -15, 2, 7],\n [-9, 12, 11, 9, -4, -4],\n [-10, 12, 7, 4, -14, 9]]\n\nPresent the answer in LaTex for... | 256 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, 2, -5, -8, 12, -6],\n [2, 11, -2, -4, 2, -4],\n [-5, -2, -9, 2, 2, 4],\n [-8, -4, 2, 8, -3, 3],\n [12, 2, 2, -3, 15, -8],\n [-6, -4, 4, 3, -8, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex forma... | 76 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -6, 7, 7, 7, -12],\n [-4, -11, -12, 14, -7, 4],\n [-15, 0, -8, -3, 6, 2],\n [-15, 10, 14, 14, -9, -2],\n [-8, 0, -2, -6, -7, 11],\n [4, -9, -11, -2, 2, 3]]\n\nPresent the answer in LaTe... | 492 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 1, 0, -10, -6, -14],\n [1, 7, -10, -8, -3, -6],\n [0, -10, 15, 5, 9, 4],\n [-10, -8, 5, 10, 5, 0],\n [-6, -3, 9, 5, 11, -7],\n [-14, -6, 4, 0, -7, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex ... | 357 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[15, -8, 11, 13, 12, -2],\n [7, -12, 4, -14, -7, -10],\n [13, 11, 3, 15, -13, 13],\n [-3, 11, -5, 12, -2, 1],\n [2, -11, 9, -13, -9, -10],\n [11, -13, 11, 4, -3, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the a... | 867 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 11, -5, -11, -15, 13],\n [0, 4, 9, 2, 10, -2],\n [0, 0, 6, -11, -6, -6],\n [0, 0, 0, 13, 8, -10],\n [0, 0, 0, 0, -4, -1],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\b... | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -14, -13, -7, 3, 1],\n [9, -14, 10, -10, -5, 13],\n [12, 14, -5, 7, -7, 12],\n [12, 0, 8, 6, 4, 14],\n [4, 14, -2, 4, -5, -6],\n [-14, -9, -15, -11, -1, -5]]\n\nPresent the answer i... | 148 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 2, -7, 12, -15, 4],\n [0, 4, 10, -6, -12, 2],\n [0, 0, -4, 10, 9, -7],\n [0, 0, 0, -2, 8, -7],\n [0, 0, 0, 0, 2, -7],\n [0, 0, 0, 0, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 488 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 12, 7, 4, 7, -11],\n [-15, 0, -5, -12, -11, 0],\n [11, 13, -4, 14, -4, -12],\n [7, 1, -7, -10, 12, -8],\n [-8, 9, 5, -8, -8, 13],\n [-1, -2, -10, -6, 11, -8]]\n\nPresent the answe... | 614 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 2, 15, -9, -15, -9],\n [-15, -2, -3, 5, -3, 1],\n [-8, 1, 14, -3, 6, 15],\n [1, -1, -14, -3, 4, 13],\n [12, -8, -13, 15, 8, -9],\n [12, 6, 10, 1, 15, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer i... | 192 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 2, 8, 0, -8, 0],\n [2, -1, -6, 5, 8, -2],\n [8, -6, -3, -4, 0, 2],\n [0, 5, -4, 0, 0, 4],\n [-8, 8, 0, 0, -4, -2],\n [0, -2, 2, 4, -2, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: ... | 472 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 1, 4, -3, 8, 0],\n [0, -10, 14, -3, 10, -4],\n [0, 0, -12, 8, -4, 4],\n [0, 0, 0, 11, -2, 5],\n [0, 0, 0, 0, -6, 13],\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 format:... | 920 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-15, 4, 1, 10, 11, -15],\n [-11, 8, 1, -11, -5, 8],\n [-13, 13, 6, 7, -6, 14],\n [15, 8, -2, 3, 13, -5],\n [-15, -4, 10, 8, 4, -14],\n [-15, -1, -3, 6, -3, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer... | 25 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -6, -3, 10, 14, 0],\n [-6, -8, -1, 10, -6, 6],\n [-3, -1, -4, 3, -4, -7],\n [10, 10, 3, 4, 4, 4],\n [14, -6, -4, 4, 0, 4],\n [0, 6, -7, 4, 4, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 192 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -9, -2, -2, -2, 0],\n [-9, 13, 0, 6, -2, 2],\n [-2, 0, -11, 6, -1, 0],\n [-2, 6, 6, 9, 14, -8],\n [-2, -2, -1, 14, 5, -4],\n [0, 2, 0, -8, -4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 580 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 3, 1, 13, 3, 7],\n [0, 1, -2, -2, 4, 7],\n [0, 0, 14, 12, 3, -9],\n [0, 0, 0, 7, -7, 10],\n [0, 0, 0, 0, 4, -4],\n [0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 720 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[13, 6, -6, -8, -5, 0],\n [6, 1, 4, -8, -6, -2],\n [-6, 4, 1, -7, -10, 6],\n [-8, -8, -7, 0, -12, -8],\n [-5, -6, -10, -12, 10, 6],\n [0, -2, 6, -8, 6, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in L... | 181 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 9, 4, -1, 4, 6],\n [0, -2, -13, -13, 9, 7],\n [0, 0, -14, -12, -8, -7],\n [0, 0, 0, 8, -13, -5],\n [0, 0, 0, 0, -7, 13],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\bo... | 360 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -8, 8, -1, -6, 7],\n [0, -10, 13, 15, 0, -6],\n [0, 0, -3, -8, 15, -12],\n [0, 0, 0, -5, -15, -5],\n [0, 0, 0, 0, 13, 8],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 3, -14, -15, -2, -4],\n [-1, 3, 6, 10, 1, 14],\n [2, -7, -15, -15, -7, 3],\n [-10, 12, 3, 2, 11, -13],\n [10, -12, -5, 1, -13, 7],\n [-14, 7, -12, 7, -5, -13]]\n\nPresent the answe... | 802 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 5, 0, 0, 4, 4],\n [5, -13, -8, 8, -11, 6],\n [0, -8, 10, -7, 4, 6],\n [0, 8, -7, 3, 0, 0],\n [4, -11, 4, 0, -8, 3],\n [4, 6, 6, 0, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 183 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -12, -11, 8, 1, -5],\n [-12, 10, 10, 13, -1, -9],\n [-11, -2, -15, -9, -3, -3],\n [-15, -1, -14, -8, 9, -8],\n [8, -2, 6, 7, -12, 12],\n [-3, -11, -2, 2, -6, 11]]\n\nPresent the ans... | 316 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 3, -15, 6, 8, 15],\n [0, -8, 0, 11, -12, 6],\n [-1, -2, -15, 6, 12, -15],\n [-12, -1, 15, 9, -10, -12],\n [10, 4, -12, -6, -9, 11],\n [9, -10, 7, 15, -12, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the ans... | 428 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 15, -15, 13, -11, -5],\n [-5, -5, -1, -15, -5, -10],\n [12, 1, 2, -5, -7, 11],\n [13, -4, -3, 15, -13, 9],\n [14, -12, 5, 0, 7, -12],\n [12, 11, -4, -6, 10, 13]]\n\nPresent the answ... | 974 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 11, -15, 6, -6, 12],\n [0, -3, -10, -3, -4, 7],\n [10, 10, -11, 13, -9, -14],\n [2, -6, 8, 6, 5, 3],\n [4, 8, -6, -9, -3, 9],\n [-3, -5, 3, 6, -9, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex ... | 806 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 0, 0, -4, -8, -8],\n [0, -15, 6, 2, 11, 10],\n [0, 6, 8, 14, -6, -7],\n [-4, 2, 14, 10, -10, -12],\n [-8, 11, -6, -10, -12, 6],\n [-8, 10, -7, -12, 6, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer i... | 968 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 3, 1, 0, 6, 0],\n [3, 7, 0, -8, -2, 4],\n [1, 0, 0, 6, -1, -2],\n [0, -8, 6, -5, -2, -8],\n [6, -2, -1, -2, -9, -7],\n [0, 4, -2, -8, -7, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 618 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 3, 5, 8, -15, -5],\n [-15, 7, 1, 3, -8, -7],\n [5, -1, 6, 13, -8, -13],\n [1, 9, 2, 12, -5, 14],\n [9, -5, -14, 8, 0, -13],\n [-3, 9, 10, -3, 4, 8]]\n\nPresent the answer in LaTex... | 823 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -1, -6, 10, -8, 5],\n [-1, 14, 4, -4, 10, 8],\n [-6, 4, -8, 10, -6, 6],\n [10, -4, 10, -7, 5, 0],\n [-8, 10, -6, 5, -7, 12],\n [5, 8, 6, 0, 12, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 520 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 5, -4, -11, 8, 3],\n [0, 1, -15, 3, 1, 11],\n [0, 0, 3, 11, -7, 5],\n [0, 0, 0, -14, 6, -2],\n [0, 0, 0, 0, 10, 4],\n [0, 0, 0, 0, 0, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 840 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -11, -3, -6, -13, -5],\n [-11, 6, 9, 9, -12, 10],\n [-11, -8, 14, -7, -1, -15],\n [3, -4, -3, -12, 0, 9],\n [-4, -1, -15, -2, 11, 14],\n [10, -1, -8, 13, -14, 0]]\n\nPresent the an... | 592 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -8, 4, 4, 2, 3],\n [-8, 6, 1, -3, 11, 8],\n [4, 1, -12, 0, 4, -6],\n [4, -3, 0, 0, -12, 2],\n [2, 11, 4, -12, 2, 6],\n [3, 8, -6, 2, 6, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format... | 704 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -8, -15, 10, 15, 5],\n [0, 15, 13, 13, -10, -11],\n [0, 0, -1, 6, 3, 14],\n [0, 0, 0, 10, 1, 5],\n [0, 0, 0, 0, 3, 6],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 0, -7, -3, -3, 7],\n [0, 3, -14, -11, 2, 2],\n [-7, -14, 4, 2, 7, 6],\n [-3, -11, 2, 6, 6, -2],\n [-3, 2, 7, 6, 13, 9],\n [7, 2, 6, -2, 9, 5]]\n\nPresent the answer in LaTex format: \\bo... | 299 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 7, 3, 8, 5],\n [0, -9, -9, -10, 3, -5],\n [0, 0, -3, 9, 2, -14],\n [0, 0, 0, -14, -15, -4],\n [0, 0, 0, 0, 6, -11],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format:... | 472 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -2, 4, -7, -5, -5],\n [0, 9, 4, -14, -1, 2],\n [0, 0, 6, 6, 7, 13],\n [0, 0, 0, 13, 15, -4],\n [0, 0, 0, 0, -7, 11],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\... | 248 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 2, -2, 0, -1, 2],\n [2, -4, 0, 2, 2, -2],\n [-2, 0, 4, 5, -3, -2],\n [0, 2, 5, 12, -2, -10],\n [-1, 2, -3, -2, -15, 4],\n [2, -2, -2, -10, 4, 5]]\n\nPresent the answer in LaTex form... | 420 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, -4, 4, 6, -2],\n [7, 0, -3, 10, -3, -1],\n [-5, 12, 7, -8, -7, -11],\n [-14, -6, 12, -3, -1, 5],\n [-2, -5, -2, -9, 13, -2],\n [-13, -6, 5, -10, -10, 4]]\n\nPresent the answer in LaTex... | 866 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 15, 15, -1, 4, 10],\n [-2, -10, -15, -8, 15, 12],\n [-12, -3, -13, 13, 9, -14],\n [8, -5, -10, 13, -3, 6],\n [10, 6, -14, -2, -5, 12],\n [7, -8, 8, -6, -1, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex form... | 596 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 7, -13, 14, -4, 5],\n [0, -1, -5, -13, 3, -5],\n [0, 0, -14, -14, -4, -8],\n [0, 0, 0, -5, 0, -5],\n [0, 0, 0, 0, -5, 6],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 650 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -5, -5, 2, 2, 4],\n [-5, 13, -1, -12, -12, 10],\n [-5, -1, -1, -6, 4, 2],\n [2, -12, -6, 4, 10, -8],\n [2, -12, 4, 10, 12, 0],\n [4, 10, 2, -8, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex fo... | 280 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -5, 8, -5, -3, -7],\n [0, 0, -15, 3, 7, 12],\n [3, 14, 5, -12, -11, -13],\n [3, -3, 12, 12, 10, -3],\n [8, 3, -3, 8, -11, 1],\n [2, -4, 7, 1, 2, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex f... | 178 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 9, -2, -15, 4, 12],\n [0, -10, -14, 10, -7, 0],\n [0, 0, -5, 4, -10, 15],\n [0, 0, 0, -4, -1, 9],\n [0, 0, 0, 0, 7, 4],\n [0, 0, 0, 0, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -3, -11, -1, -4, -7],\n [0, -4, -1, -4, 8, 6],\n [0, 0, 11, 3, -1, 9],\n [0, 0, 0, -4, -4, 2],\n [0, 0, 0, 0, 3, 7],\n [0, 0, 0, 0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 760 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -8, 3, -6, -3, 8],\n [-8, -8, -8, 0, -8, 6],\n [3, -8, -12, -2, 4, 6],\n [-6, 0, -2, 4, 7, 0],\n [-3, -8, 4, 7, -13, -7],\n [8, 6, 6, 0, -7, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 284 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 4, -11, 14, 5, 0],\n [0, -12, 11, 1, -3, -13],\n [0, 0, 8, -5, -12, 9],\n [0, 0, 0, 8, -12, -14],\n [0, 0, 0, 0, 14, 1],\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: \... | 48 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 6, -5, -4, -3, -4],\n [6, 4, 10, -4, -6, 14],\n [-5, 10, -4, -4, 6, -8],\n [-4, -4, -4, 1, 2, 10],\n [-3, -6, 6, 2, 13, -6],\n [-4, 14, -8, 10, -6, 0]]\n\nPresent the answer in LaTex form... | 300 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -14, -6, -13, 10, -14],\n [0, -14, 10, -14, -10, 15],\n [0, 0, 4, -6, 4, -15],\n [0, 0, 0, 12, -14, -2],\n [0, 0, 0, 0, -7, -5],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex forma... | 896 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 0, -10, -8, -4, -2],\n [0, -10, -4, -8, -2, 2],\n [-10, -4, 8, 2, 1, -2],\n [-8, -8, 2, -14, 3, -2],\n [-4, -2, 1, 3, -7, -2],\n [-2, 2, -2, -2, -2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 332 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -14, -6, -9, -13, -15],\n [0, 15, -12, -13, -11, 1],\n [0, 0, 11, -15, -3, -9],\n [0, 0, 0, 5, 2, 9],\n [0, 0, 0, 0, -15, -14],\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: \\boxe... | 500 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -12, -8, 12, -15, -2],\n [-7, 2, 8, 7, 10, -4],\n [-14, 10, 10, -10, -11, 7],\n [2, -2, -1, 10, -3, 15],\n [-7, 12, 3, -15, -8, 0],\n [7, -9, 0, -3, -3, 4]]\n\nPresent the answer in LaTex... | 730 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[15, -8, 10, 4, -13, -4],\n [-8, -1, -5, -3, 10, 7],\n [-8, -3, 0, 2, 0, -3],\n [-2, -8, 13, 4, -14, 4],\n [-8, 13, 12, 11, -10, -3],\n [-13, -9, -10, -11, 11, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answ... | 540 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 6, -13, -11, -13, -1],\n [0, -1, 11, -3, 14, -14],\n [0, 0, -12, -14, 14, 4],\n [0, 0, 0, -2, -13, 15],\n [0, 0, 0, 0, 13, 7],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format... | 960 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 14, -3, 0, 4, -11],\n [0, -5, 1, 6, 14, -6],\n [0, 0, 9, -5, -8, 3],\n [0, 0, 0, -15, 9, 10],\n [0, 0, 0, 0, 6, -6],\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: \\boxed{Your answe... | 300 | MATH |
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