messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 13, -6, -3, 9, -2, -3],\n [14, 5, -13, -4, 6, -1, -18],\n [-3, -17, 6, -3, -10, -17, 6],\n [15, 17, -12, -11, 11, 12, -4],\n [-5, 12, -16, -11, -7, -2, 0],\n [0, 6, 3, 14, 15, -17... | 784 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 2, -4, 6, 4, 4, -1],\n [2, -9, -4, -2, 0, 1, 0],\n [-4, -4, -8, -2, -7, 7, -10],\n [6, -2, -2, 1, -4, -12, -4],\n [4, 0, -7, -4, 4, 2, -8],\n [4, 1, 7, -12, 2, 14, 10],\n [-1, 0, -10, -4, -8, 10, 6]]\nRound to the nearest integer, then take the result modulo 10... | 381 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 12, 8, -9, 2, 6, -14],\n [12, -18, -16, -5, 0, -2, -11],\n [8, -16, -14, 4, 0, 1, -8],\n [-9, -5, 4, 5, -4, 0, 6],\n [2, 0, 0, -4, 1, 0, -10],\n [6, -2, 1, 0, 0, 2, 14],\n [-14, -11, -8, 6, -10, 14, -16]]\nRound to the nearest integer, then take the result modu... | 525 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -10, -17, -11, 9, -6, 9],\n [0, 9, -17, -1, -11, 9, 10],\n [0, 0, -4, 11, 2, -17, 17],\n [0, 0, 0, -2, 13, 0, 8],\n [0, 0, 0, 0, 16, -16, 1],\n [0, 0, 0, 0, 0, 1, 14],\n [0, 0, 0, 0, 0, 0... | 496 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, -4, -6, -4, -8, 2],\n [4, 4, 2, -4, 0, 4, -6],\n [-4, 2, -12, -2, 10, -6, -6],\n [-6, -4, -2, -6, -10, -3, -6],\n [-4, 0, 10, -10, 2, -7, -8],\n [-8, 4, -6, -3, -7, -15, 10],\n [2, -6, -6, -6, -8, 10, -17]]\nRound to the nearest integer, then take the result... | 872 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 8, -15, -15, -15, 18, 9],\n [0, 2, -14, -15, 8, 10, 12],\n [0, 0, -15, -2, 8, -5, -15],\n [0, 0, 0, 12, 9, 5, 3],\n [0, 0, 0, 0, 5, -3, -16],\n [0, 0, 0, 0, 0, 15, 9],\n [0, 0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, -2, 18, 10, -5, 16, 7],\n [16, 14, 12, -16, -17, -18, -9],\n [-11, -18, 5, -9, 18, 5, 1],\n [8, -5, 14, 13, -2, -4, 18],\n [12, 13, 16, -18, 1, 6, 16],\n [15, 15, -10, 5, -18, -18, 3],\... | 811 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[18, -13, -5, 10, -4, -7, 16],\n [-13, 10, 8, -7, -10, 4, -8],\n [-5, 8, 10, 2, 3, 8, -4],\n [10, -7, 2, 5, -18, 13, -11],\n [-4, -10, 3, -18, -5, 2, 4],\n [-7, 4, 8, 13, 2, -16, 13],\n [16, -8, -4, -11, 4, 13, -10]]\nRound to the nearest integer, then take the res... | 884 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, -2, -11, -15, -10, 5],\n [0, 2, -4, 1, -15, 18, 4],\n [0, 0, -13, 7, 12, 13, 8],\n [0, 0, 0, -3, 8, -16, 9],\n [0, 0, 0, 0, 10, 1, 9],\n [0, 0, 0, 0, 0, 2, 1],\n [0, 0, 0, 0, 0, 0, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPr... | 920 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 14, 14, -2, 11, 10, 18],\n [0, 16, -6, -4, 9, -15, 9],\n [0, 0, 10, 11, -8, -3, 12],\n [0, 0, 0, 15, 11, 13, -3],\n [0, 0, 0, 0, 4, -3, -9],\n [0, 0, 0, 0, 0, 4, 11],\n [0, 0, 0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer mo... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 17, -13, 12, 6, -17, -10],\n [0, -5, -4, -13, 18, 14, 5],\n [0, 0, -14, 5, 8, 10, 7],\n [0, 0, 0, -9, 3, -12, -6],\n [0, 0, 0, 0, -10, -4, 8],\n [0, 0, 0, 0, 0, 16, 3],\n [0, 0, 0, 0, 0, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-17, -4, 10, 9, -3, -1, 0],\n [-4, 18, -9, 2, -2, -2, -2],\n [10, -9, -3, 8, -14, -10, 10],\n [9, 2, 8, 3, 9, -2, 11],\n [-3, -2, -14, 9, -15, 2, -15],\n [-1, -2, -10, -2, 2, -6, -7],\n [0, -2, 10, 11, -15, -7, 7]]\nRound to the nearest integer, then take the resu... | 900 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 2, -2, -4, 18, -12, -5],\n [-6, 1, 12, 7, -2, -16, -9],\n [16, -3, -6, -8, -12, -16, 14],\n [-8, -11, 7, 16, -2, 10, -17],\n [17, -17, 9, 13, 11, -13, 13],\n [-4, -5, -3, 6, 10, 8, 17],\n [-12, -6, 10, -1, -8, -5, 11]]? Round to the nearest integer, t... | 644 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 1, 0, 10, 7, -12, -10],\n [1, 14, -4, -11, -12, -12, 14],\n [0, -4, 0, -14, 4, 2, 0],\n [10, -11, -14, 5, -15, -10, 4],\n [7, -12, 4, -15, -8, 6, -4],\n [-12, -12, 2, -10, 6, 10, -3],\n ... | 920 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, -8, -1, 14, -11, -18, 8],\n [18, 0, -16, -8, -14, -7, -18],\n [2, 12, -14, -2, 2, -14, 0],\n [-1, 16, 15, -3, 4, -10, 15],\n [-17, -11, 15, 1, -11, 0, -2],\n [-4, -3, -18, 2, 5, -14, 9],\n [-1, 7, -7, -18, -16, 14, 6]]? Round to the nearest integer, th... | 788 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 17, -4, -14, 18, 15, -10],\n [0, -2, -4, 4, 10, 9, -14],\n [0, 0, 12, -13, 6, -9, 2],\n [0, 0, 0, -17, -12, -13, -3],\n [0, 0, 0, 0, -13, -13, -12],\n [0, 0, 0, 0, 0, 2, -13],\n [0, 0, 0, 0, 0, 0, 14]]\nRound to the nearest integer, then take the result modulo... | 512 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, -2, 3, 5, -15, 12, -3],\n [0, 16, 6, 17, 11, -4, 14],\n [0, 0, -9, -17, 7, 17, -4],\n [0, 0, 0, 2, 14, 5, -15],\n [0, 0, 0, 0, 16, -11, 0],\n [0, 0, 0, 0, 0, 3, 3],\n [0, 0, 0, 0, 0, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\n... | 336 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -1, -1, -18, -7, 15, 15],\n [0, 1, -2, 6, 18, -3, 3],\n [0, 0, -6, 18, 1, 18, -8],\n [0, 0, 0, -5, -15, 5, 8],\n [0, 0, 0, 0, -2, 16, 4],\n [0, 0, 0, 0, 0, 18, -1],\n [0, 0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nP... | 320 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -6, -10, 14, -12, -8, 13],\n [-18, -15, -3, -6, -11, -12, 3],\n [-16, 1, -11, 4, 16, 15, -1],\n [-3, 8, -14, -8, -2, -6, 16],\n [-12, 18, 7, 17, -7, -4, -3],\n [-13, 11, 5, 9, 18, 13, -18],\n [18, -8, 1, -7, -14, -9, -15]]? Round to the nearest integer... | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -3, 4, 4, 5, -12, -2],\n [-3, -16, 3, 5, -1, 2, 0],\n [4, 3, -4, -2, -14, -13, 4],\n [4, 5, -2, -3, 2, -11, -6],\n [5, -1, -14, 2, -13, 10, 12],\n [-12, 2, -13, -11, 10, 17, -1],\n [-2, ... | 544 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 7, -11, 10, -4, -8, -10],\n [0, 12, 13, -8, 13, 13, 11],\n [0, 0, -11, -11, 17, -4, 17],\n [0, 0, 0, 1, 1, 0, -1],\n [0, 0, 0, 0, -5, -6, -13],\n [0, 0, 0, 0, 0, -8, -13],\n [0, 0, 0, 0, ... | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -18, -4, 8, 7, 12, -1],\n [0, -5, 0, -9, -16, 1, 5],\n [0, 0, 1, -14, 9, 4, 17],\n [0, 0, 0, 13, -9, 0, 16],\n [0, 0, 0, 0, 10, 7, -10],\n [0, 0, 0, 0, 0, -10, -2],\n [0, 0, 0, 0, 0, 0, 3]]? Round to the nearest integer, then express your answer modulo... | 500 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 4, -7, 6, -8, 13, 9],\n [4, -11, -8, -7, -1, 0, -7],\n [-7, -8, 6, -12, 6, -4, -6],\n [6, -7, -12, -7, -2, 0, -4],\n [-8, -1, 6, -2, 8, -8, -2],\n [13, 0, -4, 0, -8, 9, -1],\n [9,... | 521 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[18, -6, 15, 14, 5, 14, -11],\n [0, -10, -7, 11, 15, 11, 1],\n [0, 0, 10, -17, -7, 2, -13],\n [0, 0, 0, 2, -5, -9, 4],\n [0, 0, 0, 0, -10, 12, 17],\n [0, 0, 0, 0, 0, 1, -14],\n [0, 0, 0, 0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -11, 2, -4, 17, -14, 4],\n [3, 14, -14, -18, -5, 17, -18],\n [2, 8, 14, -10, 12, -12, -9],\n [-4, -1, 9, -12, 17, -12, -18],\n [7, -2, 15, -1, -5, 0, 9],\n [-12, -15, 10, 4, -16, ... | 443 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-16, -4, -12, -6, -18, 3, -2],\n [0, -14, -18, 18, 17, -16, -18],\n [0, 0, 2, 5, -7, -14, -10],\n [0, 0, 0, 4, -18, 8, -2],\n [0, 0, 0, 0, 13, 6, -11],\n [0, 0, 0, 0, 0, 6, 17],\n [0, 0, 0, 0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 10... | 104 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -8, -11, -14, -16, 3, 5],\n [0, 8, 12, -10, -7, -15, -5],\n [0, 0, 8, 10, -14, -7, -12],\n [0, 0, 0, 1, 15, -15, -3],\n [0, 0, 0, 0, -12, -8, 6],\n [0, 0, 0, 0, 0, 1, -7],\n [0, 0,... | 432 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -6, -12, -9, -8, 0, -1],\n [0, 8, -8, -2, 13, 6, 18],\n [0, 0, -8, -13, -6, 4, 12],\n [0, 0, 0, -7, 0, -8, 7],\n [0, 0, 0, 0, -3, -8, -9],\n [0, 0, 0, 0, 0, -15, 17],\n [0, 0, 0, 0, 0, 0,... | 40 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 15, -2, -18, -18, -3, 1],\n [0, -11, -7, 1, -7, -1, 7],\n [0, 0, -11, -6, 18, -9, -2],\n [0, 0, 0, -16, -2, 8, -13],\n [0, 0, 0, 0, -12, -18, 9],\n [0, 0, 0, 0, 0, -11, -2],\n [0, 0, 0,... | 240 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 0, 0, 3, -10, 2, 4],\n [0, -2, 14, 14, 2, -16, 3],\n [0, 14, 12, 0, 11, 8, 12],\n [3, 14, 0, -6, -10, 2, -2],\n [-10, 2, 11, -10, 15, -10, -8],\n [2, -16, 8, 2, -10, -9, 10],\n [4, 3, 12, -2, -8, 10, -1]]? Round to the nearest integer, then express your... | 299 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 16, 0, -11, 0, -5, -3],\n [-4, 18, -10, -11, -16, 17, 8],\n [14, 14, -18, 6, -11, 7, -14],\n [17, -17, -9, 1, 14, 10, 0],\n [9, 1, 8, 0, -7, 4, 12],\n [-17, -8, -10, 0, -18, 6, -17],\n [-2, 17, 6, -16, 3, -1, 5]]\nRound to the nearest integer, then gi... | 704 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -8, 16, 7, -9, 14, 4],\n [-8, 10, 14, -8, -10, -7, -17],\n [16, 14, 11, 3, 7, 4, -4],\n [7, -8, 3, 12, -4, 0, 12],\n [-9, -10, 7, -4, -5, -4, 8],\n [14, -7, 4, 0, -4, 3, -8],\n [4... | 288 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[14, 14, 6, 9, -9, -14, 2],\n [14, -9, 4, -6, -15, -16, 9],\n [8, -14, -7, -15, 7, 16, 5],\n [-4, 15, -18, 4, 8, 12, 14],\n [-3, 3, -11, -11, -14, -1, 9],\n [-10, 2, -2, -13, 1, -1, 18],\n [15, 8, -3, 18, 5, 17, 3]]\nRound to the nearest integer, then take the resu... | 614 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 8, -6, -18, 6, -8, -2],\n [8, 2, -7, 4, 10, -4, -7],\n [-6, -7, 4, 4, 6, 6, 0],\n [-18, 4, 4, -6, -3, 0, -6],\n [6, 10, 6, -3, -15, 0, 2],\n [-8, -4, 6, 0, 0, 8, -6],\n [-2, -7, 0, -6, 2, -6, 2]]? Round to the nearest integer, then express your answer... | 496 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, -8, 9, -9, 16, -15],\n [14, -18, 10, 8, -1, 8, -17],\n [-4, -8, -5, 18, -4, -15, 3],\n [-2, -8, -9, -18, -16, -2, -3],\n [-11, 11, 4, -2, 15, -4, 6],\n [8, 16, -3, -10, -1, 0, -... | 32 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-16, -15, -11, -3, 0, -7, -15],\n [2, -5, 2, 2, 11, -17, 8],\n [7, -16, 15, -11, 9, -9, -1],\n [4, -17, -14, 18, 1, -13, 15],\n [6, -14, -8, 10, 5, 10, -1],\n [-10, 3, 6, -17, -16, -3, 7],\n [0, -7, -5, 1, 4, -11, -14]]\nRound to the nearest integer, then... | 90 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 2, -10, -6, 6, 0, 4],\n [2, 1, -2, 7, 0, 6, -4],\n [-10, -2, 18, -11, 1, 5, 3],\n [-6, 7, -11, -17, 4, 0, -1],\n [6, 0, 1, 4, 13, -2, 6],\n [0, 6, 5, 0, -2, 9, -14],\n [4, -4, 3, -1, 6, -14, 3]]\nRound to the nearest integer, then give your answer as d... | 661 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -3, 11, 0, 8, -14, -16],\n [0, 4, 13, 14, -3, 3, -8],\n [0, 0, 11, -16, -8, 3, -4],\n [0, 0, 0, 10, -18, 7, -9],\n [0, 0, 0, 0, -8, 5, -10],\n [0, 0, 0, 0, 0, 16, 11],\n [0, 0, 0, 0, 0, 0, -16]]\nRound to the nearest integer, then take the result modulo 1000.... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -6, -13, -10, -8, 4, 13],\n [17, 17, -13, 1, 14, 10, 15],\n [-5, 5, 3, 6, -4, 5, -3],\n [18, 8, 13, -4, -4, 10, -17],\n [14, 7, -11, 18, -14, -17, 3],\n [10, -5, 7, 4, -7, 18, -12],\n [11, -10, -1, 5, -16, 17, -4]]\nRound to the nearest integer, then take the ... | 10 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 14, 8, 10, -4, -2, -12],\n [14, 15, 9, 1, -11, 14, 2],\n [8, 9, -2, 15, -6, 13, -16],\n [10, 1, 15, -7, -10, -1, -8],\n [-4, -11, -6, -10, 14, 14, -6],\n [-2, 14, 13, -1, 14, 12, 9],\n [-12, 2, -16, -8, -6, 9, 14]]\nRound to the nearest integer, then take the r... | 480 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -13, 0, 18, 6, -2, -12],\n [0, -5, 7, 7, -12, -14, 1],\n [0, 0, 2, -15, 10, -3, 4],\n [0, 0, 0, -5, 18, -9, 9],\n [0, 0, 0, 0, -13, 5, -11],\n [0, 0, 0, 0, 0, 1, -4],\n [0, 0, 0, 0, 0, 0, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\... | 450 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, 9, 4, -11, 13, -15, -4],\n [14, -6, 2, -6, 11, 13, -10],\n [13, -1, -15, -5, -11, 7, 18],\n [-16, 12, 16, 13, 4, 2, 15],\n [12, 14, -3, 1, -5, 7, 1],\n [1, -1, -14, 0, 2, 13, 18],\n [-1, -15, -14, -11, 7, -12, -6]]? Round to the nearest integer, then e... | 28 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, 5, -12, 5, 2, 17, 10],\n [-12, -11, 8, 6, -12, 11, 0],\n [-10, 10, 14, -9, 1, -18, -9],\n [-12, -5, 4, -7, -5, -7, 15],\n [2, 13, -4, -12, -9, 8, 9],\n [-16, 0, 14, -18, 18, 5, -12... | 430 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, -9, -17, 1, 4, 14, 4],\n [9, -2, 14, -8, 15, 12, 2],\n [-18, 1, 5, 1, 4, 13, 11],\n [17, -12, 7, 18, -17, -15, 0],\n [14, 11, -2, 16, -4, 17, -8],\n [12, -8, -16, 5, 7, -3, 10],\n [9, -4, -16, 17, -17, -12, 10]]? Round to the nearest integer, then exp... | 227 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 15, 1, 10, 16, 18, -6],\n [0, 8, 14, 5, 3, -3, 5],\n [0, 0, -8, 14, -4, -9, 7],\n [0, 0, 0, -14, -15, 11, -1],\n [0, 0, 0, 0, -7, -10, 14],\n [0, 0, 0, 0, 0, -14, -5],\n [0, 0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\... | 480 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-17, -10, 0, 9, -9, 11, -18],\n [14, -15, 13, -6, 8, -18, 11],\n [-13, 12, -14, 6, 12, 5, -18],\n [-5, -16, 10, -16, 13, 2, 18],\n [4, -3, -14, -10, -7, -4, 0],\n [9, 3, -13, -13, -4, 7, -16],\n [5, -11, 10, -11, -4, 3, 4]]? Round to the nearest integer, t... | 496 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -5, 16, 10, 12, 14, 12],\n [-2, 4, 13, 10, 4, -7, -11],\n [-2, 15, -16, 4, 7, 16, -9],\n [15, -4, -8, 15, 2, 14, 16],\n [-16, 4, -2, -10, -10, 2, 9],\n [7, -2, 11, -4, 12, -3, 15],\n [1, 9, 6, -2, 16, 18, -4]]\nRound to the nearest integer, then take the resul... | 450 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 17, 1, 18, 4, -14, -16],\n [0, 2, -11, -12, -6, -3, 15],\n [0, 0, -4, 6, 13, 17, 2],\n [0, 0, 0, 2, -18, -16, -4],\n [0, 0, 0, 0, 14, -12, -10],\n [0, 0, 0, 0, 0, -8, -15],\n [0, 0, 0, 0... | 264 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -2, -6, 14, -8, -6, 4],\n [-2, -13, -14, 17, -2, 12, 1],\n [-6, -14, 2, -11, -3, 10, 6],\n [14, 17, -11, -11, 6, 11, 4],\n [-8, -2, -3, 6, 16, -2, -4],\n [-6, 12, 10, 11, -2, -13, 10],\n [4, 1, 6, 4, -4, 10, 0]]\nRound to the nearest integer, then take the res... | 578 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[12, 8, -5, -4, -7, -9, 11],\n [0, -11, -12, -13, 15, 1, -14],\n [0, 0, 7, -1, -10, 16, -11],\n [0, 0, 0, -1, -13, -17, 15],\n [0, 0, 0, 0, -2, 14, 8],\n [0, 0, 0, 0, 0, -15, -15],\n [0, 0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, 1, -12, 0, -4, 11, 17],\n [0, 11, -5, -17, 0, 9, -10],\n [0, 0, -11, -16, 9, -8, 11],\n [0, 0, 0, -1, -12, 17, -14],\n [0, 0, 0, 0, -3, -6, 3],\n [0, 0, 0, 0, 0, -11, -6],\n [0, 0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer... | 790 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 4, -2, 5, -6, -18, 12],\n [0, -2, -1, 17, -15, -16, 2],\n [0, 0, 15, 3, 9, 14, -14],\n [0, 0, 0, -5, 15, -9, 7],\n [0, 0, 0, 0, -15, 10, 10],\n [0, 0, 0, 0, 0, 13, 14],\n [0, 0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -6, -14, 5, 3, 15, -17],\n [15, -11, -1, 17, 0, 11, -5],\n [18, 14, 2, 1, 7, -11, -11],\n [-9, -12, -11, -5, -7, -1, -13],\n [1, -6, 9, 1, 13, -6, 16],\n [2, 16, -13, 7, -15, 11, 8... | 741 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -10, 0, 6, -5, -16, -12],\n [-10, -4, -9, 4, 1, 8, 2],\n [0, -9, 12, 2, -6, 4, -8],\n [6, 4, 2, 2, -6, -8, -8],\n [-5, 1, -6, -6, 2, 4, -15],\n [-16, 8, 4, -8, 4, 14, -12],\n [-12, 2, -8... | 572 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -2, -1, 3, 11, -4, -8],\n [0, 10, -13, -8, 7, 0, 16],\n [0, 0, -18, 10, -8, 18, 16],\n [0, 0, 0, 10, -4, 6, -7],\n [0, 0, 0, 0, -8, 5, 1],\n [0, 0, 0, 0, 0, 10, 16],\n [0, 0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then give your answer as det... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -5, 12, 0, 4, -10, -4],\n [-5, 15, 16, -2, -9, -4, -10],\n [12, 16, -15, 4, 6, 4, 8],\n [0, -2, 4, 8, -2, 6, 4],\n [4, -9, 6, -2, -2, 2, 7],\n [-10, -4, 4, 6, 2, -10, -6],\n [-4, -10, 8, 4, 7, -6, -14]]\nRound to the nearest integer, then give your an... | 968 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-17, 3, 13, 18, -6, -2, 1],\n [1, -3, 15, -4, 1, -9, 12],\n [-15, 13, 14, -11, 6, 16, 18],\n [-16, 16, -14, 2, 13, 16, 18],\n [16, 5, 10, -5, -18, -5, 9],\n [-11, -4, -7, 10, 13, -1, -9],\n ... | 208 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-16, -13, 16, 11, -11, 2, 3],\n [0, -7, -17, -3, 17, 7, -17],\n [0, 0, -2, 4, 17, 7, 10],\n [0, 0, 0, -11, -1, -1, -5],\n [0, 0, 0, 0, 2, -16, -12],\n [0, 0, 0, 0, 0, 3, -16],\n [0, 0, 0, 0, 0, 0, -2]]? Round to the nearest integer, then express your answe... | 432 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 11, 8, 16, 17, 16, 0],\n [0, -5, 0, 3, 14, 12, -11],\n [0, 0, -2, -8, -9, 14, -12],\n [0, 0, 0, 10, -8, -17, 6],\n [0, 0, 0, 0, -1, 11, 8],\n [0, 0, 0, 0, 0, 9, 1],\n [0, 0, 0, 0, 0, 0, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPr... | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -9, -11, -4, -11, -9, 6],\n [0, 2, 6, -9, -10, -18, 2],\n [0, 0, 15, -6, -2, -12, 5],\n [0, 0, 0, -3, 10, -17, 2],\n [0, 0, 0, 0, 4, 16, -13],\n [0, 0, 0, 0, 0, 16, -1],\n [0, 0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer mo... | 360 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 4, -5, -5, 15, -3, 8],\n [1, -1, -2, -11, -2, -17, -9],\n [-13, 12, 0, 10, 3, -12, -18],\n [-14, -6, -15, 14, -1, 5, -8],\n [-1, 13, 4, -17, -11, 6, -3],\n [16, 0, 8, -8, 12, -15, -... | 624 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[18, 6, 11, 17, 12, 9, 11],\n [15, -14, -11, -10, -12, -12, -18],\n [-9, -15, 2, -15, -2, -12, -6],\n [-8, 14, -8, -18, 4, 15, -11],\n [-10, -16, 18, -10, 17, 9, -3],\n [15, -1, -9, 5, -3, 0,... | 198 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 12, -8, 6, -8, 4, 3],\n [12, -3, -12, 5, 6, -16, -12],\n [-8, -12, -5, -2, -8, -6, 4],\n [6, 5, -2, -12, -1, 6, 4],\n [-8, 6, -8, -1, -9, 8, 4],\n [4, -16, -6, 6, 8, 18, 2],\n [3, -12, 4, 4, 4, 2, -5]]? Round to the nearest integer, then express your a... | 212 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -12, 7, 11, 12, -18, 3],\n [-4, -12, 6, 14, 5, 2, 0],\n [4, -15, -10, 14, -18, -5, -1],\n [8, -11, -18, -15, -12, 3, -10],\n [11, -9, 0, 6, -3, 8, 5],\n [16, 6, 5, -18, -7, 5, 13],\n [-... | 890 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -14, 3, 11, 0, -14, 7],\n [-15, 7, 8, 3, 2, 6, 17],\n [5, -11, -9, 9, 1, 0, -9],\n [-8, -2, 12, -15, 1, -9, -17],\n [-9, 14, 0, -13, -15, -3, 16],\n [0, -10, -14, 13, -14, 17, 10],\n [-8, 9, -15, -8, -14, -10, -9]]\nRound to the nearest integer, then ... | 689 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 14, 0, 16, 15, 14, -12],\n [6, -16, -13, 17, 16, 10, 13],\n [10, -13, -8, 15, 18, -4, 15],\n [-6, 1, -8, 12, 16, -17, -14],\n [14, 1, -4, 2, -14, -7, 16],\n [7, 0, 1, -12, -4, 11, -17],\n [10, 17, -18, -16, -18, 13, -11]]? Round to the nearest integer,... | 824 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 0, -3, 1, 10, -3, -4],\n [0, 9, 8, -4, 1, 10, -10],\n [-3, 8, 6, -10, -12, -4, 17],\n [1, -4, -10, 4, 1, 12, -6],\n [10, 1, -12, 1, -8, 10, -2],\n [-3, 10, -4, 12, 10, 18, -1],\n [-4, -10, 17, -6, -2, -1, 15]]\nRound to the nearest integer, then take the resul... | 440 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -2, -8, -18, -11, -11, -3],\n [0, 1, -8, -6, 0, 7, -6],\n [0, 0, 12, 2, 10, 10, -15],\n [0, 0, 0, -4, 17, -2, 13],\n [0, 0, 0, 0, -10, -13, -7],\n [0, 0, 0, 0, 0, 12, -17],\n [0, 0, 0, 0, 0, 0, 6]]\nRound to the nearest integer, then give your answer a... | 680 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -6, -2, 8, -10, -8, -12],\n [-6, 12, -4, -6, 0, 0, -12],\n [-2, -4, 3, -7, 11, -10, 18],\n [8, -6, -7, -12, 5, 8, -4],\n [-10, 0, 11, 5, -9, -4, 10],\n [-8, 0, -10, 8, -4, 18, -10],\n [-12, -12, 18, -4, 10, -10, 7]]\nRound to the nearest integer, then... | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 9, 10, 15, -3, 7, 6],\n [0, -10, 11, -6, 13, 10, -10],\n [0, 0, -1, 8, 9, -13, -18],\n [0, 0, 0, 3, -12, 2, -7],\n [0, 0, 0, 0, -1, -14, 11],\n [0, 0, 0, 0, 0, -14, 16],\n [0, 0, ... | 520 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 8, 11, -8, 8, -3],\n [7, 12, -13, -6, 4, 14, -2],\n [8, -13, 7, 18, -6, 14, -10],\n [11, -6, 18, 16, -8, 13, 0],\n [-8, 4, -6, -8, -9, -2, 6],\n [8, 14, 14, 13, -2, -16, -8],\n [-3, -... | 604 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 4, -2, -12, -12, 14, -3],\n [4, -16, -2, 14, -7, -4, 8],\n [-2, -2, 13, 3, 16, -4, -3],\n [-12, 14, 3, 14, 8, 12, -12],\n [-12, -7, 16, 8, 4, -8, -7],\n [14, -4, -4, 12, -8, 17, -2],\n [-3, 8, -3, -12, -7, -2, 14]]\nRound to the nearest integer, then g... | 129 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, -4, -6, 4, -3, -4, 0],\n [-4, -8, -11, 6, 0, 9, 16],\n [-6, -11, -2, -1, -4, 6, -4],\n [4, 6, -1, 15, 4, 10, -5],\n [-3, 0, -4, 4, 5, 6, -2],\n [-4, 9, 6, 10, 6, 13, 8],\n [0, 16, -4, -5, -2, 8, 2]]\nRound to the nearest integer, then take the result modulo 1... | 399 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-16, 8, 5, 1, -7, 5, 15],\n [-6, 6, -10, -17, -6, -15, 17],\n [0, -11, 1, -1, 7, 7, -18],\n [5, -13, -13, 4, -3, 4, 4],\n [-15, 15, -12, -15, -9, 14, 8],\n [-11, 3, -15, -18, 3, -7, -18],\n [-7, -16, -15, 12, 9, 0, -7]]\nRound to the nearest integer, then take the... | 832 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -4, -16, -1, -9, -7, 7],\n [-1, 14, 15, 11, -6, 15, 8],\n [0, 9, 3, 1, 12, -4, 4],\n [3, 16, 5, -15, 2, -14, -14],\n [-2, 15, -11, 4, -16, -18, 0],\n [-14, 5, -12, -16, 12, 7, 5],\n [0, 9, -8, -6, 16, 4, 9]]? Round to the nearest integer, then express y... | 940 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -11, 10, -4, -4, -6, -6],\n [-11, -5, -13, -1, -1, 5, -4],\n [10, -13, -18, -14, -7, 1, 3],\n [-4, -1, -14, -10, -6, -12, -6],\n [-4, -1, -7, -6, -4, -1, 13],\n [-6, 5, 1, -12, -1... | 776 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -10, 8, 6, -1, -6, 0],\n [-10, -10, 2, 3, 2, 0, 8],\n [8, 2, 14, 10, 3, -1, 2],\n [6, 3, 10, -5, 6, -2, 2],\n [-1, 2, 3, 6, 5, 16, 2],\n [-6, 0, -1, -2, 16, 3, -11],\n [0, 8, 2, 2, 2, -11... | 745 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, -8, 6, 18, -15, 0, -4],\n [0, 1, -16, 10, -5, 8, 1],\n [0, 0, 6, -14, 9, 4, -12],\n [0, 0, 0, -3, -13, 1, 11],\n [0, 0, 0, 0, 7, -1, -11],\n [0, 0, 0, 0, 0, 3, -5],\n [0, 0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nP... | 584 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 3, 13, -8, 14, 9, 7],\n [0, 3, -15, 0, -8, -18, -10],\n [0, 0, -2, 5, 2, 8, -16],\n [0, 0, 0, -17, 1, 18, 16],\n [0, 0, 0, 0, -1, 18, 18],\n [0, 0, 0, 0, 0, -10, -11],\n [0, 0, 0, 0, 0, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\... | 640 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -11, -4, -2, -11, -10, -11],\n [-7, -16, -1, -1, 10, -12, 15],\n [12, 5, 7, 6, -18, -17, 6],\n [17, -18, 4, 2, -15, 13, 17],\n [10, 18, 0, 11, -5, -13, 8],\n [14, 15, 6, -13, -8, 13, 3],\n [-14, -2, 7, -13, -18, -14, 0]]? Round to the nearest integer, ... | 108 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -16, 8, -2, 8, 0, 10],\n [-16, 5, -9, 0, -4, -5, -12],\n [8, -9, -10, -8, 2, -6, 10],\n [-2, 0, -8, -8, 4, -6, 4],\n [8, -4, 2, 4, -12, -12, 0],\n [0, -5, -6, -6, -12, -15, 2],\n [1... | 112 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -13, -15, 7, -10, -11, 13],\n [12, -15, 9, 3, -11, 15, -5],\n [-3, 17, -4, -3, -8, 5, -14],\n [-8, 5, 17, 3, 0, 1, -1],\n [9, 17, 10, -7, -1, 11, -13],\n [15, 16, -13, 18, -7, 12, -14],\n [3, 11, -3, 14, -11, -2, 9]]? Round to the nearest integer, then ... | 216 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 5, -18, 13, 5, 15, -2],\n [12, -17, 4, -7, 10, 18, 18],\n [-16, -16, 6, -2, 7, 2, 3],\n [-10, 9, -1, 14, -5, 2, 0],\n [17, 16, -8, -7, -14, -1, -16],\n [-3, -8, 0, 3, 9, 16, -14],... | 684 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 12, 4, 18, 0, 6, -16],\n [0, 3, -7, -4, -6, 14, 12],\n [0, 0, -12, -9, 10, 6, 15],\n [0, 0, 0, 5, -10, 7, -14],\n [0, 0, 0, 0, -6, 14, -18],\n [0, 0, 0, 0, 0, 7, 4],\n [0, 0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then give your answer as det... | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 12, 8, 7, 2, 12, -12],\n [2, -9, 17, -18, -18, -10, 16],\n [-17, 13, 1, 14, 2, 11, 7],\n [12, -12, -14, -12, 0, -10, -3],\n [16, 10, 4, 10, -12, -17, -13],\n [7, 15, 15, -3, -18, 7, -14]... | 832 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[16, -4, 10, 8, 8, -6, 0],\n [-4, -13, 1, 8, 2, -4, -6],\n [10, 1, 15, 4, -9, 0, 14],\n [8, 8, 4, 1, 6, 5, 0],\n [8, 2, -9, 6, -10, -1, -13],\n [-6, -4, 0, 5, -1, -13, 6],\n [0, -6, 14,... | 464 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 1, -5, 18, 17, 5, -8],\n [-1, -12, 10, 9, -11, 8, 18],\n [-1, 16, -11, 7, 18, -17, -7],\n [15, 2, -6, 18, -17, 4, -7],\n [-4, -3, -16, -6, 14, 10, 5],\n [18, 7, -6, 13, -7, -2, -12],\n [13, -12, 14, 7, -18, -1, 0]]\nRound to the nearest integer, then ... | 661 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -12, 9, -7, 15, -17, 2],\n [15, -8, 4, -11, 2, 18, 2],\n [6, -6, -6, -11, -13, 2, 10],\n [-11, 13, -14, 8, 12, -1, -14],\n [0, 13, -6, -12, 3, 3, -12],\n [-6, -12, 10, -15, 14, 11, 16],\... | 852 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 17, -1, -5, 10, 15, 3],\n [0, -2, -5, 7, 8, 2, -5],\n [0, 0, 6, 14, 3, -18, -12],\n [0, 0, 0, 13, 15, -9, 7],\n [0, 0, 0, 0, -14, -16, -14],\n [0, 0, 0, 0, 0, -4, -16],\n [0, 0, 0, ... | 72 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 12, -10, 13, -3, -16, -3],\n [0, 2, -8, 14, 3, -15, -5],\n [0, 0, 13, 17, 5, -16, -8],\n [0, 0, 0, 5, -18, 13, -5],\n [0, 0, 0, 0, -3, 6, 3],\n [0, 0, 0, 0, 0, -13, -15],\n [0, 0, ... | 50 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, 5, -11, 16, -11, 0, 17],\n [15, 5, -13, 16, -4, -1, 13],\n [4, -1, 1, -8, 10, 17, -5],\n [15, -7, 10, 17, -10, -16, 16],\n [-16, 8, 8, -1, -15, 7, 8],\n [5, 17, 8, 11, 15, -12, 14],\n [13, -18, 18, -1, 0, -16, -18]]\nRound to the nearest integer, then take th... | 310 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 14, 7, 17, -8, 5, -2],\n [2, 10, -18, 9, -10, -5, -1],\n [5, -8, -13, 3, 15, 12, -16],\n [-10, -4, -14, 0, -10, -16, 13],\n [11, 18, 4, 14, 2, -3, -6],\n [-15, -2, -8, -17, -1, 4, -2],\n [4, -16, 13, -11, 9, -5, -16]]\nRound to the nearest integer, the... | 344 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -14, 0, 15, 7, 18, -5],\n [4, 1, -6, -14, 8, -9, -17],\n [13, 7, 15, -17, 5, 1, -4],\n [6, 4, -12, 18, -3, -13, -16],\n [-5, 13, -9, -16, -9, 12, 15],\n [1, -9, 16, 9, -5, -11, -14],\n [3, -18, -14, -5, -1, 10, 3]]\nRound to the nearest integer, then take the r... | 120 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-16, -12, -15, -3, -9, 18, 4],\n [15, -18, 17, -16, 15, 17, -5],\n [11, 10, 16, -18, -11, -14, 7],\n [-1, -13, -14, 3, -6, -9, 2],\n [-18, -11, -12, -14, 18, -8, 0],\n [17, -16, 9, -2,... | 299 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -13, 6, -4, -13, 10, -6],\n [0, -5, 9, 11, -9, -18, 11],\n [0, 0, 15, 14, 3, 3, 12],\n [0, 0, 0, 7, 4, -15, -7],\n [0, 0, 0, 0, -7, 6, -12],\n [0, 0, 0, 0, 0, 5, -5],\n [0, 0, 0, 0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n... | 125 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 7, 5, -18, -9, 2, 10],\n [-14, -11, -11, 5, 16, 5, -17],\n [-16, -12, -17, 10, -13, -5, 0],\n [-8, -6, 10, -14, 0, 15, -2],\n [-7, 11, -5, 13, 14, 11, 14],\n [9, 1, -3, 17, 2, -10, 2],\n... | 346 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, 5, -3, 15, 2, 9],\n [0, -1, 18, 0, 13, -8, 14],\n [0, 0, -4, 2, 6, -11, -17],\n [0, 0, 0, 4, 2, -1, 2],\n [0, 0, 0, 0, -13, 9, 15],\n [0, 0, 0, 0, 0, 1, 9],\n [0, 0, 0, 0, 0, 0, 13]]\... | 256 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 1, -7, -15, -9, -5, -3],\n [-9, 10, 9, 8, -8, -7, -17],\n [0, 4, -1, -5, 3, 12, 10],\n [-17, -10, -5, -15, 9, -15, -9],\n [15, 2, 18, 6, -12, -18, -4],\n [-3, 0, 13, 6, 13, -11, 8],\n [-... | 533 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 0, 8, 7, -4, 0],\n [4, 8, 4, 16, 5, 4, -9],\n [0, 4, -2, -1, 4, -8, 14],\n [8, 16, -1, -10, -4, 8, 10],\n [7, 5, 4, -4, -2, 0, 6],\n [-4, 4, -8, 8, 0, 12, 8],\n [0, -9, 14, 10, 6... | 940 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 9, 8, -5, 15, 9, 7],\n [0, 9, -1, 2, 16, -5, -6],\n [0, 0, 11, 7, -16, -5, -14],\n [0, 0, 0, 14, -11, -16, 12],\n [0, 0, 0, 0, -2, 13, -11],\n [0, 0, 0, 0, 0, 8, 7],\n [0, 0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nP... | 880 | MATH |
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