messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -7, 8, -15, -11, 3, -6, -16, 18],\n [0, -22, 20, -4, -22, -1, 3, -2, -18],\n [0, 0, -3, -1, 5, 0, -5, 22, 13],\n [0, 0, 0, -22, -16, -23, 12, 9, 13],\n [0, 0, 0, 0, -2, -14, 23, 2, 19],\n... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-19, 3, 5, -13, 19, 23, -3, -23, 12],\n [21, -20, 9, -15, 16, -10, 12, 3, 21],\n [-2, -24, -18, -15, -25, 0, 10, 20, 15],\n [24, -19, -8, 1, -11, 23, 10, 2, 7],\n [25, -4, -4, -17, 18, 24, -8, 4, 18],\n [9, 10, -7, -15, -7, 5, 5, -18, -15],\n [-19, -2, 3, ... | 824 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 24, 4, -22, -11, -15, 16, 17, -10],\n [0, 19, -7, 11, -1, 6, -8, 3, -1],\n [0, 0, 17, 19, 13, -22, -1, 23, 18],\n [0, 0, 0, -20, 10, -17, -4, -13, 1],\n [0, 0, 0, 0, 11, 2, -4, 15, 2],\n [0, 0, 0, 0, 0, -17, 1, 15, 18],\n [0, 0, 0, 0, 0, 0, 15, 19, -13... | 600 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-17, -13, -4, 0, 0, -18, -2, 2, -2],\n [-13, 25, -11, 7, 0, -11, -6, 6, 2],\n [-4, -11, -2, 12, 0, -9, 8, 0, 13],\n [0, 7, 12, -3, -10, -8, 4, 2, -1],\n [0, 0, 0, -10, -11, -20, 14, 13... | 972 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[16, -10, -4, -25, -7, -6, -12, -9, 17],\n [0, 19, -6, 25, -1, -13, 1, 12, 25],\n [0, 0, 5, 17, 17, 20, 8, -10, 17],\n [0, 0, 0, 7, -20, -3, 19, -5, -17],\n [0, 0, 0, 0, -11, 12, -25, -20, -12],\n [0, 0, 0, 0, 0, 2, -3, 2, 5],\n [0, 0, 0, 0, 0, 0, -13, 23, ... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -6, 3, 17, 19, 12, -15, 20, -3],\n [0, -7, 10, 20, 19, -24, -23, -10, -19],\n [0, 0, 21, 21, 19, 25, 0, -21, 12],\n [0, 0, 0, -6, -4, -5, 18, -24, 4],\n [0, 0, 0, 0, -7, 19, -10, -7, 9],\n [0, 0, 0, 0, 0, -5, -2, 16, -20],\n [0, 0, 0, 0, 0, 0, -17, -24... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 6, 17, -23, 18, 7, -13, -1, -15],\n [6, -21, -16, 25, -11, -3, -23, -17, 5],\n [-20, 11, 17, 1, 25, 0, 16, 23, -24],\n [-9, 21, -1, 7, -20, -2, -10, 21, -15],\n [-16, 4, 6, -20, -22, 24, 25, -6, -1],\n [0, -18, 14, 19, -21, 2, -4, -14, -23],\n [-5, -21,... | 343 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, 6, -2, 12, -8, -14, 0, -14, -18],\n [6, -5, -10, 10, 12, -1, 6, -4, -8],\n [-2, -10, 15, 20, -10, -8, 0, 1, -4],\n [12, 10, 20, -17, -1, -4, 18, 6, -8],\n [-8, 12, -10, -1, -11, -10, -12, -9, 2],\n [-14, -1, -8, -4, -10, -4, 4, 2, 6],\n [0, 6, 0, 18, -... | 665 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -12, 0, 4, -1, 24, -7, -10, 13],\n [-12, 4, 8, -2, 12, -2, 6, 23, 2],\n [0, 8, -9, -4, -14, -4, 6, -1, -4],\n [4, -2, -4, 16, 2, 13, 17, 2, -22],\n [-1, 12, -14, 2, 10, 14, -6, 6, -4],\n [24, -2, -4, 13, 14, 20, 6, 10, 4],\n [-7, 6, 6, 17, -6, 6, 24, 2, 12],\n... | 708 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[19, -24, -17, 20, -20, -23, -21, -23, 13],\n [0, 16, 1, 16, 4, 12, -19, -6, 7],\n [0, 0, 1, 11, 12, 2, 23, 0, -11],\n [0, 0, 0, -25, -3, 5, -3, 14, 14],\n [0, 0, 0, 0, 20, 10, 13, 15, -7],\n... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -5, -5, 25, -18, -7, 1, -17, 12],\n [-19, 19, -7, 11, -21, -14, -3, -16, 11],\n [-15, 10, 7, 1, -21, 0, -16, -24, 20],\n [-25, 14, 6, 18, -20, -16, -18, -10, 21],\n [-9, -22, -18, 1, 6, -14, -4, 3, -10],\n [-22, -7, -12, -17, 1, 20, -9, -4, -14],\n [-4, -11, 8... | 738 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-19, -10, -5, 6, -1, 0, 11, 12, -7],\n [-10, -6, 22, 2, -4, -13, 7, -10, -5],\n [-5, 22, 4, 22, 6, -4, 0, 10, 18],\n [6, 2, 22, 8, -19, -10, 13, 7, 10],\n [-1, -4, 6, -19, 25, 0, 12, 20, -1],\n [0, -13, -4, -10, 0, 20, 0, -2, -10],\n [11, 7, 0, 13, 12, 0, ... | 448 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 8, 20, -9, 20, -13, 6, 8, -2],\n [8, -19, -4, 5, 19, 2, -8, 7, 2],\n [20, -4, -25, -15, 2, 17, 13, -2, 7],\n [-9, 5, -15, -1, -6, 12, -2, -10, -3],\n [20, 19, 2, -6, 12, 4, -2, 12, -8],\n [-13, 2, 17, 12, 4, -13, -4, -3, 14],\n [6, -8, 13, -2, -2, -4, ... | 268 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 9, -24, 6, 8, 2, -12, 0, -1],\n [0, -20, -19, -4, 24, -24, 19, 7, -20],\n [0, 0, -8, -4, 10, 23, 11, 22, -3],\n [0, 0, 0, 6, -23, -9, -9, -18, -2],\n [0, 0, 0, 0, -16, -5, 2, 25, -17],\n ... | 560 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-18, 3, -5, 6, -24, 4, -10, -8, -2],\n [3, -5, 20, 0, 22, -8, -12, -2, -20],\n [-5, 20, -25, 15, 2, 1, 2, -4, -10],\n [6, 0, 15, -15, -16, 9, 2, 14, -21],\n [-24, 22, 2, -16, -22, 4, 14, -6,... | 28 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -16, 7, -2, -2, 16, -12, 2, 10],\n [-16, 7, 20, -5, -18, -16, 12, 3, -22],\n [7, 20, -13, 2, 6, -5, 20, 22, 15],\n [-2, -5, 2, 25, 0, -8, -1, 12, -2],\n [-2, -18, 6, 0, 22, -5, 10, -12, -3],\n [16, -16, -5, -8, -5, -1, 2, 20, 8],\n [-12, 12, 20, -1, 10, 2, 2, -... | 150 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[23, 8, -16, 4, 16, 1, 0, -16, 7],\n [8, 2, -14, -14, -14, -7, 4, 8, -3],\n [-16, -14, 25, 2, 12, 9, -6, -2, -10],\n [4, -14, 2, 17, -10, 2, -9, 10, -21],\n [16, -14, 12, -10, -3, 20, -11, -1... | 712 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[23, 3, -10, -5, 13, 12, 20, -12, 0],\n [3, 1, 10, 10, 0, 0, -16, 7, 17],\n [-10, 10, -16, -4, 20, -2, -4, 12, 2],\n [-5, 10, -4, -15, 10, 0, 0, -4, 7],\n [13, 0, 20, 10, -20, -7, -4, 2, -2],\n [12, 0, -2, 0, -7, 13, 10, 4, -7],\n [20, -16, -4, 0, -4, 10, ... | 688 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 8, -16, 9, -19, -25, -5, 17, 9],\n [-8, 24, -6, 11, 24, -15, -15, 12, 13],\n [-19, -25, 6, -22, -18, 15, 13, -7, 24],\n [-4, -12, -10, -10, 21, -6, 11, -15, -10],\n [23, 13, -1, -24, 19, 19, -25, 0, -11],\n [25, 10, 19, 10, -20, 23, -23, 5, -5],\n [-22... | 346 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 12, -18, 4, -1, 3, 12, -12, -23],\n [12, -13, 8, -8, 6, -14, -17, -4, 10],\n [-18, 8, 12, -18, -2, -3, 8, -10, -4],\n [4, -8, -18, 1, -10, 4, 5, -8, -16],\n [-1, 6, -2, -10, -24, -11, 11, -11, 16],\n [3, -14, -3, 4, -11, -20, -22, 0, 16],\n [12, -17, 8,... | 877 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, -16, -21, -25, -21, -18, 3, -15, -7],\n [-13, -16, -14, 3, 3, 7, 2, 10, -4],\n [-16, 23, -19, 11, 23, 16, 24, 7, 25],\n [18, -20, 5, -11, -17, 8, 1, 3, -20],\n [2, -22, 2, -9, -23... | 144 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -16, -7, 14, 11, 8, 14, 2, -18],\n [0, 21, 3, 18, 24, 16, -5, 9, 19],\n [0, 0, 12, -18, -23, 18, 14, -16, -20],\n [0, 0, 0, -4, -9, 16, 17, 3, 2],\n [0, 0, 0, 0, -25, 8, 4, 5, -2],\n [0, 0, 0, 0, 0, 21, -7, 20, -5],\n [0, 0, 0, 0, 0, 0, -4, -8, -1],\n [0, 0, 0,... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[18, -13, -5, -12, -15, 15, -20, -18, 1],\n [0, -15, 13, -25, -1, -22, -16, 18, 1],\n [0, 0, -20, 16, -23, 24, -17, 7, 20],\n [0, 0, 0, -9, 24, -1, 14, 16, 18],\n [0, 0, 0, 0, 20, -14, 18, -9, 9],\n [0, 0, 0, 0, 0, -2, 9, 1, 13],\n [0, 0, 0, 0, 0, 0, -3, -4... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 11, -6, 25, 25, 2, 21, 19, -18],\n [0, 14, -25, 11, 17, 21, -23, 0, 20],\n [0, 0, 18, 19, 1, -7, 0, -4, 12],\n [0, 0, 0, -3, -20, 16, 6, 2, -8],\n [0, 0, 0, 0, 7, -16, 22, -22, -23],\n [0, 0, 0, 0, 0, 4, 9, -4, 3],\n [0, 0, 0, 0, 0, 0, 16, 10, -18],\n... | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[17, 7, -11, 19, -14, 9, 9, -13, 9],\n [23, -2, -20, -16, -6, -5, 0, 23, -19],\n [11, -12, -1, -14, 7, 7, -3, -6, -23],\n [-25, -16, -11, -21, 24, -13, 13, 23, -18],\n [16, 9, 3, 18, -3... | 100 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 7, 2, -4, -1, -18, -6, -2, 14],\n [7, 5, -4, 7, 8, -18, -10, 2, -8],\n [2, -4, 8, -14, -6, -10, -10, 0, 2],\n [-4, 7, -14, -11, 10, 6, 9, -12, -5],\n [-1, 8, -6, 10, 3, 12, -12, 8, 4],\n [-18, -18, -10, 6, 12, -17, -12, 18, -17],\n [-6, -10, -10, 9, -... | 856 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 12, -19, 17, 6, 22, 11, 16, 9],\n [-7, 1, -18, -8, 7, 2, 14, 24, 23],\n [17, -25, -3, 22, -16, 7, -14, -12, -17],\n [21, 10, -4, -1, -23, 15, 5, 18, 17],\n [-19, 22, -16, 11, -17, 10, -15, -13, 17],\n [14, -25, -19, 3, -11, 23, -12, -3, -18],\n [14, 19, 3, -11,... | 928 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 10, 10, -8, -6, 20, -3, 3, 18],\n [10, 16, 17, 5, 11, -23, 13, -6, -8],\n [10, 17, 13, 11, 0, -6, -14, -5, -3],\n [-8, 5, 11, -5, 12, 14, 14, -24, 14],\n [-6, 11, 0, 12, 19, 12, -8, -24, 12],\n [20, -23, -6, 14, 12, -12, 18, -4, -13],\n [-3, 13, -14, 14... | 167 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -20, 13, 20, -10, -16, -10, -25, 11],\n [-18, -11, -8, 22, -4, -11, -24, 17, 18],\n [-20, -3, -16, -17, 3, 5, 24, 4, -11],\n [14, 25, -19, -19, 8, -12, 3, -7, 2],\n [13, 9, 6, -15, 22, 2... | 944 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[19, 2, -6, 9, -18, 2, -9, 3, -6],\n [0, 2, 22, -10, -3, 11, -9, -16, 25],\n [0, 0, 15, -22, -15, -17, -11, -9, 3],\n [0, 0, 0, 1, -7, -15, 13, 21, -14],\n [0, 0, 0, 0, -9, 1, 19, 4, 11],\n [0, 0, 0, 0, 0, 15, -25, 13, -24],\n [0, 0, 0, 0, 0, 0, -13, -8, -... | 50 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -4, 17, 18, -21, 4, 3, -25, 16],\n [7, 13, 13, -1, 2, 1, -14, -24, -17],\n [-15, -20, -8, -7, 10, 11, 4, -21, 15],\n [11, 4, 8, -13, -10, -24, 24, -10, 20],\n [25, 3, -22, 9, -14, ... | 182 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[20, -3, -8, 12, 14, -4, 8, -14, -3],\n [-3, 11, -16, 0, 6, 16, 2, -2, -8],\n [-8, -16, 14, 3, -12, 2, -8, 2, -1],\n [12, 0, 3, -24, 17, -4, 6, 5, -4],\n [14, 6, -12, 17, -9, -2, 14, -9, 4],\n [-4, 16, 2, -4, -2, 23, -8, -6, 16],\n [8, 2, -8, 6, 14, -8, -2... | 36 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-22, 6, -3, -1, -9, 20, 4, 20, 8],\n [13, 19, -15, -5, -18, -18, -9, 9, 9],\n [-1, -25, -6, 9, 22, -1, 22, -16, -7],\n [8, -13, -2, -21, -22, -4, 18, 21, -3],\n [11, 19, -24, 22, -22, -3, 10, 20, 17],\n [-15, 20, 9, 14, 19, 14, -19, -16, -16],\n [-19, -19... | 92 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -9, 22, -12, -22, 8, -2, 2, -14],\n [-9, -24, 5, 10, 0, -9, 1, 4, 2],\n [22, 5, -15, -8, 19, 18, 3, -12, -12],\n [-12, 10, -8, -20, -8, 24, 14, 1, -19],\n [-22, 0, 19, -8, 10, -2, -12, ... | 746 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[21, 20, 8, -9, -2, 15, -18, -20, -24],\n [-3, -5, -10, 21, -6, -14, 24, 14, -24],\n [-5, -23, -21, 15, 2, 1, -2, 22, -19],\n [-19, 4, -19, 16, -5, 13, 23, 3, 4],\n [-24, 22, -25, -11, -13, -... | 160 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -12, 18, 9, -8, 8, 16, -8, 4],\n [-12, 17, 0, 10, 8, 0, 0, -2, 8],\n [18, 0, 3, 2, -2, 6, -4, 4, -2],\n [9, 10, 2, -4, -4, 4, 12, 0, -2],\n [-8, 8, -2, -4, 16, 14, 6, 18, -4],\n [8, 0, 6... | 120 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-25, 23, -19, 13, 19, -25, 11, -6, 23],\n [0, 6, -7, -5, 16, 21, 6, -3, 11],\n [0, 0, 17, -16, -4, -15, -22, -13, 20],\n [0, 0, 0, -1, -15, -21, 6, 13, -20],\n [0, 0, 0, 0, -12, -8, 20... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[19, -16, -14, 20, 17, -4, 20, 4, -2],\n [-16, -11, -2, 22, -7, -1, 2, -16, 3],\n [-14, -2, 17, 4, -14, 5, 4, -7, 1],\n [20, 22, 4, -20, 11, -2, -1, 13, 0],\n [17, -7, -14, 11, 23, 16, 4, 7, 0],\n [-4, -1, 5, -2, 16, 20, -4, -6, -6],\n [20, 2, 4, -1, 4, -4, -2, 1, ... | 510 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, 0, 0, -14, 15, -3, -18, -2, 20],\n [0, 1, 5, -17, -2, -12, -2, -24, 21],\n [0, 0, -22, 3, 24, 2, 13, 7, -1],\n [0, 0, 0, -25, 19, 10, 14, -5, 20],\n [0, 0, 0, 0, -25, -9, -15, -15, 21],\n [0, 0, 0, 0, 0, -21, 22, -12, -25],\n [0, 0, 0, 0, 0, 0, -17, 25, 22],\n... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, -6, 19, -8, 10, -2, -8, 16, -13],\n [-6, 22, 14, 0, -3, 0, -6, 8, -10],\n [19, 14, -22, -21, 14, 3, -7, 16, -8],\n [-8, 0, -21, 20, 10, 22, -2, 21, 6],\n [10, -3, 14, 10, 19, 8, 15, -6, 18],\n [-2, 0, 3, 22, 8, -14, -3, 16, 8],\n [-8, -6, -7, -2, 15, -... | 785 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -4, -14, 18, -10, -14, -17, 2, -6],\n [-4, -2, 5, 2, -18, -3, 18, -10, -2],\n [-14, 5, 24, 10, 1, -2, 10, 2, -8],\n [18, 2, 10, 16, -10, -12, -10, 9, -8],\n [-10, -18, 1, -10, -15,... | 675 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[24, -12, -2, 18, -24, -6, -4, -23, 7],\n [-12, -19, -4, -4, 14, 14, 18, -12, -9],\n [-2, -4, 22, 0, -10, -2, 16, 12, 0],\n [18, -4, 0, 2, 22, -1, 3, 1, 2],\n [-24, 14, -10, 22, -15, -11, 2, 10, 4],\n [-6, 14, -2, -1, -11, 17, -13, -13, 3],\n [-4, 18, 16, ... | 30 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, -8, -12, 6, 9, -2, 18, 9, 18],\n [-17, 23, 0, -7, -22, 8, -18, 22, 9],\n [-14, -3, 2, 23, -15, -3, 14, 17, -21],\n [-10, 22, 0, 2, -1, -18, 20, -25, 4],\n [19, 18, -12, -23, -23, 15, -22, 13, 9],\n [13, 2, -8, -12, -25, -10, 7, 15, -25],\n [-4, -24, -... | 572 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -25, -14, -12, 8, 5, 21, -22, -3],\n [21, 2, 22, -7, -23, -3, 11, -11, -23],\n [0, 14, -13, 0, 15, 3, 8, -22, -2],\n [5, -21, -15, -20, -23, -12, -15, 14, -8],\n [-11, -10, 0, -1, 16, 7, -16, 22, 25],\n [10, 24, 8, -10, 0, -17, -3, -11, -9],\n [-2, 7,... | 756 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 3, 2, 9, 22, -12, -7, 13, 7],\n [0, -22, -21, -3, 4, -15, 5, -11, -13],\n [0, 0, -19, -3, 25, -11, -2, -8, 18],\n [0, 0, 0, -10, -15, -9, -6, 18, 10],\n [0, 0, 0, 0, -23, 11, 8, 18... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -23, 7, -25, 12, -11, -14, 2, -3],\n [18, -13, 4, 11, -3, -4, -3, -16, -5],\n [22, -18, -8, 1, 7, -9, -10, 11, 6],\n [15, 11, -6, 9, 20, -9, 4, 5, 17],\n [-13, -5, -24, -24, -9, -8, -13, 24, 2],\n [14, -6, -2, 16, 15, 19, 7, -11, -2],\n [-6, 8, -20, -2, -8, -21... | 543 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 19, -8, -5, 2, -18, 12, -8, 5],\n [19, 23, -4, 1, 18, 12, 10, 8, 0],\n [-8, -4, 14, 11, 10, 3, -8, 6, -17],\n [-5, 1, 11, -22, 17, 6, 4, -18, 0],\n [2, 18, 10, 17, -15, -16, 3, 14, -10],\n [-18, 12, 3, 6, -16, -25, -17, -6, 6],\n [12, 10, -8, 4, 3, -17, -17, -... | 152 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-21, 11, -11, -21, -20, -2, 2, 8, -9],\n [0, 16, -14, 10, 14, 10, 5, -15, -17],\n [0, 0, 15, 10, -13, -10, 24, 6, -9],\n [0, 0, 0, -21, 10, -8, -10, 14, -5],\n [0, 0, 0, 0, -1, -9, 2, -17, -24],\n [0, 0, 0, 0, 0, 21, -17, -23, -9],\n [0, 0, 0, 0, 0, 0, -11, -20, 1... | 120 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[18, 15, 4, 0, 1, -21, -24, 0, 23],\n [-5, 5, -4, -5, 17, 22, 8, 0, 16],\n [24, -17, 24, 17, -24, -16, 16, 24, 10],\n [-1, 20, -23, -12, 13, -13, 23, -23, 6],\n [-14, -17, 5, -16, 4, 24, -18, 1, 25],\n [-17, 8, -25, 11, 18, 13, 0, -14, -8],\n [-20, 13, 14, 8, 3, -2... | 890 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-23, -22, -3, -20, 5, -19, -10, 22, -20],\n [0, 18, 15, 9, 3, -3, 17, -17, 21],\n [0, 0, 19, 5, 1, -1, 20, -1, 23],\n [0, 0, 0, -10, -5, 25, -1, 5, -15],\n [0, 0, 0, 0, -6, 22, -21, -18, 6],\n [0, 0, 0, 0, 0, -2, 2, 5, -18],\n [0, 0, 0, 0, 0, 0, -6, 0, 8],\n [0, 0... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[25, 1, 19, -6, -10, -9, 25, 19, -18],\n [0, 23, -15, 3, -4, 12, -5, 25, 24],\n [0, 0, 25, -19, -8, -17, 10, -20, 3],\n [0, 0, 0, -15, 14, -24, -20, -16, -13],\n [0, 0, 0, 0, 3, -15, -20, 19, 6],\n [0, 0, 0, 0, 0, 14, -8, -8, -22],\n [0, 0, 0, 0, 0, 0, 25,... | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -16, -2, 23, 18, -14, -15, 0, 8],\n [0, -11, -5, -15, -20, -2, -11, 17, 5],\n [0, 0, 8, 12, -9, -18, -1, -1, 1],\n [0, 0, 0, -15, 0, -9, 25, -7, 24],\n [0, 0, 0, 0, -10, -3, -14, 0, 6],\n [0, 0, 0, 0, 0, -14, -12, -15, 8],\n [0, 0, 0, 0, 0, 0, 23, -13, ... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -11, 19, 21, 18, -5, 19, -25, 11],\n [19, 5, -16, 4, 20, 6, 12, -23, 13],\n [-15, -23, -9, 19, -25, -22, -4, 10, 8],\n [17, -13, -4, -9, -16, -5, 0, -20, -19],\n [-8, -10, -1, 1, -2, -20, -25, 17, -8],\n [-21, -6, 15, -25, 25, -7, -16, -10, -2],\n [12, ... | 325 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-24, 17, 9, -11, -19, 15, 11, -17, -2],\n [0, -14, -8, 1, 13, 12, -13, -1, -4],\n [0, 0, -10, 23, 10, 18, 11, -24, 25],\n [0, 0, 0, -22, 20, 13, 13, 2, 20],\n [0, 0, 0, 0, -17, -8, 19, 7, -10],\n [0, 0, 0, 0, 0, -25, 23, 15, -19],\n [0, 0, 0, 0, 0, 0, 10, ... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -8, 20, 14, -12, -1, -14, 12, 2],\n [-8, 9, -1, -16, 17, -16, 0, -2, -20],\n [20, -1, 23, -20, 1, 15, 2, -18, 6],\n [14, -16, -20, -14, -10, 12, 14, 1, -10],\n [-12, 17, 1, -10, 10, -10, -18, 2, 0],\n [-1, -16, 15, 12, -10, 4, 16, -18, 12],\n [-14, 0, 2, 14, -1... | 136 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -2, -12, -19, 1, 4, 11, -23, 24],\n [0, -14, 5, 13, 25, -15, -21, 20, -14],\n [0, 0, -13, -3, -12, 16, -7, 1, 18],\n [0, 0, 0, 2, 19, -7, -16, 23, -16],\n [0, 0, 0, 0, 8, 11, 10, 5, -7],\n [0, 0, 0, 0, 0, -22, 16, -19, 19],\n [0, 0, 0, 0, 0, 0, -19, -1... | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, -17, -1, 15, -2, -10, -3, -11, -2],\n [-17, 9, 6, 2, 7, 12, -1, 8, -8],\n [-1, 6, 24, 4, -3, 0, 2, 13, -14],\n [15, 2, 4, 4, 8, 0, -9, -4, 6],\n [-2, 7, -3, 8, 21, -15, -6, -18, 18],\n [-10, 12, 0, 0, -15, 25, 11, 1, -22],\n [-3, -1, 2, -9, -6, 11, -20... | 953 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, 1, -20, -2, -5, -10, -23, 20],\n [-2, 5, 7, 16, -15, 1, -16, 4, -20],\n [1, 7, -7, 8, 9, -11, -8, 10, 4],\n [-20, 16, 8, -19, -4, -8, -12, -14, 11],\n [-2, -15, 9, -4, -23, -8,... | 380 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -14, 6, 23, 13, -7, -4, -7, 22],\n [0, -18, -11, -15, 6, 21, 11, -5, 15],\n [0, 0, 3, -2, -1, -23, 13, -22, 3],\n [0, 0, 0, -10, 12, 5, 18, 9, 12],\n [0, 0, 0, 0, -6, 5, -22, 6, -5... | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -11, 14, -5, -7, 13, 13, 4, -23],\n [0, 11, -3, -19, -18, -24, 22, 12, -18],\n [0, 0, 8, -3, -4, 17, 10, -1, 22],\n [0, 0, 0, -5, -2, -13, 13, -23, -13],\n [0, 0, 0, 0, 15, -2, -2, 20, -19],\n [0, 0, 0, 0, 0, 15, -8, 21, 14],\n [0, 0, 0, 0, 0, 0, -18, ... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, 9, 17, 12, 21, 6, -1, -25, 3],\n [-20, -13, 10, -15, 15, -17, 21, 0, 21],\n [-24, -16, 16, -5, -15, 12, -5, -25, 2],\n [3, 22, -15, 6, -9, 5, -16, -14, 19],\n [17, -5, -7, 4, -19, -1, -6, -6, 24],\n [1, 19, -18, 3, -19, 21, 14, 14, 16],\n [-16, 14, -8,... | 280 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -13, 10, -4, 8, -3, 13, -17, -11],\n [-1, 16, -3, -20, 20, -18, 6, -12, 19],\n [-13, -19, 1, -2, -17, -25, 7, -20, -24],\n [-4, 4, -13, 25, -19, 1, -12, -22, 2],\n [13, 7, -23, -24, 17, 2, 15, 18, -10],\n [9, -6, 22, 17, 7, -3, 2, -7, 18],\n [-18, -15, 4, -6, -... | 602 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -3, -1, 23, -20, -20, 18, -19, -15],\n [0, -19, 20, -6, 4, -14, -15, -21, -7],\n [0, 0, 15, -16, -18, 12, 6, 16, 8],\n [0, 0, 0, 2, 17, 9, -6, -5, 6],\n [0, 0, 0, 0, -17, -1, -16, 21, 22],\n [0, 0, 0, 0, 0, -25, 18, -9, -24],\n [0, 0, 0, 0, 0, 0, 8, 23,... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -4, -11, 1, -20, 15, 4, -15, -22],\n [0, -15, -12, 17, 19, 13, -15, -4, 13],\n [0, 0, 24, -24, -19, 19, -2, 24, 13],\n [0, 0, 0, 9, -17, -20, -7, -18, -5],\n [0, 0, 0, 0, 13, -3, -1, 15, 5],\n [0, 0, 0, 0, 0, -9, 3, -13, 6],\n [0, 0, 0, 0, 0, 0, 9, -1, ... | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-22, -18, 21, 14, 3, -10, 4, 2, -3],\n [-18, -10, 10, 17, 7, 2, -10, -6, 10],\n [21, 10, 4, -8, -15, 0, -6, -20, -18],\n [14, 17, -8, -4, -4, -2, 5, -6, 6],\n [3, 7, -15, -4, 16, 4, -1... | 980 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -15, -15, -4, 13, 18, 15, 10, -8],\n [-15, -2, 7, -7, 13, -4, -4, 6, 0],\n [-15, 7, -17, 10, -10, -17, 2, 7, 10],\n [-4, -7, 10, -13, 5, -12, -1, -20, 4],\n [13, 13, -10, 5, 23, -13, -16,... | 403 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 9, -15, 20, -23, 0, 12, -25, 22],\n [17, -8, 20, -1, -11, -16, -18, -23, 15],\n [2, 6, -4, 18, 5, -22, 15, -19, -21],\n [15, 12, 16, -2, -22, 2, 12, 3, 20],\n [-18, -3, -10, 12, -21, 18, 15, 1, -10],\n [-22, 22, 8, -18, -8, -11, 12, -21, 13],\n [-16,... | 758 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 25, 16, 8, -10, -10, -15, 19, -6],\n [0, -17, 13, 24, -4, 16, -6, 0, 21],\n [0, 0, 9, -22, -23, 11, -24, -22, -19],\n [0, 0, 0, 5, -6, -19, 4, 11, 21],\n [0, 0, 0, 0, 17, -14, 19, -14, 9],\n [0, 0, 0, 0, 0, 7, 15, -3, 16],\n [0, 0, 0, 0, 0, 0, -3, 1, 11],\n [0... | 660 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 19, 24, -3, -23, 17, 23, -12, 4],\n [-13, -18, -17, -10, 1, -15, -11, 11, -18],\n [23, 20, 0, 18, 10, -17, -6, -20, 23],\n [-17, -3, 17, -7, 23, -14, -11, 6, -23],\n [-21, 9, 9, 18, 8, -4, -14, 0, 2],\n [6, -1, -19, 7, 7, 18, 6, 22, -10],\n [6, 19, -8, ... | 232 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 0, -3, 21, -12, 15, 13, 17, 8],\n [5, 11, -5, 1, 16, -3, -5, 6, -17],\n [15, 10, -12, 6, 0, -15, 19, 8, 23],\n [-4, -14, 24, 8, 10, -24, -18, 15, 18],\n [3, 9, 3, 4, -18, -23, 13, -9, -11],\n [7, -5, -6, 24, 21, -12, 11, -2, -19],\n [5, -16, -24, 3, 2... | 120 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 16, 1, 19, -18, 18, 14, 3, -12],\n [16, 21, 18, -11, 20, -12, -14, 6, 6],\n [1, 18, 12, -4, 10, -5, 2, 12, -4],\n [19, -11, -4, 2, -20, 12, 10, -5, 0],\n [-18, 20, 10, -20, 6, 23, 0, -14... | 348 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-19, -8, -23, 10, 25, 9, -21, 5, -2],\n [0, 11, -2, 14, -23, -22, 11, -9, 24],\n [0, 0, 9, 23, -2, 25, -7, -24, -23],\n [0, 0, 0, -23, -16, 1, 14, -18, -19],\n [0, 0, 0, 0, 6, -1, 13, ... | 220 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -16, 14, 1, -15, 10, -21, -16],\n [-2, 6, 7, 2, -18, 17, -1, 16, -8],\n [-16, 7, 9, 20, 4, -4, 14, -18, -12],\n [14, 2, 20, 9, 4, -8, -10, 12, -2],\n [1, -18, 4, 4, -9, -16, 5, ... | 652 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -23, -9, -12, 6, -3, 6, -23, 24],\n [-21, -23, -2, 9, -1, 13, -23, -10, 8],\n [-1, -4, 1, 10, -1, 3, 20, 22, 23],\n [12, 11, -8, 4, -14, -2, 1, 1, -16],\n [-18, 5, 23, -5, 15, -20, -1, -19, 21],\n [-4, 15, -19, -3, 23, -18, -11, -16, -9],\n [-15, -1, 7... | 164 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-22, 18, 0, 0, -10, 10, -20, 0, 17],\n [18, -2, 6, 8, -4, 6, 0, -8, -13],\n [0, 6, -6, -12, 2, -2, 20, 14, -6],\n [0, 8, -12, -16, 0, -14, -5, -3, -2],\n [-10, -4, 2, 0, 10, -12, 0, 0, -12],\n [10, 6, -2, -14, -12, -11, 4, -8, -2],\n [-20, 0, 20, -5, 0, 4, 6, 16, ... | 472 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 19, 11, -6, -16, 14, -22, 14, 16],\n [0, 25, 15, 0, -11, 9, -12, 1, 22],\n [0, 0, -23, 7, -17, 3, -7, -8, 23],\n [0, 0, 0, -14, -6, 7, -17, -8, -14],\n [0, 0, 0, 0, 7, -17, -19, -4, -13],\n [0, 0, 0, 0, 0, 20, 9, -8, 9],\n [0, 0, 0, 0, 0, 0, 8, 16, -22]... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-25, -18, 2, 0, -20, -7, 20, 7, -9],\n [0, -15, -22, 23, -23, 17, -14, -7, 10],\n [0, 0, -6, 7, -15, 16, -19, -24, 11],\n [0, 0, 0, -23, 13, 14, -24, 18, 10],\n [0, 0, 0, 0, -1, -10, -17, -2... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-20, 12, 20, 15, 21, 15, 1, 16, 0],\n [12, 7, -22, 4, 2, -14, 0, -6, 11],\n [20, -22, 10, -5, 2, 7, 10, -4, 0],\n [15, 4, -5, -23, 9, 12, 10, 10, -8],\n [21, 2, 2, 9, 12, 6, -4, 6, 7],\n [15, -14, 7, 12, 6, -3, 12, -11, -2],\n [1, 0, 10, 10, -4, 12, 3, -7... | 246 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-19, 16, 10, -12, 16, -21, -5, 6, 11],\n [16, 9, 9, -15, -7, 2, 12, -4, -6],\n [10, 9, -17, 0, -10, -4, -7, -3, -20],\n [-12, -15, 0, -3, -14, 2, -17, -2, 2],\n [16, -7, -10, -14, 23, 4, 12, 13, -24],\n [-21, 2, -4, 2, 4, -8, 2, -14, -1],\n [-5, 12, -7, -17, 12, 2... | 256 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -21, -23, 21, -10, -20, 8, -8, 10],\n [0, 24, 0, -4, 20, -3, -24, 5, 25],\n [0, 0, -13, 5, -16, 12, -16, -23, -24],\n [0, 0, 0, -14, 6, 16, 22, 6, -6],\n [0, 0, 0, 0, 3, 6, 19, -3, -2],\n [0, 0, 0, 0, 0, -24, 14, 9, 12],\n [0, 0, 0, 0, 0, 0, 24, -10, 16... | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 21, 23, 7, -20, 8, -5, 7, 1],\n [0, -24, -8, -21, 18, 6, -19, 15, 0],\n [0, 0, -19, 23, 19, -7, -21, -19, -17],\n [0, 0, 0, -1, -9, 20, -18, -13, -11],\n [0, 0, 0, 0, -1, 19, -13, -4, -1... | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-25, 8, 5, 20, 7, 12, -15, -10, -7],\n [0, 13, -7, 5, -4, 7, 9, -24, -15],\n [0, 0, 19, -9, 16, 15, 18, -16, -20],\n [0, 0, 0, -13, -12, 12, 12, 23, 14],\n [0, 0, 0, 0, -16, -23, -8, -5, -6]... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[14, 6, -10, 6, -22, 6, 18, -18, 22],\n [15, 12, 15, 24, 23, -12, 6, -25, -4],\n [-4, 11, 17, 15, 9, 2, 18, 6, -24],\n [23, 22, -14, 20, -8, 8, -5, 2, -3],\n [-7, -24, 1, 13, 25, -15, 15, 22, -12],\n [-11, -13, 7, 3, 5, 7, -13, -7, -22],\n [18, 16, -15, 25, 21, -24... | 812 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-20, 12, 2, -3, 22, -7, -16, -5, -2],\n [25, 10, 4, -4, 5, 19, 16, 15, 3],\n [8, -18, 11, 18, 15, 20, -4, 3, -11],\n [22, 24, -25, 24, -2, 6, 18, 22, 1],\n [8, 22, 23, 16, 16, 7, -17, -12, -... | 888 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 6, -8, 8, -3, -16, 6, 2, -19],\n [6, -8, 6, -18, -3, 0, 13, 9, 16],\n [-8, 6, 13, 18, 1, 11, -4, 0, -12],\n [8, -18, 18, 13, 6, 10, -16, -10, -5],\n [-3, -3, 1, 6, 7, 5, 10, -5, 13],\n [-... | 592 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, 9, 12, 6, -6, 6, 2, 0],\n [0, 9, 23, 11, 4, -14, 12, 2, 13],\n [0, 0, -1, 20, 6, 24, -9, 12, -24],\n [0, 0, 0, -19, 20, -10, -7, 22, 11],\n [0, 0, 0, 0, -21, -25, -16, 5, -13],\n [0, 0... | 876 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -4, 18, -19, -6, -4, -20, -10, 1],\n [-4, -4, -16, 12, -6, 0, -10, -5, 6],\n [18, -16, -14, 1, 7, 0, 10, 5, 16],\n [-19, 12, 1, -9, 2, -5, 17, 2, -2],\n [-6, -6, 7, 2, 20, -3, -12... | 504 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, 4, -17, -23, 7, -13, -3, 7, 4],\n [0, 11, 3, 14, 6, -21, -3, 24, -15],\n [0, 0, -18, -9, 16, 11, 12, 6, -24],\n [0, 0, 0, 7, -12, -6, -15, 5, 3],\n [0, 0, 0, 0, 2, 6, 14, -14, 0],\n [0, 0, 0, 0, 0, -1, 8, 16, -13],\n [0, 0, 0, 0, 0, 0, 21, 24, -23],\n [0, 0, 0... | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -7, 9, -2, -13, -6, 0, -10, 0],\n [6, -5, 1, -24, 6, 21, -23, 8, -15],\n [-12, -6, -22, 21, 19, -3, 13, 11, -11],\n [20, -18, -23, -17, -21, 17, 25, 5, -4],\n [9, 16, 25, 6, -3, -25, -1... | 608 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, -24, 10, 1, 12, 14, 1, 4],\n [-2, 11, -9, 16, 18, -2, 0, 2, 8],\n [-24, -9, 12, -2, 9, 6, 2, -10, 6],\n [10, 16, -2, -8, -5, -4, 13, -5, -5],\n [1, 18, 9, -5, 25, 10, 2, -4, 15],\n [... | 465 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, -2, -5, -16, -23, 6, 11, 0, 2],\n [-2, 14, -9, 2, -2, 4, -5, -19, -1],\n [-5, -9, 17, -8, -8, 12, -6, 0, -4],\n [-16, 2, -8, 14, -2, 12, -4, 16, 3],\n [-23, -2, -8, -2, 6, -16, 18, 20, 0],\n [6, 4, 12, 12, -16, -18, 16, 0, -6],\n [11, -5, -6, -4, 18, 16, 12, ... | 894 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-15, -6, 14, -11, 16, -12, 16, 22, -10],\n [-6, -19, 12, -3, 12, 6, -16, -4, 7],\n [14, 12, 8, 6, -16, 6, -18, -6, 5],\n [-11, -3, 6, -13, -10, -6, -4, 8, 12],\n [16, 12, -16, -10, -11, 4, 6, 0, 18],\n [-12, 6, 6, -6, 4, 5, 16, -9, 16],\n [16, -16, -18, -4... | 986 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 8, -16, -15, 15, 2, -16, -13, 20],\n [17, 8, -9, -9, -23, 18, 1, 18, -9],\n [-4, -18, 1, -4, -6, -25, -24, -14, 10],\n [22, 4, 11, -6, -9, 5, 22, -23, 11],\n [-23, -25, -3, -20, 9,... | 998 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -20, -1, -6, -20, -3, -18, -3, 24],\n [0, 3, 8, -17, 11, -8, 19, 10, 8],\n [0, 0, -11, -7, 17, -24, 12, -5, -3],\n [0, 0, 0, -7, -1, -3, 6, -9, -17],\n [0, 0, 0, 0, -9, 1, -18, 3, 9],\n [0, 0, 0, 0, 0, 3, 3, 1, 9],\n [0, 0, 0, 0, 0, 0, -19, 3, 12],\n [... | 412 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 18, -10, 13, -22, 7, -20, 2, -24],\n [0, 14, 17, -19, -19, 7, 6, 17, -22],\n [0, 0, 17, -19, -21, -1, 9, 17, -16],\n [0, 0, 0, -3, -15, 22, 17, -12, 5],\n [0, 0, 0, 0, -7, -2, -8, 1... | 844 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[20, -21, -8, -1, 18, -10, 25, 2, 9],\n [6, -25, -25, 10, -23, 1, 21, -11, -10],\n [17, -2, -6, -19, 20, 12, 10, -7, 10],\n [-16, -9, 25, -23, 7, 16, 9, 24, 20],\n [-3, 17, 7, 20, 7, 9,... | 224 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 12, -23, -25, 15, 11, -22, 25, -22],\n [-18, -18, 7, -19, 4, -3, 10, 18, 24],\n [17, 22, 3, -23, 23, -25, 5, -14, 11],\n [-16, -25, -10, 16, -18, -6, -1, -9, -24],\n [2, 13, 2, -9, -16, 13, -17, -25, -18],\n [-2, -23, 17, -5, 20, 22, -23, 4, 21],\n [0,... | 373 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, 2, -1, 5, -11, 4, -2, -8, -7],\n [2, 12, 6, -10, 5, 6, 4, 10, 0],\n [-1, 6, -11, -2, -12, -24, 13, 5, 0],\n [5, -10, -2, 17, -4, -3, 11, 10, 11],\n [-11, 5, -12, -4, 17, -2, 13, 14, -2],\n [4, 6, -24, -3, -2, 20, -18, -20, -3],\n [-2, 4, 13, 11, 13, -1... | 623 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -4, 3, -4, 0, 10, -5, -25, -4],\n [0, -7, 10, -12, -7, -3, 7, -1, 24],\n [0, 0, 7, 2, -21, -4, -7, 22, 2],\n [0, 0, 0, -18, 5, 5, 16, -16, -11],\n [0, 0, 0, 0, -1, 23, -24, -1, -2... | 880 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -10, 6, 4, -9, -4, -3, -10, 8],\n [-10, -15, 4, 12, -14, 1, -1, 2, -3],\n [6, 4, -9, -2, 14, -1, -14, -10, 10],\n [4, 12, -2, -15, -1, 20, 9, 10, -2],\n [-9, -14, 14, -1, -17, 18, -8, 2, -18],\n [-4, 1, -1, 20, 18, 6, -14, -8, 18],\n [-3, -1, -14, 9, -... | 189 | MATH |
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