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[[-16, 3, 2, -6, 14, -10, 11, -12, 14],\n [3, 10, 1, 0, 4, -8, 10, 10, 6],\n [2, 1, 15, -1, 18, -1, -2, 0, 2],\n [-6, 0, -1, -11, -16, -12, 0, -14, 7],\n [14, 4, 18, -16, -2, 12, -8, 0, 0],\n ... | 920 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -25, 19, -1, -25, -10, -21, 6, -7],\n [3, 10, 12, 23, 5, -18, 6, 2, 10],\n [-4, -1, 12, 4, 11, 2, 3, -1, 21],\n [16, -22, 2, 13, -11, -8, -4, -23, 4],\n [4, 18, -3, -13, -23, 20, 18, 7, 12],\n [-7, 5, 0, 24, -8, 2, -9, -11, -7],\n [12, 1, -7, -24, 17, -... | 580 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -15, -5, 2, 7, 14, 17, -3, -21],\n [0, 17, 1, 16, -21, 9, 3, 5, 17],\n [0, 0, -24, -12, -12, 19, -14, -15, 22],\n [0, 0, 0, 1, 8, 21, 17, -19, -14],\n [0, 0, 0, 0, 20, -25, 7, -22, -18],\n [0, 0, 0, 0, 0, 7, 3, 4, -7],\n [0, 0, 0, 0, 0, 0, 23, 1, -11],... | 320 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-17, -21, 7, 0, 21, -6, -9, 7, -23],\n [-25, -3, 21, -15, -24, -12, -10, 6, 6],\n [8, -23, 20, 18, 10, -12, 16, -22, 16],\n [-10, 12, 25, -2, -8, -13, 15, -15, 16],\n [19, -16, -19, 11... | 396 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[15, 7, -6, 10, 0, 0, 19, 0, 11],\n [7, 11, 8, 20, 10, -2, 11, 22, 5],\n [-6, 8, -16, -12, -6, -7, 12, 20, -3],\n [10, 20, -12, 18, 12, -12, 6, -4, -17],\n [0, 10, -6, 12, -24, -13, -6, -15, -2],\n [0, -2, -7, -12, -13, -17, 8, 14, -14],\n [19, 11, 12, 6, ... | 764 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 15, 3, 10, -22, -17, -6, 22, -25],\n [0, -1, 8, 1, 16, 2, 15, 10, -20],\n [0, 0, -6, 17, -22, 15, 5, 19, -2],\n [0, 0, 0, 25, 22, 3, 22, 20, -18],\n [0, 0, 0, 0, 22, 12, 12, 19, 25]... | 800 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -16, -4, 2, 22, 23, -14, 24, -24],\n [0, -5, 20, 14, -6, 15, 3, 17, -10],\n [0, 0, -7, -24, 5, 8, 14, -9, 23],\n [0, 0, 0, -1, -18, -5, 12, 19, -16],\n [0, 0, 0, 0, -8, -22, 22, 23, 8],\n [0, 0, 0, 0, 0, -4, -23, -21, 2],\n [0, 0, 0, 0, 0, 0, 11, 17, -... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[22, 5, 24, -20, 2, 18, -23, 7, 4],\n [0, -2, 10, 24, -9, 2, 21, 23, 12],\n [0, 0, 3, 24, 19, -20, -25, 24, -5],\n [0, 0, 0, -17, 21, -18, -20, 15, 10],\n [0, 0, 0, 0, 10, 15, 15, -2, -2],\n [0, 0, 0, 0, 0, 9, 5, 12, 18],\n [0, 0, 0, 0, 0, 0, 21, -22, -21],\n [0, 0... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 2, 3, -11, 21, -21, -8, 8, 6],\n [5, 23, 15, 20, 1, 21, -2, -2, 17],\n [19, -23, -13, -18, 20, -4, -20, 4, -2],\n [11, -16, 23, -14, 14, -14, 19, 2, 0],\n [16, 16, -17, 4, 6, 6, 8, 13, 4],\n [19, -22, 16, -7, 4, 22, -18, 14, -7],\n [9, -17, 2, 21, 21,... | 595 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -20, -22, -12, -11, 2, -16, 20, 6],\n [0, 1, 21, 18, 13, 19, 19, 13, 10],\n [0, 0, -2, -19, 3, -18, -11, -4, -23],\n [0, 0, 0, 3, 16, -18, 6, -13, -15],\n [0, 0, 0, 0, 7, 3, -16, 14, 9]... | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -7, 0, 14, 16, 3, 10, 2, 24],\n [-7, 21, -16, -21, 11, 10, -2, -3, 0],\n [0, -16, 6, 6, -12, 11, 2, -9, -4],\n [14, -21, 6, -2, -19, 22, 6, -4, 11],\n [16, 11, -12, -19, 17, -8, -8, 0, ... | 618 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 0, 8, -11, 2, -1, -12, -8, 2],\n [0, 24, -5, -7, -3, -12, 7, 8, -9],\n [8, -5, 24, 8, 6, 3, 2, -12, 20],\n [-11, -7, 8, -7, -1, -12, 1, -4, -6],\n [2, -3, 6, -1, -7, 4, -6, 0, -20],\n [-... | 456 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[23, 18, -11, 2, -6, -2, 2, -2, -4],\n [18, 12, -2, -10, 13, -8, 2, -2, -16],\n [-11, -2, -25, 9, -9, -2, 17, -8, 14],\n [2, -10, 9, -10, -18, -8, -6, -6, 16],\n [-6, 13, -9, -18, -9, -6, -8, 2, -2],\n [-2, -8, -2, -8, -6, -9, 1, 12, -12],\n [2, 2, 17, -6,... | 948 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-16, 2, -5, -2, -4, -14, -13, 4, -4],\n [2, -10, 0, -8, -2, 6, 8, -1, 14],\n [-5, 0, -23, 8, 14, -9, 6, 2, 10],\n [-2, -8, 8, -10, -20, -8, -8, -12, -2],\n [-4, -2, 14, -20, 25, -5, 4, 6, 7],\n [-14, 6, -9, -8, -5, -24, 17, -4, -11],\n [-13, 8, 6, -8, 4, ... | 174 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[25, -5, 8, 0, 19, -18, -2, 2, -4],\n [-5, -8, 15, -12, -6, 1, 2, -10, 11],\n [8, 15, 14, 13, 8, -2, -8, -21, -2],\n [0, -12, 13, -14, 1, 8, -14, -9, -1],\n [19, -6, 8, 1, -17, 4, -18, 21, 2],\n [-18, 1, -2, 8, 4, 8, 5, -10, 16],\n [-2, 2, -8, -14, -18, 5, ... | 544 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-25, -3, -12, 4, -4, 16, -8, -9, -16],\n [-3, 5, 16, 16, 8, -4, 10, 5, -12],\n [-12, 16, -25, 3, 10, 0, -2, -12, -8],\n [4, 16, 3, -10, 4, 8, 3, -6, 4],\n [-4, 8, 10, 4, -13, -4, -4, -10, -1... | 884 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-22, -12, -14, 3, 14, 5, -4, 11, 0],\n [-12, 2, -2, 13, -2, 2, 9, -5, -6],\n [-14, -2, 21, 9, -8, 10, 3, 7, -6],\n [3, 13, 9, 20, -7, -12, 0, 18, 4],\n [14, -2, -8, -7, 8, -20, 8, 7, 12],\n ... | 124 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -8, 13, 4, -2, -11, 0, -1, -16],\n [-8, 10, 12, 2, -2, 0, 2, -15, 12],\n [13, 12, -12, -1, 10, -17, 8, -2, -12],\n [4, 2, -1, 12, 2, -6, -17, 11, 8],\n [-2, -2, 10, 2, 12, -2, 19, -... | 874 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, -13, -16, 23, -9, -24, 14, 16, -15],\n [0, 22, 13, -2, 2, -24, -10, 4, 5],\n [0, 0, 24, -5, 6, -3, -23, 14, 4],\n [0, 0, 0, 11, -5, 4, -8, -24, 6],\n [0, 0, 0, 0, 23, -20, -14, -5, 5],\n [0, 0, 0, 0, 0, -1, -7, 16, 5],\n [0, 0, 0, 0, 0, 0, -16, -20, 1... | 448 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[19, 25, 23, 17, -12, -21, -19, -1, 1],\n [0, 13, -16, 10, -13, 5, -25, -20, -18],\n [0, 0, 23, 8, -20, -11, 18, -8, -23],\n [0, 0, 0, -12, -16, -25, 19, -17, 15],\n [0, 0, 0, 0, 18, 25, -9, -12, -22],\n [0, 0, 0, 0, 0, -24, -7, 24, -14],\n [0, 0, 0, 0, 0, 0, 17, 5... | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-16, -4, -8, -2, -25, -8, 3, 5, -1],\n [21, -11, 12, 19, 15, 18, -12, -5, 8],\n [-12, -14, -18, -14, 0, 7, -18, 3, 5],\n [-19, 24, 22, -6, -11, -3, 24, 20, 4],\n [22, 20, 10, 13, 7, -18, 15, 11, -25],\n [-25, -19, -9, -18, 20, -9, -9, -7, -3],\n [-2, -23, ... | 871 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[20, 19, -3, 0, 25, 18, 13, -18, -9],\n [22, 16, 1, -23, 2, 9, -9, 0, 9],\n [2, -8, -2, -13, 16, -19, -14, 0, -3],\n [-17, -13, 15, 8, 18, 21, 8, -4, -17],\n [6, -3, 20, 23, 16, -8, 17,... | 358 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 16, 12, 12, -1, 0, -2, -2, -4],\n [16, 12, -6, 8, -2, 14, -8, 6, -2],\n [12, -6, -10, 20, 15, 8, 14, 2, -8],\n [12, 8, 20, 5, 2, -4, 16, -6, 7],\n [-1, -2, 15, 2, -17, 16, 9, 2, 4],\n [0, 14, 8, -4, 16, 6, -13, -12, -8],\n [-2, -8, 14, 16, 9, -13, -1... | 608 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -20, -3, -10, 3, -6, -10, -8, -6],\n [-20, 11, 7, 0, -11, -8, 4, -6, -9],\n [-3, 7, 8, -4, 3, 1, 8, 6, 4],\n [-10, 0, -4, 14, 5, -4, 11, 0, 16],\n [3, -11, 3, 5, -1, -12, -14, 2, 5],\n [-6, -8, 1, -4, -12, 25, 8, -11, -18],\n [-10, 4, 8, 11, -14, 8, ... | 736 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, -19, -16, 6, 20, -9, 10, 11, 19],\n [14, -5, -1, 14, -17, 5, -17, -9, -13],\n [-7, -8, 0, 11, -19, 17, -20, -7, 18],\n [20, -2, -22, -8, 4, 5, -14, 15, 23],\n [21, -8, -4, -10, -1, -15, -18, 7, -21],\n [-18, 20, 20, 6, 21, 23, 7, -3, 5],\n [1, -12, -1... | 216 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 4, -4, 5, 16, -5, -16, 6, 16],\n [4, 17, -19, -5, -2, 1, -12, 6, 12],\n [-4, -19, -13, -15, 4, -2, -5, 20, -6],\n [5, -5, -15, -25, -7, 12, -14, 14, 2],\n [16, -2, 4, -7, 9, 1, 6, 8, -8],\n [-5, 1, -2, 12, 1, 4, 6, -2, -17],\n [-16, -12, -5, -14, 6, 6, 16, -2, ... | 546 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[20, 15, -25, 6, 9, -21, 0, -3, 10],\n [-9, -24, -24, 25, 13, 25, 20, 16, 23],\n [-5, 0, 25, -20, 9, -25, -2, -9, -14],\n [4, -5, 2, -4, -5, -3, 6, 17, -20],\n [15, 11, -12, 5, -22, 3, -2, 0, 10],\n [21, 23, 11, -5, -15, 12, -15, 1, -9],\n [11, 20, 1, 15, 10, 19, 1... | 984 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 9, -12, -4, 6, -12, -2, 7, -24],\n [-21, 4, 18, 23, -3, -2, -20, -5, -5],\n [-3, -18, 19, 20, -13, -13, -23, -25, 11],\n [-21, -14, -6, 3, -8, -12, -9, -5, -5],\n [11, 9, 3, -15, -19, 14,... | 835 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 10, 24, 12, 19, -22, 8, -21, -20],\n [0, -6, -8, 17, -13, -1, 10, 5, -20],\n [0, 0, 2, -11, -25, 0, 20, 20, -13],\n [0, 0, 0, -2, -13, -25, -19, 24, 22],\n [0, 0, 0, 0, -20, -4, 8, 4, 13]... | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[22, 0, -4, -2, -18, 0, -4, 17, -8],\n [0, 23, 2, 2, 0, -9, -7, -2, -2],\n [0, 0, -7, 24, 20, 24, -17, -5, 10],\n [0, 0, 0, 23, 25, -14, 21, -17, -11],\n [0, 0, 0, 0, 11, -1, 14, 3, -23],\n [0, 0, 0, 0, 0, -25, -24, 6, -1],\n [0, 0, 0, 0, 0, 0, -13, 25, 12... | 150 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 14, 22, 3, 4, 18, -5, 2, 4],\n [-8, 5, 16, -7, -11, -15, 22, 17, 23],\n [-22, -12, -20, -21, -20, -10, 3, -9, 20],\n [16, -19, -1, 11, -13, -17, 9, 10, -8],\n [-22, 2, -13, -5, -4, 21, 6, -18, 25],\n [-2, -3, 21, -10, 10, -13, 6, -14, 11],\n [-15, -14, 22, 7, ... | 542 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -18, 14, 2, 14, -7, -10, 7, -10],\n [-18, -18, 16, 3, 0, 12, -14, 14, -22],\n [14, 16, 15, 10, 12, -4, -2, 14, -2],\n [2, 3, 10, -19, 14, -18, -5, -6, -1],\n [14, 0, 12, 14, 8, 6,... | 212 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, -25, 23, -16, -17, -22, -1, -5, 13],\n [-6, 12, -6, -8, -3, 14, -7, 5, 9],\n [21, 9, -19, 6, 21, 20, -9, 20, -20],\n [4, -13, -12, -15, -1, 16, -21, -19, 14],\n [-8, -23, -18, -25, -21,... | 124 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[22, -4, 20, 24, -21, 4, -10, -9, 16],\n [10, 2, -16, -24, 2, 22, 16, -25, -13],\n [-16, -9, -20, -5, 23, 2, -22, -2, -7],\n [-24, 10, -14, 6, 7, 2, 17, 6, 8],\n [9, -24, 4, -14, 3, 13, 5, 25, -9],\n [15, 7, 10, -20, -8, -19, 23, -15, -17],\n [22, 23, -8, -25, 2, 2... | 767 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[18, 17, 21, -23, 21, -22, 11, -6, 4],\n [22, -5, -5, -24, -20, 20, 2, -20, -2],\n [5, -1, -6, 0, -3, 17, 0, 16, -12],\n [10, 0, -13, 24, 1, -23, -12, -12, 7],\n [18, -6, 1, -16, -24, 2... | 179 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -20, -16, 5, 15, 12, 15, 18, -25],\n [0, -19, 3, -5, 22, 17, -8, -16, 6],\n [0, 0, -5, -15, 8, -21, 8, -20, 17],\n [0, 0, 0, -4, -9, 19, 4, -6, -15],\n [0, 0, 0, 0, -20, 18, 5, 16,... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-22, 25, -16, -5, 24, -20, -19, 19, 4],\n [0, -12, 15, 9, -4, -22, 9, -11, 21],\n [0, 0, -23, 12, -23, 0, -12, 10, -25],\n [0, 0, 0, -17, -13, 11, 23, -17, 7],\n [0, 0, 0, 0, -14, 25, -1, -2... | 760 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 0, -19, 20, -6, -7, -10, -16, -23],\n [3, -9, -10, -3, 10, 5, 6, 14, -23],\n [13, 4, 14, 21, -17, -11, 23, 13, -12],\n [7, 17, -10, 16, -16, -8, 4, -9, -5],\n [-15, 3, -15, 0, -17, 22, -11, -16, 20],\n [-14, 6, 3, 25, -8, 15, 11, 9, 1],\n [-13, 7, 13, ... | 908 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, -2, 4, -7, 2, 14, 10, -8, 1],\n [-2, 24, 6, 5, 12, 17, 12, 11, 8],\n [4, 6, -11, -10, 19, -10, 4, -2, 8],\n [-7, 5, -10, -9, -6, 6, -12, -11, 12],\n [2, 12, 19, -6, -22, 20, -2, -11, 16],\n [14, 17, -10, 6, 20, 15, 16, 2, -6],\n [10, 12, 4, -12, -2, ... | 419 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-20, -11, 23, -1, -15, 5, -9, 21, 13],\n [0, -12, -13, 7, 0, -20, 18, -13, -4],\n [0, 0, 20, 12, 19, 0, 19, -23, -1],\n [0, 0, 0, -25, -25, -3, -5, -25, 4],\n [0, 0, 0, 0, 16, 18, 21, 5, 13],\n [0, 0, 0, 0, 0, 5, -12, 17, 9],\n [0, 0, 0, 0, 0, 0, 14, -8, -... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -2, -18, -22, -1, -3, -22, 2, 12],\n [0, -19, -17, 19, -4, 24, -17, -11, -10],\n [0, 0, -7, 6, 12, -8, 13, -11, 9],\n [0, 0, 0, 12, 25, -6, -19, 9, 1],\n [0, 0, 0, 0, 23, 6, -19, 6, 13],\n [0, 0, 0, 0, 0, 13, 24, -19, 14],\n [0, 0, 0, 0, 0, 0, -12, -2... | 376 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[16, -17, -25, -9, -6, -14, 23, 3, -16],\n [0, -13, 16, 12, 11, 15, -11, -22, 14],\n [0, 0, -21, -2, 6, 22, -25, -8, 8],\n [0, 0, 0, 2, -8, -10, -23, 12, 20],\n [0, 0, 0, 0, -7, 8, 4, 0, 13],\n [0, 0, 0, 0, 0, 5, 20, 7, -18],\n [0, 0, 0, 0, 0, 0, 16, -10, ... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, 6, -5, 6, 7, 16, -8, 12],\n [4, -9, 1, -6, 15, 1, -8, 2, -7],\n [6, 1, -15, -14, 10, -4, 0, 2, -18],\n [-5, -6, -14, -23, 18, 10, 0, -6, 8],\n [6, 15, 10, 18, -3, -12, 0, 4, -8],\n [7, 1, -4, 10, -12, 13, -2, 6, -14],\n [16, -8, 0, 0, 0, -2, -8, 0, 12],\n [-... | 808 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 17, -23, -9, -17, -17, 20, -12, -19],\n [11, 21, 5, 11, -11, 12, -16, 25, 21],\n [-20, 22, -17, 8, 9, -3, 5, -19, -15],\n [15, -24, -5, -24, -3, 3, -20, -5, -18],\n [15, -4, 19, 18, -7, -8, -7, 5, -11],\n [-8, -13, 12, -22, 17, 21, -9, -9, -10],\n [-21... | 979 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -9, 16, -15, -10, -24, -9, 23, -7],\n [-16, 19, 3, -15, -7, -7, 24, -2, -17],\n [-22, 15, -17, -24, -13, 24, 5, 22, 16],\n [2, -24, -5, -19, -14, 8, -1, -23, 8],\n [19, -18, 1, -22, -15, 14, 18, 0, 15],\n [-10, -15, -5, -13, 14, 12, -7, 8, 21],\n [19, ... | 222 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[22, -5, 14, 8, 0, -3, -4, -8, 1],\n [-5, -14, -9, 2, -11, 4, 6, 0, 20],\n [14, -9, -13, 10, -4, -4, 8, -8, -10],\n [8, 2, 10, -4, 0, -6, 6, 5, 0],\n [0, -11, -4, 0, 13, -2, -4, -14, -10],\n [-3, 4, -4, -6, -2, 7, -8, -24, 1],\n [-4, 6, 8, 6, -4, -8, 2, -4, 20],\n ... | 512 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[17, 15, 4, 10, -8, 22, 0, 6, -1],\n [15, -13, 13, -18, -18, -12, -17, -8, 5],\n [4, 13, -18, -16, 18, -1, 10, 9, 16],\n [10, -18, -16, -23, -6, -12, 0, -12, -2],\n [-8, -18, 18, -6, -2, 22, -10, -14, 8],\n [22, -12, -1, -12, 22, -25, -4, 19, 12],\n [0, -1... | 440 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 7, -20, 16, -9, -8, 9, 14, 20],\n [12, 19, 5, 11, -1, -14, 12, 4, 24],\n [-1, 24, 19, -9, 17, -13, -2, 4, 3],\n [0, -11, 4, 18, -14, -3, 2, 8, -20],\n [7, -25, -7, -8, 16, 2, 21, -8, -12],\n [24, 2, -18, 9, -5, 7, 2, 21, -24],\n [13, -6, 1, -21, 23, 11, 9, 14... | 869 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[19, -8, -21, -22, 24, 17, -4, -18, -12],\n [0, -25, -10, -16, 6, -4, 4, -4, 11],\n [0, 0, 7, 11, 9, 22, -8, 18, -6],\n [0, 0, 0, 2, 23, -14, -5, 14, -22],\n [0, 0, 0, 0, 24, -1, 18, 21, 14],... | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-22, -1, 0, 10, 12, 6, 8, 14, 0],\n [-1, -4, 2, -7, -18, -12, -2, 20, -10],\n [0, 2, -22, -4, 5, -10, 4, 4, -13],\n [10, -7, -4, 25, -8, -2, 0, -2, 0],\n [12, -18, 5, -8, -7, -22, -1, 18, -16],\n [6, -12, -10, -2, -22, -10, 12, 14, -10],\n [8, -2, 4, 0, -1... | 438 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-19, 14, 6, 4, -2, 15, -2, 5, -4],\n [14, -15, -6, 8, 4, -8, 4, 0, 0],\n [6, -6, 1, 12, -12, -8, -20, 0, -2],\n [4, 8, 12, 9, -2, 0, -6, 0, 18],\n [-2, 4, -12, -2, -21, 7, 10, -12, -20],\n [... | 608 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, -20, 24, 10, 17, 18, 22, -17, -9],\n [-14, 19, 23, 23, -2, -6, 4, -7, 5],\n [-2, 12, 17, -19, -2, 6, -19, -3, 18],\n [14, 8, 16, -16, 15, -24, -13, 3, 7],\n [5, -24, 8, -13, -11, 6, 14, -14, -4],\n [20, -4, 6, -16, 6, -2, -8, -21, -1],\n [-6, 1, -16, -3, 10, -... | 336 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[23, 14, -14, 4, 15, -6, -10, -5, -14],\n [14, -4, -8, 20, -8, 12, 0, 5, -2],\n [-14, -8, 12, 10, 16, -4, 10, 2, -12],\n [4, 20, 10, -8, 0, 5, 18, 21, -14],\n [15, -8, 16, 0, -25, 12, 4, -11,... | 876 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, 16, 2, -9, -18, -23, 22, -2],\n [0, -16, -17, 23, -17, 16, -17, -25, 16],\n [0, 0, -2, -18, 3, -20, 11, 19, 1],\n [0, 0, 0, -4, -21, -22, 9, -23, 7],\n [0, 0, 0, 0, 3, -16, 16, -1, -1... | 952 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -15, -6, 14, 8, -10, -4, -3, 15],\n [0, 19, -11, -24, -6, -10, 5, -23, 25],\n [0, 0, 20, -15, 0, -14, 4, 23, 15],\n [0, 0, 0, -7, -6, 3, 13, -15, 18],\n [0, 0, 0, 0, 22, 14, -9, 3, 24],\n [0, 0, 0, 0, 0, -3, -2, -22, 21],\n [0, 0, 0, 0, 0, 0, -21, -4, ... | 480 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 8, -10, 11, -6, -4, 0, 11, 16],\n [0, 11, -10, -20, -3, 6, 6, -13, 3],\n [0, 0, 24, -2, 9, -11, -17, 7, -3],\n [0, 0, 0, 16, -2, -24, 4, 2, -5],\n [0, 0, 0, 0, 2, 25, 5, 16, 4],\n [0, 0, 0, 0, 0, 4, 11, 22, 21],\n [0, 0, 0, 0, 0, 0, -1, 14, 15],\n [0, ... | 328 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[13, -2, -8, -20, 1, -2, -8, 6, -2],\n [-2, -5, 8, 8, 2, 2, -2, 4, -6],\n [-8, 8, -17, -14, -12, -15, 21, 9, -5],\n [-20, 8, -14, 11, 8, 13, 2, 3, -4],\n [1, 2, -12, 8, 15, -14, -4, 2, -14],\n [-2, 2, -15, 13, -14, 5, 11, -11, -5],\n [-8, -2, 21, 2, -4, 11... | 264 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-16, 7, 22, 0, -3, -18, 22, 22, 10],\n [0, 12, -11, 10, -18, 16, 2, 24, 16],\n [0, 0, 22, -25, -25, -10, 12, 25, 12],\n [0, 0, 0, 10, 5, -20, -10, 0, -15],\n [0, 0, 0, 0, -8, 25, 20, -4, 2],... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 16, 10, -1, -10, 12, -1, 2, 3],\n [16, 9, 9, 14, 11, 1, -11, -3, 8],\n [10, 9, -3, 6, 2, 18, -9, 16, 3],\n [-1, 14, 6, -24, 4, -14, -18, -18, 8],\n [-10, 11, 2, 4, 22, 6, 17, 2, -14],\n [12, 1, 18, -14, 6, -17, -4, 6, -2],\n [-1, -11, -9, -18, 17, -4, ... | 22 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-22, 4, 6, 2, 17, -14, -18, -25, -20],\n [0, 24, -17, -6, -21, -23, 22, 1, -10],\n [0, 0, 12, -3, 22, -6, 1, -20, 22],\n [0, 0, 0, 13, 1, 10, 5, -16, 12],\n [0, 0, 0, 0, -6, -6, 16, -3... | 760 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-15, -12, 6, 0, -20, -8, 2, 4, 10],\n [-12, -8, 2, -4, 11, 8, 0, 4, -10],\n [6, 2, -10, 7, -4, -15, -8, -4, 4],\n [0, -4, 7, -1, -5, 18, -16, 20, -16],\n [-20, 11, -4, -5, 8, 1, -1, 14, 10],\n [-8, 8, -15, 18, 1, 6, 11, 5, 6],\n [2, 0, -8, -16, -1, 11, 14... | 301 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[20, 16, -6, 1, -4, 5, -2, 12, -6],\n [16, -21, 16, -2, -6, 2, -15, 6, 4],\n [-6, 16, 15, -16, 17, -2, -12, -20, 12],\n [1, -2, -16, 14, 0, -3, 3, 3, 5],\n [-4, -6, 17, 0, 7, 2, 3, -18, 14],\n [5, 2, -2, -3, 2, -11, -2, -22, -5],\n [-2, -15, -12, 3, 3, -2,... | 132 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-21, 12, 8, -16, -25, 21, 18, -2, 20],\n [17, -10, -20, -18, -16, 15, -20, 13, -1],\n [21, -2, -12, 25, 16, -14, -18, -12, -16],\n [7, 4, -15, -6, 1, -20, 4, 4, 7],\n [17, 0, -25, 12, -20, -... | 147 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -20, -16, 16, -20, -7, -6, -8, -1],\n [-20, -25, -3, -4, 4, 6, 14, 4, -24],\n [-16, -3, -17, 18, 14, 8, 13, -13, 18],\n [16, -4, 18, 20, 6, 6, -8, 8, 0],\n [-20, 4, 14, 6, -25, 8, 14, 14... | 872 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 14, 16, -8, -1, -8, 2, -9, -13],\n [14, -12, 12, 5, -6, 19, 2, -10, 8],\n [16, 12, -16, 9, 20, -7, 2, -2, -6],\n [-8, 5, 9, 16, 0, 4, 2, -4, 14],\n [-1, -6, 20, 0, -4, 2, 4, 15, 23],\n ... | 592 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-17, 14, 18, 24, -24, 25, -1, 10, -13],\n [0, -6, -16, 20, -9, 12, -20, 2, -24],\n [0, 0, 24, 4, 16, -5, 22, -2, -1],\n [0, 0, 0, 7, -15, 6, 11, 11, 0],\n [0, 0, 0, 0, 8, -8, 2, -7, -8... | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-20, 15, -5, 12, 16, -17, -4, 3, -18],\n [-22, -3, 5, 2, -9, 5, 13, 23, -22],\n [24, -23, 19, 12, 25, -16, 22, -21, -25],\n [-21, -1, -23, -13, 23, -9, 9, 3, -6],\n [19, -7, -10, -6, 1... | 10 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -18, -3, -1, 2, 12, 20, -25, 15],\n [0, -18, 5, 17, 0, 7, 22, -1, -12],\n [0, 0, -17, 22, 2, -13, -12, -10, -15],\n [0, 0, 0, -6, -3, -21, -12, 9, 8],\n [0, 0, 0, 0, 13, 4, -23, -15, 1],\n [0, 0, 0, 0, 0, 1, 3, 9, -18],\n [0, 0, 0, 0, 0, 0, -6, 16, 8],... | 280 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -2, 6, 4, -18, 0, 18, -4, -12],\n [-2, -21, 10, 17, -2, -8, 14, -13, -12],\n [6, 10, 11, -14, -16, 6, 11, -2, 16],\n [4, 17, -14, 14, -2, 8, 4, 11, 20],\n [-18, -2, -16, -2, 20, 4, 4, 4, 2],\n [0, -8, 6, 8, 4, 6, 4, 15, -18],\n [18, 14, 11, 4, 4, 4, -... | 984 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[13, 23, 14, 7, -20, -10, 25, 15, 19],\n [0, 21, -23, 17, 18, 13, 18, -9, -5],\n [0, 0, -19, -25, 21, 4, 3, 0, 23],\n [0, 0, 0, -8, 21, 5, -3, -7, 25],\n [0, 0, 0, 0, -24, 16, -17, 10, -8],\n [0, 0, 0, 0, 0, -25, 13, 15, -25],\n [0, 0, 0, 0, 0, 0, 20, 5, -... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 15, -10, 0, 25, -18, -10, -19, -17],\n [-21, -17, -4, 10, 4, -6, -6, 5, 3],\n [-13, 0, 21, -2, -16, 15, -12, 8, 8],\n [16, 13, -9, -3, -16, 25, 6, -11, 16],\n [-3, 24, -5, 23, -21, 18, 17, -25, 0],\n [7, 16, -5, -13, 4, 21, 1, 21, -7],\n [-15, -14, 15, 16, -13,... | 13 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[25, -16, -15, 4, 18, -1, 16, 14, -9],\n [-16, -14, 3, 0, -6, 14, -20, 0, 8],\n [-15, 3, 19, 4, 11, 6, -14, -22, -2],\n [4, 0, 4, 2, -4, 14, -6, -13, 16],\n [18, -6, 11, -4, -7, 4, -4, 6, 10],\n [-1, 14, 6, 14, 4, -13, -12, 5, -23],\n [16, -20, -14, -6, -4, -12, 25... | 8 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, -12, 6, 6, -13, -19, 6, 0, 2],\n [-12, -5, -16, -10, -14, 14, 0, 10, -16],\n [6, -16, 17, -13, 0, 10, -8, -12, 24],\n [6, -10, -13, -21, -10, 4, -10, 14, -2],\n [-13, -14, 0, -10, 12, 0, 0, 5, -5],\n [-19, 14, 10, 4, 0, 16, 20, -9, 8],\n [6, 0, -8, -10... | 872 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-24, 0, 12, -17, -13, -11, 5, 10, -2],\n [0, 19, -4, 9, 2, 4, -6, -4, -15],\n [12, -4, -15, -12, 6, -20, -1, 7, 4],\n [-17, 9, -12, 8, 8, 16, -20, -6, 14],\n [-13, 2, 6, 8, -5, -16, -20, 12, -11],\n [-11, 4, -20, 16, -16, 20, 0, 4, 3],\n [5, -6, -1, -20, ... | 683 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -25, 9, -22, -22, 5, 21, 14, -22],\n [-23, 23, -15, -7, 0, -16, 19, -21, -19],\n [8, 14, -20, 14, 14, -24, 8, -25, 10],\n [2, -15, 18, 15, -7, 4, 2, 0, -22],\n [-17, -24, -12, -16, 5, -12, -15, 7, 14],\n [-17, -3, -17, 20, 5, 14, 10, -16, -8],\n [-18, 17, 13, ... | 16 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-23, -18, 15, 23, -3, -12, 0, -20, 21],\n [-14, 13, -13, 7, 25, -3, -18, -23, -10],\n [-24, -9, -21, -8, -22, -1, 24, 0, 9],\n [-5, 8, -3, -20, 7, 23, 0, -9, -20],\n [15, -13, 18, 18, 3, 15, -22, 8, 4],\n [-3, -21, -18, -10, 0, 14, 23, -20, 8],\n [-19, -1, -7, -19... | 438 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[23, -14, -23, 6, 16, -19, 9, 24, -10],\n [1, 20, 19, 18, -16, 23, 21, -14, -18],\n [-7, -13, -17, 4, 24, 24, 5, -17, 1],\n [12, -1, -6, 17, 11, -12, -25, 21, 5],\n [10, 25, 1, -13, -11, 9, 25, 15, -25],\n [8, 22, 1, 3, -13, 24, -1, 4, 23],\n [23, 11, 10, ... | 564 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-21, -13, -1, -7, 19, -25, 14, -18, -14],\n [0, -21, -24, 7, 20, -11, -7, 10, -20],\n [0, 0, -2, -8, -14, -9, -20, 12, -13],\n [0, 0, 0, -15, -15, -14, 18, -19, -9],\n [0, 0, 0, 0, -8, -23, -15, 11, 0],\n [0, 0, 0, 0, 0, -7, 12, 21, -4],\n [0, 0, 0, 0, 0, ... | 560 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[17, 0, -2, -2, -6, 2, -17, 10, 0],\n [0, -13, -6, 10, 0, -3, -15, -2, 12],\n [-2, -6, 8, -16, -7, 5, 4, -6, -6],\n [-2, 10, -16, -16, 7, -20, -7, -24, -10],\n [-6, 0, -7, 7, 7, 16, 5, 2, 9],\n [2, -3, 5, -20, 16, 11, 11, -9, 2],\n [-17, -15, 4, -7, 5, 11, 20, -3, ... | 8 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -21, 10, 9, 8, -17, 12, -5, 18],\n [0, 20, -8, -18, -7, -18, -2, -15, 24],\n [0, 0, -8, -24, -21, -3, -10, -6, 19],\n [0, 0, 0, -2, -3, -12, -10, 17, 9],\n [0, 0, 0, 0, -15, -16, 3, 15, -2],\n [0, 0, 0, 0, 0, -19, -9, -25, 19],\n [0, 0, 0, 0, 0, 0, -14... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -5, -3, -10, 15, -21, -25, 21, 14],\n [1, -7, 16, 12, 1, -16, -16, 21, 12],\n [11, 18, 10, 8, 12, -14, 16, 7, -14],\n [-7, -7, 22, 22, 22, 19, 6, -8, -7],\n [-16, -5, -22, 14, -9, 13, -4, -1, -13],\n [2, -6, 9, 24, -21, 24, -10, -11, -14],\n [-10, 10, 9, 2, -2... | 296 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-18, 16, -1, -2, -13, 23, 1, -15, 14],\n [-4, 5, 22, -15, 21, -3, -13, -3, 14],\n [16, 3, -10, 22, -2, -21, -25, 23, -1],\n [-25, 6, -20, -24, -21, 18, -10, 25, -2],\n [-13, 13, 22, -7, 13, 6, -4, 23, 7],\n [-4, -18, -18, -5, -12, -12, 0, -3, 4],\n [-21, ... | 367 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -20, 20, -16, 21, -19, -19, 2, 16],\n [0, 23, -7, 21, 13, -20, 8, -20, -17],\n [0, 0, -21, 10, -3, 24, -19, -6, 11],\n [0, 0, 0, -4, -19, 4, -17, -10, 2],\n [0, 0, 0, 0, -1, 21, -4... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -8, -7, -6, 20, -12, 6, -8, -2],\n [-8, -15, -6, -1, 4, -20, -8, -16, 2],\n [-7, -6, 22, -20, -2, -6, -10, 2, 14],\n [-6, -1, -20, -11, 7, -3, 9, 2, -8],\n [20, 4, -2, 7, 21, 10, 4, -6, 6],\n [-12, -20, -6, -3, 10, -13, -15, 4, -18],\n [6, -8, -10, 9, 4, -15, -... | 32 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, 17, -22, -16, 14, -3, -8, -25, 7],\n [0, 16, -6, 11, 17, 14, -3, -22, 4],\n [0, 0, 9, 8, 8, 17, -3, -16, 5],\n [0, 0, 0, -2, 1, -19, 23, 12, -9],\n [0, 0, 0, 0, -5, -21, 24, 13, 22],\n [0, 0, 0, 0, 0, -3, -22, -7, -16],\n [0, 0, 0, 0, 0, 0, -11, 2, -22... | 800 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-17, 6, 6, 7, -4, 10, -4, -9, -20],\n [-20, -13, -8, -16, -25, 7, -9, 3, -12],\n [-16, 6, 3, -5, -2, -10, -22, 22, -3],\n [-9, -23, -18, 8, 0, -1, -14, 10, 3],\n [-22, 22, 0, 11, 20, -4, 22, -15, -5],\n [14, 23, -17, 6, 12, 1, 8, 18, 7],\n [-24, -19, 22, ... | 885 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[23, -13, -7, 10, -7, -15, -25, -18, 13],\n [0, -24, 20, -3, -18, 19, -7, 19, -10],\n [0, 0, 3, -6, -20, 5, -22, -14, 24],\n [0, 0, 0, 5, 11, -22, -2, -11, 25],\n [0, 0, 0, 0, -6, -3, 22, 21,... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 5, 0, 10, -6, 18, -1, 11, 13],\n [5, 0, -6, 0, -10, -2, 4, -16, 8],\n [0, -6, 24, 12, -2, -9, 0, 16, 6],\n [10, 0, 12, 17, 2, 8, -9, 9, 20],\n [-6, -10, -2, 2, -1, -7, 5, 16, 1],\n [18, -2, -9, 8, -7, -18, -8, -12, 0],\n [-1, 4, 0, -9, 5, -8, -5, -20,... | 411 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 10, -6, -6, -2, 14, -4, -6, -3],\n [10, 12, -3, 6, 6, 16, -4, -2, 8],\n [-6, -3, -12, -10, -2, 6, 20, 4, 5],\n [-6, 6, -10, 14, 14, 5, 14, 0, -6],\n [-2, 6, -2, 14, 20, -6, -2, -6, -14],\n [14, 16, 6, 5, -6, 6, 6, -6, -10],\n [-4, -4, 20, 14, -2, 6, 5, 0, -2]... | 780 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, -19, -15, 19, -20, 11, -4, 23, -22],\n [-12, 14, 25, -2, 21, -8, -7, -4, -2],\n [17, 17, 24, 18, -21, -20, -9, -11, 18],\n [-25, 21, -15, 22, -2, 12, -20, 21, 4],\n [-20, -16, -21, -12, -20, -2, 0, -17, -25],\n [2, 17, 17, 4, 9, 1, -5, -13, 11],\n [-1... | 524 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[23, 16, 1, -13, 10, 6, -19, 6, -17],\n [-11, -17, -8, -1, 12, 0, 5, 13, -12],\n [-13, 8, -18, -17, 8, 4, -2, -17, -20],\n [-6, 10, 23, -12, 8, -13, 24, 16, -10],\n [-6, -16, 6, 13, -3, -15, -22, -18, -25],\n [-18, -12, 18, 15, 0, -23, 5, 5, 21],\n [20, -4,... | 545 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[16, -20, 22, 4, 23, 11, -1, -24, -5],\n [0, 1, -10, -25, 0, 19, 7, 2, -24],\n [0, 0, -19, 1, 22, -1, -13, -15, 2],\n [0, 0, 0, -20, 25, -21, 21, -14, -15],\n [0, 0, 0, 0, -15, -2, 1, 23, -6],\n [0, 0, 0, 0, 0, 1, -7, -8, 12],\n [0, 0, 0, 0, 0, 0, 22, -10, -4],\n [... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-16, 1, 7, 25, 17, 3, 20, -15, 4],\n [-17, -22, -20, 11, -25, -10, -2, -2, 10],\n [-4, -6, -10, 7, -8, 16, 0, -15, -24],\n [-3, -15, -10, 0, 15, 8, 8, -17, -5],\n [14, 13, -10, -14, -1, 19, 24, 22, -23],\n [6, -16, 17, -4, -14, -17, 13, 24, 22],\n [-13, 7, 22, -25... | 528 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -3, 2, -17, -2, -18, -15, -13, 15],\n [-3, 20, -2, 18, -8, 0, 14, -16, 0],\n [2, -2, -8, -10, 11, 2, -10, -10, -1],\n [-17, 18, -10, 12, 1, 0, 19, -2, -11],\n [-2, -8, 11, 1, -8, -... | 816 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 21, -9, -24, 23, 5, 14, -9, 5],\n [15, 13, -20, 4, -4, -2, 19, -3, -7],\n [21, -14, -12, -10, -8, -3, 18, 3, 7],\n [22, -15, 14, -1, 16, -24, 9, 21, 7],\n [-20, 5, 25, -13, -6, 20, 14, 0, -7],\n [-14, -2, -14, 20, 14, -6, -9, -1, 23],\n [-16, 14, -13, -19, 20,... | 798 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-22, 4, -22, 18, 8, 2, 0, 12, 2],\n [4, -21, 20, -4, 7, 10, 0, -5, 11],\n [-22, 20, -4, -10, -2, -12, -7, -9, 10],\n [18, -4, -10, -4, 2, 6, -4, -4, 4],\n [8, 7, -2, 2, -19, -10, -20, ... | 832 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-19, -9, -9, 1, -22, 22, 14, -4, 15],\n [7, -11, 2, 3, 24, 25, 10, -22, 24],\n [-1, 3, 19, 13, -2, 23, 11, 6, 15],\n [-8, -21, -10, 19, -24, -12, 1, 24, 18],\n [-20, -18, 5, 9, 20, -14... | 27 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -20, 2, -20, -18, 6, 6, 9, -11],\n [-2, -23, -10, 20, -20, -1, -12, -21, 16],\n [-8, -18, -21, -3, 14, 20, 25, -25, -25],\n [16, -14, -6, -4, -6, 20, -22, 1, -21],\n [14, 14, 1, 3, 2, 18... | 284 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -1, 0, 20, 10, 0, 11, -1, -16],\n [-1, -22, -8, -6, -2, 14, 10, -2, 0],\n [0, -8, 15, -5, 4, -8, 2, -14, -5],\n [20, -6, -5, -9, 10, 5, -4, 10, -2],\n [10, -2, 4, 10, -10, 8, -4, 0, -8],... | 22 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -25, 7, -21, 19, 20, 15, 5, 17],\n [0, 9, -24, -14, -15, -19, 2, 18, -12],\n [0, 0, 11, 25, -17, 13, -12, 12, -17],\n [0, 0, 0, 20, -10, 22, 25, 14, -14],\n [0, 0, 0, 0, -1, 5, 16, -25, -15],\n [0, 0, 0, 0, 0, 6, 7, 22, 8],\n [0, 0, 0, 0, 0, 0, 1, -11,... | 400 | MATH |
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