messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the value of det(A) where A =\n[[15, 0, 14, -16, 1, -8, 4, 10, -18],\n [0, -19, -20, -13, -7, -18, 25, -10, 17],\n [0, 0, -22, -13, 7, 7, 11, 0, 12],\n [0, 0, 0, 7, 15, -5, 0, -15, 19],\n [0, 0, 0, 0, -20, 16, -12, -12, -16],\n [0, 0, 0, 0, 0, 18, -24, 0, -3],\n [0, 0, 0, 0, 0, 0, 5, 7, ... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 2, 5, -8, 9, -2, -8, 6, 12],\n [2, 2, -18, -12, -13, -9, 10, 8, -10],\n [5, -18, 17, 4, 10, -14, 12, -2, 11],\n [-8, -12, 4, 16, 6, -9, -4, 20, 11],\n [9, -13, 10, 6, -11, -20, 14, 6, -10],\n [-2, -9, -14, -9, -20, -10, -6, -4, -12],\n [-8, 10, 12, -... | 160 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-20, 4, 6, -20, 0, -20, 8, 12, -8],\n [4, -14, 1, -6, 22, -16, -16, -16, -7],\n [6, 1, -24, -8, 8, 0, -4, 2, 0],\n [-20, -6, -8, 10, 9, -6, -4, -6, 2],\n [0, 22, 8, 9, -4, -1, 9, -2, 2... | 92 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-16, -1, -15, 3, 5, -5, -8, 14, -10],\n [0, 18, -16, -23, -5, -25, 24, 10, -4],\n [0, 0, -24, 9, 6, 12, 14, -21, 1],\n [0, 0, 0, 21, 10, -23, -22, 25, -16],\n [0, 0, 0, 0, 9, -15, -6, 7, -3],\n [0, 0, 0, 0, 0, -4, -21, -13, 20],\n [0, 0, 0, 0, 0, 0, -16, -... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 21, 1, -4, 10, 4, 4, -4, 2],\n [21, -20, -2, -8, 20, 14, 5, -18, 6],\n [1, -2, 15, -12, -2, 8, 3, 2, 0],\n [-4, -8, -12, -3, 14, -9, -22, 22, -3],\n [10, 20, -2, 14, 0, 18, 8, 8, -4],\n [4, 14, 8, -9, 18, -21, -6, -10, 4],\n [4, 5, 3, -22, 8, -6, 2, 2, -14],\... | 236 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 16, 3, 1, -4, -7, 1, 19, 24],\n [7, -4, -25, 6, 21, -18, -19, 22, -12],\n [4, 13, 5, -22, 25, 9, 22, -19, -20],\n [-21, -15, -13, -15, 13, -4, -2, -5, 14],\n [-16, -25, -10, -1, -6, -19, -8, -14, 24],\n [-7, -16, -12, -20, -15, -16, 7, 22, -23],\n [0, -22, -5,... | 170 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 12, -3, 4, -21, -23, -19, -25, 4],\n [0, -6, -21, -15, 9, -10, -5, -1, 14],\n [0, 0, -6, 3, 13, -23, 18, -10, 21],\n [0, 0, 0, -1, 1, 20, -10, 25, 9],\n [0, 0, 0, 0, -2, 18, 22, 7, 25],\n [0, 0, 0, 0, 0, 5, 3, -1, -9],\n [0, 0, 0, 0, 0, 0, 13, 22, 25],... | 120 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -20, -11, 15, -21, 18, 18, 13, 13],\n [0, 22, 15, -9, -5, -14, 18, 12, 11],\n [0, 0, 5, 4, -14, -20, 15, 20, 15],\n [0, 0, 0, 21, -24, 11, 20, 16, 24],\n [0, 0, 0, 0, 17, 12, -25, -... | 780 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, 10, 6, -21, 12, 0, -6, 2, 20],\n [10, -19, -8, 0, -2, -8, -16, 19, -12],\n [6, -8, 20, -14, 10, -13, 4, -2, -5],\n [-21, 0, -14, 10, -8, 4, 10, 7, 6],\n [12, -2, 10, -8, -16, -12, -24, -3, 0],\n [0, -8, -13, 4, -12, -23, 4, -2, -16],\n [-6, -16, 4, 10... | 234 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, -17, -21, -16, 0, -24, 12, -5, -25],\n [13, -17, -12, -11, 19, 12, -12, 14, -1],\n [1, -11, 15, -20, -18, -3, 13, 18, -9],\n [22, -12, -17, 11, -19, 25, -21, -23, 1],\n [12, -7, 17, -13, -25, 24, 15, -16, -6],\n [-10, -8, 24, 21, -2, 7, -17, 17, -25],\n [-12, ... | 745 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -22, -25, 15, 2, 22, -14, 8, 25],\n [12, 3, -4, 4, -20, -11, 16, 24, 2],\n [-24, 9, -25, 17, 3, -2, -16, 16, -6],\n [20, 9, -6, 11, 25, -6, -4, -25, 13],\n [-1, -22, 2, 9, 22, 20, 13, -23, -4],\n [25, -10, -11, -5, -13, 15, 21, -12, -11],\n [22, -13, 11, -10, ... | 182 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -8, 2, -2, -16, 5, 24, -13, -4],\n [-8, -22, -22, 2, -6, -3, -2, -6, -2],\n [2, -22, 0, 7, 1, 9, 0, 1, 10],\n [-2, 2, 7, -3, -10, 14, -2, -6, -14],\n [-16, -6, 1, -10, 18, 2, -9, -20, -4],\n [5, -3, 9, 14, 2, 2, -9, -16, 14],\n [24, -2, 0, -2, -9, -9, -9, -14,... | 686 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-19, 10, -8, -23, 7, -5, 15, 13, 16],\n [0, -4, -1, -1, 16, -18, 25, 7, -19],\n [0, 0, 16, 10, 10, 9, -22, -22, 21],\n [0, 0, 0, -6, -5, -7, -19, -22, 11],\n [0, 0, 0, 0, 4, 0, 5, -7, -25],\... | 456 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-16, 17, -21, -15, -6, 20, -18, 13, 22],\n [-23, -13, -25, 2, -7, -17, -21, 12, 13],\n [-20, 23, 13, 3, -21, 24, 17, -1, 5],\n [13, -1, -24, -18, 12, 6, 6, 4, -15],\n [23, 0, 3, -1, 5,... | 683 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -10, 1, -18, -21, -11, -1, -17, -7],\n [9, -17, -14, 13, -10, 23, -24, 5, 20],\n [13, -20, -8, 2, -13, 2, -14, 7, 24],\n [-16, -10, 19, 12, 3, 20, 15, 2, -8],\n [-16, 7, -11, -20, 4, -9, 16, 23, 23],\n [-4, -23, 14, -1, 10, -7, -9, -1, -23],\n [-9, 3, 7... | 891 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, 11, 20, -2, 14, 6, -7, -23],\n [0, 3, 14, -24, -12, -20, 6, -1, -22],\n [0, 0, 1, 7, 3, -9, 1, 12, 13],\n [0, 0, 0, 25, 21, 21, -25, -22, -21],\n [0, 0, 0, 0, 18, -10, 22, -1, -... | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 4, -22, 4, -23, -5, 2, 14, 9],\n [0, 7, 6, 10, 6, -2, 5, 8, 15],\n [0, 0, 19, -24, -19, -7, 5, 3, -4],\n [0, 0, 0, -22, 0, -10, -18, -12, -6],\n [0, 0, 0, 0, 3, -25, 3, -8, -25],\n... | 888 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 15, -17, 13, 20, 3, 19, 13, -17],\n [-1, 7, -3, 2, 24, -11, 0, 10, 6],\n [-6, 11, 15, 7, 22, -1, -8, -12, 8],\n [25, 13, 21, 21, -25, 4, 20, 1, -25],\n [5, -23, -13, -10, 2, 10, -12, -15, -1],\n [15, 3, -8, -25, -17, -2, 8, -7, 24],\n [-14, 5, 19, -23, ... | 420 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-23, 1, -12, -10, -1, -3, -10, 9, -8],\n [1, 22, -12, -6, 12, 9, 14, 4, 16],\n [-12, -12, -9, -14, -3, -14, -5, 4, 2],\n [-10, -6, -14, -11, 9, -7, -11, 0, -4],\n [-1, 12, -3, 9, -7, 8, 10, 18, 4],\n [-3, 9, -14, -7, 8, -17, 12, -4, -10],\n [-10, 14, -5, -11, 10, ... | 959 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, -19, -9, 17, -7, -23, -6, 22, -22],\n [0, -20, 13, -15, -8, -1, 19, -2, 1],\n [0, 0, 5, 8, 23, -17, 4, -19, -11],\n [0, 0, 0, 18, 12, -14, 11, -14, -11],\n [0, 0, 0, 0, -19, 23, -23, -1, 19],\n [0, 0, 0, 0, 0, -25, -13, 6, -1],\n [0, 0, 0, 0, 0, 0, 12,... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[25, 8, -4, 16, 4, -1, -10, 2, 4],\n [8, 5, -10, 10, -5, 7, -16, 16, -15],\n [-4, -10, 12, 0, 5, 13, 2, 10, -12],\n [16, 10, 0, 9, -14, 6, -8, 9, -5],\n [4, -5, 5, -14, 5, -13, -9, -2, -3],\n... | 583 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 2, 3, -24, -25, -10, 9, -16, 21],\n [-18, 19, -4, 23, 12, 3, -9, -10, -19],\n [-7, 10, -16, 18, -25, 7, -8, -19, 1],\n [15, 20, 2, -5, 9, 8, -25, 7, 14],\n [18, 14, -13, 0, -13, -25, 23, 14, -14],\n [-2, 13, 6, 8, -13, -21, -22, -10, -9],\n [-23, 5, -1,... | 924 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, 8, -8, -6, -1, -14, -1, 12, 4],\n [8, -9, -8, -8, -2, 0, -2, -16, -4],\n [-8, -8, 25, 3, 9, -7, 8, -4, -17],\n [-6, -8, 3, -13, -2, -4, 0, -4, 2],\n [-1, -2, 9, -2, -10, -16, 15, 3, -8],\n [-14, 0, -7, -4, -16, -5, -8, 11, 9],\n [-1, -2, 8, 0, 15, -8... | 122 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -7, 1, -1, -19, -25, 23, -25, -1],\n [0, 15, 3, -23, -23, -16, -16, 6, -20],\n [0, 0, -23, 15, -16, -18, 14, 11, 18],\n [0, 0, 0, 15, 8, 25, -9, -6, 5],\n [0, 0, 0, 0, -8, 22, -19, -5, -... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 15, -25, -3, 9, -25, 1, 15, 11],\n [0, 18, -7, -16, -7, 19, -1, 2, -12],\n [0, 0, -20, -19, 25, 2, -4, -16, 20],\n [0, 0, 0, 25, 24, 22, 15, 5, -3],\n [0, 0, 0, 0, -21, -19, -8, 11, -7],\n [0, 0, 0, 0, 0, 16, -9, -18, 11],\n [0, 0, 0, 0, 0, 0, 3, 22, 14... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 22, 2, 18, 4, 10, -2, -24, 2],\n [22, 6, -6, -20, 19, 8, 4, -2, 6],\n [2, -6, 13, -6, 6, -15, -8, -4, -6],\n [18, -20, -6, -21, -11, 2, 2, 21, 12],\n [4, 19, 6, -11, -17, 4, 2, 4, 8],\n ... | 112 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, 0, 4, -5, -8, 0, 9, 6, 16],\n [0, 12, -1, -4, 14, 15, -10, -10, -5],\n [4, -1, -3, -1, 4, -12, 0, 4, 0],\n [-5, -4, -1, 7, 20, -10, -8, 0, 0],\n [-8, 14, 4, 20, 25, 12, 5, -6, 0],\n [0, 15, -12, -10, 12, 18, 20, -6, 14],\n [9, -10, 0, -8, 5, 20, -4, -3, -6],\... | 992 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -6, 0, -15, 2, 4, 21, -12, 4],\n [-6, 20, 2, -2, 2, 10, 2, 3, 9],\n [0, 2, -9, 8, -12, 6, 22, 10, 12],\n [-15, -2, 8, -13, -11, 0, -2, 8, -2],\n [2, 2, -12, -11, -16, -7, -17, 8, -10],\n [4, 10, 6, 0, -7, 14, 6, -12, -10],\n [21, 2, 22, -2, -17, 6, 19, ... | 869 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 25, -24, 17, -5, -2, -16, -17, 16],\n [0, 25, 21, -14, 25, -18, 17, 15, 10],\n [0, 0, 4, -16, -25, 16, 24, -15, -19],\n [0, 0, 0, 1, -4, -25, -13, -24, -13],\n [0, 0, 0, 0, 1, -20, -8, 13, 4],\n [0, 0, 0, 0, 0, 2, 4, -3, -11],\n [0, 0, 0, 0, 0, 0, 3, ... | 600 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 24, -22, 10, 15, -6, 0, 18, -5],\n [0, -20, -2, -25, -3, 18, -18, -13, 21],\n [0, 0, 11, 5, -2, 3, 15, 25, 9],\n [0, 0, 0, -23, 1, 19, -19, -13, 24],\n [0, 0, 0, 0, 15, 20, -8, -4,... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-17, -2, -23, 2, 3, 4, 20, 8, -6],\n [-2, 0, 8, -10, 7, 6, 2, 19, -9],\n [-23, 8, 9, 20, -3, -5, 4, 12, -14],\n [2, -10, 20, 8, -3, 0, 0, 8, 2],\n [3, 7, -3, -3, 19, -2, -18, 2, 0],\n ... | 719 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 13, -12, -8, 4, 13, 18, 0, -22],\n [13, 11, 1, 12, 1, -10, 6, 8, -18],\n [-12, 1, -7, -1, -12, -20, 17, 6, -4],\n [-8, 12, -1, 16, 2, 8, 4, -10, 5],\n [4, 1, -12, 2, -2, -6, 12, -12, -2],\n [13, -10, -20, 8, -6, 3, -6, 10, -10],\n [18, 6, 17, 4, 12, -6... | 439 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 6, -1, 14, 0, 4, -8, 14, 15],\n [6, 17, 0, 4, 18, 2, 15, 8, -10],\n [-1, 0, 16, -4, 11, 16, -6, 8, 10],\n [14, 4, -4, 24, 14, 6, -14, -6, -6],\n [0, 18, 11, 14, 21, -2, -13, 10, 16],\n [4... | 492 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 10, -8, -8, -4, -8, -10, -6, 10],\n [10, 21, 16, 12, -2, -12, -6, -12, 4],\n [-8, 16, 9, 9, -10, -11, 2, 6, 3],\n [-8, 12, 9, -16, 18, -10, 12, -2, 13],\n [-4, -2, -10, 18, 25, 2, -1, -20, -2],\n [-8, -12, -11, -10, 2, -7, -6, 8, 10],\n [-10, -6, 2, 12, -1, -6... | 448 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -4, -16, -20, 23, -1, 20, 8, 11],\n [0, 2, 24, -4, 13, 24, -18, 3, 23],\n [0, 0, 2, -1, 24, 4, 5, 20, 7],\n [0, 0, 0, -18, -21, 10, 7, -4, 3],\n [0, 0, 0, 0, 1, 11, -9, -9, -13],\n [0, 0, 0, 0, 0, -2, -7, 24, 15],\n [0, 0, 0, 0, 0, 0, -2, 1, -21],\n [0,... | 176 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -4, 13, -6, -24, -25, -21, 2, 0],\n [0, -4, -13, -21, -25, -3, 20, 18, -12],\n [0, 0, -13, -18, 15, -22, -15, 15, -14],\n [0, 0, 0, -15, 25, -13, -18, -24, 12],\n [0, 0, 0, 0, -3, ... | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -6, 0, -2, -4, 16, -22, -6, 2],\n [-6, 19, 2, -6, 14, 5, -16, 18, -24],\n [0, 2, 22, 13, -4, 13, -2, 0, 2],\n [-2, -6, 13, 12, -17, -11, 12, -8, 4],\n [-4, 14, -4, -17, -20, 4, 8, 0... | 808 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[17, 4, -4, 22, 5, -18, -19, -9, -23],\n [0, 17, -17, 2, -23, 18, 7, -7, 19],\n [0, 0, 12, -23, -7, -11, 8, -6, -19],\n [0, 0, 0, 14, -21, -20, 2, 4, 15],\n [0, 0, 0, 0, -6, -14, 11, 15, 9],\n [0, 0, 0, 0, 0, -19, 1, -23, -11],\n [0, 0, 0, 0, 0, 0, 12, -23... | 496 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -19, -19, 5, 24, 9, 18, 1, 6],\n [25, -24, -14, -21, 16, -11, 22, -3, 14],\n [-23, 21, 2, 10, 18, -18, 20, 0, 6],\n [-22, -3, -15, -12, 22, 2, 22, -25, -19],\n [-13, 14, -7, -21, 6, 24, 13, 7, 18],\n [-6, -7, 18, 7, -10, -8, 18, -17, 18],\n [-13, 19, -1... | 367 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[21, -12, -21, 17, -5, 6, -11, -19, -3],\n [0, 16, 3, 24, -12, 3, 20, -8, 17],\n [0, 0, 19, 21, -20, 8, 20, -3, 15],\n [0, 0, 0, -17, -9, -24, 10, 25, 0],\n [0, 0, 0, 0, 20, 14, 3, 8, -17],\n [0, 0, 0, 0, 0, 16, -20, 23, 9],\n [0, 0, 0, 0, 0, 0, -18, -14, ... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, -5, -8, -25, -16, 8, -7, 23, -16],\n [0, 4, -9, -25, -11, 2, -21, -15, 1],\n [0, 0, -25, 14, -3, -9, 4, -10, -4],\n [0, 0, 0, -2, 15, 11, 3, -9, -16],\n [0, 0, 0, 0, -14, 11, 13, 1, -16... | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 12, 25, -15, -14, -17, -21, -14, 11],\n [7, -4, -3, -13, -12, 19, 8, -14, 22],\n [17, -6, -1, -10, -25, -24, -9, 13, -7],\n [-6, -5, -25, 20, 7, 23, -4, -20, -17],\n [-13, 5, 17, 11, 8, 9, -11, 23, -7],\n [9, -6, -9, 22, -12, -21, 13, 18, 25],\n [9, 1... | 984 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[17, -9, -19, -19, 12, 24, 7, -1, -22],\n [-8, 21, 7, 12, 4, -7, 8, -6, -23],\n [11, 3, 8, 7, 13, -6, -6, 24, 4],\n [23, 2, 16, 25, 15, 13, -19, 5, -22],\n [18, -3, -4, 13, 21, 16, -12, 0, -3],\n [-20, 0, 16, -24, 6, -4, 12, -15, -23],\n [15, 20, -4, 15, -1... | 155 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -18, -1, -20, -2, 11, -1, 6, 24],\n [15, -12, -9, 14, 22, 3, -6, -12, 22],\n [-20, 9, 5, -19, -1, -7, 4, 23, -12],\n [-11, -16, 2, -24, -17, -6, 11, 6, -2],\n [22, -18, 2, 21, 1, -13, -2... | 569 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, 6, 8, 13, -6, -6, -2, 19, 14],\n [6, 19, 6, 4, 4, -4, 2, -9, 0],\n [8, 6, 20, 6, -7, -19, -16, -7, -8],\n [13, 4, 6, 0, -12, -15, 2, 5, -5],\n [-6, 4, -7, -12, -17, 6, 1, -8, 4],\n [-6, -4, -19, -15, 6, -14, 0, 14, -8],\n [-2, 2, -16, 2, 1, 0, 2, 10, 2... | 378 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 2, -2, 12, 5, 4, -13, 2, 12],\n [2, -16, 18, 5, -7, 4, 4, 8, 6],\n [-2, 18, -14, 2, -6, 4, -10, -4, 8],\n [12, 5, 2, -12, -10, -6, -5, 20, -4],\n [5, -7, -6, -10, 17, -2, 2, 0, 7],... | 864 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[19, 4, 4, 14, -2, 11, 0, -4, -6],\n [4, 18, 6, 2, 6, -2, -10, 16, 7],\n [4, 6, 0, -2, -3, -6, -7, -4, -6],\n [14, 2, -2, 11, 12, 2, 4, 11, 5],\n [-2, 6, -3, 12, -17, 10, -6, 13, 0],\n [11, -2, -6, 2, 10, -20, -19, 6, -6],\n [0, -10, -7, 4, -6, -19, 8, -8, 4],\n [-... | 933 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-18, 18, -20, 12, 6, -12, 18, -3, -1],\n [18, 2, -10, 10, 12, -4, 8, -4, -10],\n [-20, -10, -3, 9, -4, 22, -10, 18, -5],\n [12, 10, 9, -9, -1, -12, 2, -18, 6],\n [6, 12, -4, -1, 13, 13, -6, -13, 6],\n [-12, -4, 22, -12, 13, 22, 2, -20, -3],\n [18, 8, -10, ... | 104 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 4, -11, -8, -16, -16, -10, 6, 4],\n [4, 25, -2, 14, 14, -7, 2, -10, -10],\n [-11, -2, 10, 4, 6, -2, -10, -4, -3],\n [-8, 14, 4, 1, 1, 10, -3, -18, 12],\n [-16, 14, 6, 1, 6, 8, 0, 2, -6],\n [-16, -7, -2, 10, 8, 18, -7, 4, -8],\n [-10, 2, -10, -3, 0, -7, ... | 520 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -23, 2, 12, -7, 12, -4, 14, -1],\n [-23, -19, 0, -1, 1, -9, -1, 11, 0],\n [2, 0, 22, -14, 0, -10, -2, 10, 12],\n [12, -1, -14, -11, -18, -14, -10, 4, 7],\n [-7, 1, 0, -18, 11, -14, -10, -... | 734 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, 5, -2, -5, -17, -18, -4, -6],\n [0, -25, -12, 9, -10, 4, -9, 0, 14],\n [5, -12, 18, -2, -2, -2, 14, -9, -12],\n [-2, 9, -2, -19, 9, 20, -2, 4, -16],\n [-5, -10, -2, 9, -24, 8, 6, -2, 1... | 376 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-18, 23, 15, 10, -19, 6, 22, 1, -15],\n [0, 5, 24, 5, 24, 13, -3, 4, 17],\n [0, 0, 2, 1, -14, 14, 21, -17, -21],\n [0, 0, 0, -18, 4, 18, -25, 14, -8],\n [0, 0, 0, 0, 15, 3, 13, 9, 6],\n [0, 0, 0, 0, 0, -2, -9, 23, 12],\n [0, 0, 0, 0, 0, 0, 15, 13, 15],\n ... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -12, 19, -8, -25, -8, 9, 10, 5],\n [20, 15, -7, -25, 7, 16, -1, -13, 25],\n [-3, 19, -17, 1, -2, -17, 9, -14, 11],\n [19, 21, -1, 20, 18, -2, 20, -12, 5],\n [4, -19, -25, 22, 1, 3, -19, 8, 7],\n [-1, 12, 8, 8, 19, 5, 11, -1, -17],\n [-6, 10, 7, 4, -22, -11, 14,... | 4 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 11, 14, -5, -16, 1, -3, -6, -16],\n [17, 21, 10, -7, 17, -1, 11, -3, 16],\n [8, 12, 9, 6, 25, -16, -9, -11, 24],\n [-17, -3, 0, 25, -23, 5, 16, -17, 7],\n [-7, -23, 12, -6, 3, 17, 15, 8,... | 108 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -14, -2, 1, 16, 19, -16, -1, 10],\n [0, -8, 9, -1, -18, 3, -18, 19, -14],\n [0, 0, -19, 3, 13, -11, 21, 10, -11],\n [0, 0, 0, -3, -6, 19, 13, -23, -25],\n [0, 0, 0, 0, -1, 7, -18, 10, -... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -5, 15, -15, -20, -23, 7, -18, 21],\n [14, 21, 14, -10, 24, -13, -2, 9, 25],\n [22, -6, -15, 5, 8, 17, -3, -2, -1],\n [25, 8, -18, -2, 21, 19, 20, 22, -15],\n [1, 0, -25, 20, -6, -... | 395 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-21, -20, -24, -23, -23, 21, 22, 4, 12],\n [-6, 10, 7, 21, 20, 1, 15, -21, -9],\n [-16, -12, 5, -24, 0, -19, -4, 14, 21],\n [-18, 24, 8, -23, 15, -12, 17, -2, 24],\n [0, 21, 25, -1, -17, 23,... | 768 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[19, 19, -19, -3, -5, -11, 25, -4, -25],\n [0, -14, -24, 7, 6, 0, 16, 19, -19],\n [0, 0, -17, -23, 11, 10, 10, 17, -6],\n [0, 0, 0, -17, 3, 2, -5, 20, -19],\n [0, 0, 0, 0, -25, 14, -19,... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[17, 14, 25, 8, -4, 23, -10, -10, 18],\n [-17, -6, -3, 2, -15, -18, -3, 24, -11],\n [22, -2, 25, 3, 15, -7, -25, -6, 11],\n [-16, -6, 1, 16, 12, 8, -23, 9, -2],\n [17, 25, 9, -9, 21, 21... | 710 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 23, -20, 6, 0, 17, 11, 13, -6],\n [23, 10, 6, 7, -6, 5, -10, -4, -6],\n [-20, 6, 20, -6, 12, -4, -4, -20, -14],\n [6, 7, -6, -15, 5, -10, 6, 3, -14],\n [0, -6, 12, 5, 14, 7, 4, 10, 6],\n ... | 584 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -18, -7, -4, -6, -1, -13, -20, 20],\n [0, 6, -13, -21, -8, -8, -17, -23, -2],\n [0, 0, -2, 13, -2, 16, 13, -20, 12],\n [0, 0, 0, -3, -3, 16, 20, 12, 14],\n [0, 0, 0, 0, 1, 4, -23, ... | 840 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 1, 4, -1, 10, -6, 4, 0, -24],\n [1, 22, -12, 5, 6, -12, 10, 3, -1],\n [4, -12, -16, -12, 0, -2, 18, 10, 2],\n [-1, 5, -12, -14, 1, 18, 4, 2, -14],\n [10, 6, 0, 1, 6, -8, 11, 24, -21],\n [-6, -12, -2, 18, -8, -19, -5, -4, 0],\n [4, 10, 18, 4, 11, -5, 14, -21, 0]... | 520 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -8, -5, -13, 0, 9, -24, 2, -2],\n [-8, -5, -14, 13, 6, -5, -4, -4, 0],\n [-5, -14, 12, -2, -7, -22, -25, -16, 21],\n [-13, 13, -2, 3, 7, -1, 14, -6, -4],\n [0, 6, -7, 7, -9, 4, -17... | 891 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[22, -22, 6, -11, -5, 6, -3, 10, -3],\n [0, -25, -14, 13, -1, 20, 25, -17, 20],\n [0, 0, -2, -25, 18, -13, -22, -6, 4],\n [0, 0, 0, 3, 23, 6, -12, -2, -9],\n [0, 0, 0, 0, -8, -15, 4, 11, -9],\n [0, 0, 0, 0, 0, -19, 12, -12, 3],\n [0, 0, 0, 0, 0, 0, 23, 7, ... | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -18, -2, 23, 15, 14, -11, -18, -7],\n [0, -16, 8, -25, 5, -24, 12, 11, 24],\n [0, 0, -3, -9, 22, 10, 14, 25, 4],\n [0, 0, 0, -12, 3, -18, 23, 6, 24],\n [0, 0, 0, 0, 10, -5, 11, -6, -10],... | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 7, 1, -12, -20, 9, -18, -4, 2],\n [-8, 3, 8, 5, -20, -11, 12, -20, 15],\n [0, -2, 20, 23, 9, -23, -12, 3, -17],\n [-17, -1, -14, 10, -19, -3, 22, -13, -5],\n [8, -5, 12, 25, 20, 10, 12, 21, -21],\n [20, 9, -6, -9, 18, 10, 17, -15, -17],\n [-1, -19, 11, -16, -24... | 356 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, 14, 5, 4, 8, -20, 9, -20, 0],\n [-9, 25, -4, -15, 7, 8, -4, 2, 21],\n [-11, 22, -13, -21, -16, -15, 9, 15, 6],\n [-20, 21, -8, -1, -11, -11, -16, 3, 12],\n [8, -11, -9, -20, -14, 13, 10, 4, 23],\n [-14, 23, 13, -20, -3, -16, 2, 6, 20],\n [11, -19, 1,... | 10 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[22, 20, 20, 18, 24, 24, 8, -15, -21],\n [-13, 8, -21, -25, -22, 11, 12, -13, -21],\n [-12, -9, 20, -6, -3, 8, 18, -4, -14],\n [-19, -8, 4, 23, -8, -19, 15, 23, 7],\n [-19, 3, 24, 19, 8, 19, -18, 12, -12],\n [10, -8, -20, 21, 14, 15, 19, -17, 24],\n [-11, 23, 2, -3... | 990 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -21, -20, 18, -9, -17, 25, 16, 2],\n [0, 3, 3, -21, 9, -1, 21, -22, -4],\n [0, 0, -22, 21, 6, 7, 23, -4, -16],\n [0, 0, 0, -3, 10, 19, -8, -25, -15],\n [0, 0, 0, 0, 6, -12, 25, 1, -25],\n [0, 0, 0, 0, 0, 10, -6, -1, 20],\n [0, 0, 0, 0, 0, 0, 5, 22, -10... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[25, -6, 22, -4, 6, -2, 2, -4, 12],\n [-6, 10, -8, 17, -14, -18, 2, 16, 0],\n [22, -8, -3, 0, 18, 10, 1, -1, 0],\n [-4, 17, 0, -7, -6, -17, 2, 12, 6],\n [6, -14, 18, -6, -22, 21, 2, 16,... | 627 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 1, 5, 12, -7, -19, -18, 16, 12],\n [23, 5, 2, 17, 1, -23, 10, -16, -17],\n [-18, -18, 12, 25, -3, -23, 10, 7, 0],\n [22, 1, 8, 20, -11, -15, -12, 20, 5],\n [-7, 7, 19, -20, -21, 22, 12, -8, -1],\n [-25, -8, -5, -13, -12, -4, 14, 14, 19],\n [14, -1, -1... | 708 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 17, -19, 13, -3, 22, 20, 1, 21],\n [0, -20, 4, -12, -8, 7, 5, 4, -24],\n [0, 0, -15, -15, 21, -4, 3, -16, 8],\n [0, 0, 0, 24, 12, -9, 19, -15, 12],\n [0, 0, 0, 0, -6, 6, -24, -11, ... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -4, 13, 4, 25, -3, -13, 0, 5],\n [-20, 15, -6, -12, 25, -1, -4, -8, -6],\n [-4, 25, -19, 6, 6, -12, 25, 14, -5],\n [-9, 14, 22, -23, 12, 2, -24, 8, 5],\n [19, 14, -24, 0, -15, -23, -10, -8, 15],\n [-4, 2, 25, 9, -2, -15, 7, -24, -22],\n [1, 19, -19, 10, 20, 19,... | 286 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-22, -6, -16, -6, 14, 12, -1, -13, 19],\n [0, -22, 24, 17, -8, 13, 12, 17, 9],\n [0, 0, -17, -8, -15, -3, 12, 22, 13],\n [0, 0, 0, 24, -10, -18, 7, 11, -14],\n [0, 0, 0, 0, -4, 8, 18, 16, 23],\n [0, 0, 0, 0, 0, -22, -23, 22, -11],\n [0, 0, 0, 0, 0, 0, 19,... | 520 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -20, -22, 0, -9, 20, 0, 1, 17],\n [-2, 22, 7, -25, 14, -24, 1, -6, 2],\n [12, 17, 5, -13, -12, -1, -7, -14, 6],\n [-14, -17, 7, 15, -14, 2, 8, 3, -6],\n [6, -5, 12, -16, 3, -10, 9, -6, -1],\n [13, -25, -6, -21, 8, 2, -18, -2, 21],\n [6, 7, -12, -15, 2... | 524 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 7, -9, 6, 5, 12, -8, -20, 7],\n [-15, 15, -8, -7, -20, -15, -22, 18, -14],\n [8, 2, 21, -13, 13, -20, -7, 22, -5],\n [13, -7, -20, 1, -11, -10, 2, -3, 3],\n [20, 8, -8, 19, 9, 0, 12, 22, -2],\n [21, -12, -19, -19, -3, -6, -23, 11, -8],\n [9, 18, -13, -12, -19, ... | 845 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 6, -17, -6, 11, -11, -4, 16, 14],\n [0, 1, 8, -12, -18, -25, 10, -1, -23],\n [0, 0, -11, -9, 1, 14, -13, -3, -17],\n [0, 0, 0, -23, -1, 14, -19, -10, -20],\n [0, 0, 0, 0, 25, -10, 18, 3, 1],\n [0, 0, 0, 0, 0, 19, 5, 15, 10],\n [0, 0, 0, 0, 0, 0, 10, 16... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 1, 23, 9, 2, -9, 10, 8, -9],\n [0, -12, 25, 12, -18, -4, 2, 7, 3],\n [0, 0, -7, -23, -8, 24, 6, 1, 20],\n [0, 0, 0, -3, -25, -6, 24, 14, -22],\n [0, 0, 0, 0, -1, -4, 4, -24, 8],\n [0, 0, 0, 0, 0, -1, -23, -7, 22],\n [0, 0, 0, 0, 0, 0, -20, -5, 5],\n [0, 0, 0, 0... | 400 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-18, -7, -16, -25, 7, 20, 15, -8, 21],\n [16, 11, 3, 0, 21, -14, 7, 21, -5],\n [-24, -9, -8, -3, 10, 3, 7, 0, 24],\n [-1, 14, 10, -21, -1, 9, 8, -8, 8],\n [-22, 5, 24, 20, 1, 21, -19, 19, -17],\n [-10, 17, 16, 18, 24, -4, -11, -5, 5],\n [7, 15, -24, -6, -... | 118 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -1, -13, 0, 5, -7, -12, -7, -12],\n [0, -19, 16, -6, -8, 19, -10, -6, 23],\n [0, 0, 3, 16, -15, -12, -7, 20, -9],\n [0, 0, 0, -19, -12, 13, -24, -3, -2],\n [0, 0, 0, 0, -5, -19, 8, 12, -21],\n [0, 0, 0, 0, 0, 25, -16, 17, 17],\n [0, 0, 0, 0, 0, 0, -20, -23, -5... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 3, -12, -17, 25, -6, -18, 7, -10],\n [-1, -21, 20, -20, -22, 10, 2, 6, -7],\n [12, -3, 9, -21, -15, 11, 15, -13, 14],\n [13, -13, 13, 2, -18, -8, 16, -7, 14],\n [-12, 8, -13, 12, 7, -6, 8, 1, -9],\n [21, -7, 0, 25, -21, -23, -19, -16, 6],\n [-9, -22, 1,... | 145 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 2, -6, -17, 7, -17, -4, -12, -4],\n [2, 8, -5, 8, 6, 13, 0, 0, 4],\n [-6, -5, 7, 4, -8, 0, -6, 12, 4],\n [-17, 8, 4, -9, 4, 22, -6, 8, 2],\n [7, 6, -8, 4, -23, -3, 8, -4, 2],\n [-17, 13... | 626 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[17, -2, -3, 6, 6, 12, 18, -2, 14],\n [-2, -25, -10, 12, 21, -8, -1, 8, -6],\n [-3, -10, 5, -13, -8, -10, 0, -9, 6],\n [6, 12, -13, -8, 22, 10, -12, -4, -6],\n [6, 21, -8, 22, -7, 14, -14, 10, 4],\n [12, -8, -10, 10, 14, 6, 1, 6, 20],\n [18, -1, 0, -12, -14, 1, -4,... | 120 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 5, -20, -1, -23, -19, -21, -8, -14],\n [0, -17, -18, -22, 7, 18, -23, -13, 23],\n [0, 0, 9, 9, -12, 17, -20, 13, 17],\n [0, 0, 0, 14, 18, -25, -8, -10, 6],\n [0, 0, 0, 0, -19, 20, -4, -25, -15],\n [0, 0, 0, 0, 0, -2, -8, -21, -3],\n [0, 0, 0, 0, 0, 0, 2... | 976 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -13, 25, -13, 0, -12, -12, -10, -4],\n [0, 13, 9, 3, -3, 10, -16, -8, 1],\n [0, 0, 3, 19, 25, 8, 0, -8, 23],\n [0, 0, 0, -4, -25, -7, 25, 15, 3],\n [0, 0, 0, 0, 12, -21, -5, 1, -14... | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-22, 14, 11, -8, -20, -4, -11, 8, 0],\n [14, 5, -18, -2, 8, -6, -20, 7, 18],\n [11, -18, -11, 0, -10, -8, -2, 3, 11],\n [-8, -2, 0, 11, -16, 22, -4, 8, -8],\n [-20, 8, -10, -16, -12, 1... | 312 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 13, 2, 13, -20, -18, 20, 2, -10],\n [0, 12, -15, 23, 2, 23, 1, 1, 13],\n [0, 0, 9, 11, -16, -4, -2, -21, -4],\n [0, 0, 0, -8, -2, 3, 9, -15, -6],\n [0, 0, 0, 0, 19, -6, -2, 13, 8],\n [0, 0, 0, 0, 0, -3, 4, 7, -16],\n [0, 0, 0, 0, 0, 0, 19, 17, 8],\n [... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-18, -22, 18, -2, -7, -25, 22, -25, -22],\n [0, 4, 9, -8, -23, 11, -17, -17, -23],\n [0, 0, -2, 17, 17, -2, -21, -1, -6],\n [0, 0, 0, 1, -15, -6, -6, 22, -7],\n [0, 0, 0, 0, -18, -12, -11, 7, 4],\n [0, 0, 0, 0, 0, -11, 19, -23, 21],\n [0, 0, 0, 0, 0, 0, -5, -11, -... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-25, -25, 5, -19, 11, -17, -23, 25, 12],\n [0, 24, 14, -20, -4, 3, -1, -15, -4],\n [0, 0, 24, -21, 6, 2, -6, -16, -2],\n [0, 0, 0, 23, 21, 18, -20, -6, -12],\n [0, 0, 0, 0, -14, 24, -13, -21, -22],\n [0, 0, 0, 0, 0, -5, 10, 13, -16],\n [0, 0, 0, 0, 0, 0, ... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 6, 10, 2, -12, 22, 12, -6, 18],\n [6, -5, 0, -8, 6, 8, 14, 4, 20],\n [10, 0, -18, 14, -22, 15, -12, 4, 1],\n [2, -8, 14, -21, 4, -2, -4, 7, -2],\n [-12, 6, -22, 4, 22, 10, 0, -4, -6],\n [22, 8, 15, -2, 10, 19, 8, -8, -8],\n [12, 14, -12, -4, 0, 8, -13, ... | 312 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 16, -10, 15, 6, 5, -12, -1, 10],\n [16, 10, 4, 7, -8, -6, -2, 8, -15],\n [-10, 4, -22, -9, -2, 12, 18, 2, 16],\n [15, 7, -9, 8, 16, 10, 22, 13, 6],\n [6, -8, -2, 16, 11, -16, -22, -14, 15],\n [5, -6, 12, 10, -16, 17, 1, 11, 14],\n [-12, -2, 18, 22, -2... | 203 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-19, -14, 6, 6, -6, 10, 4, 2, -4],\n [-14, 7, 12, 13, -2, -8, -8, 16, 4],\n [6, 12, 19, 5, 1, 12, -6, 2, 10],\n [6, 13, 5, 17, -5, 14, 9, -14, -6],\n [-6, -2, 1, -5, -23, 5, -2, 10, -16],\n [10, -8, 12, 14, 5, -21, 8, 14, 0],\n [4, -8, -6, 9, -2, 8, 8, -11, -6],\n... | 648 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -15, -12, 19, 24, 15, -18, -25, -23],\n [3, -12, -6, -24, 8, 4, -4, -14, -21],\n [-16, -17, -15, 16, -17, 7, 9, -5, -3],\n [19, -10, -16, 24, 23, -9, 25, 22, -11],\n [16, 25, 0, 6, 18, 6... | 735 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 3, -17, 12, -12, -11, -7, -14, 10],\n [3, 25, -18, -2, -20, 8, 20, -2, 10],\n [-17, -18, 14, -2, 20, -10, 14, -4, -16],\n [12, -2, -2, -9, -10, 16, 0, -12, -12],\n [-12, -20, 20, -10, -13, 8, -18, 14, 12],\n [-11, 8, -10, 16, 8, -14, 6, -12, -11],\n [-... | 876 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-19, 13, -3, -14, -4, -11, -15, -20, -24],\n [-7, 2, 14, -10, -22, 9, -9, 16, 7],\n [-11, -2, 12, 10, 21, -5, -14, 22, 6],\n [-12, 1, 4, -7, 0, 22, -19, -7, -25],\n [-14, -5, 22, 2, 22, 3, -23, 9, -20],\n [-3, -25, -5, 23, 1, -10, 15, -6, -11],\n [9, -23, ... | 875 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 14, 12, -14, -1, 12, -16, 7, 11],\n [0, -18, 16, 13, 1, -18, -15, -13, 15],\n [0, 0, 23, -13, -21, 1, 22, -5, -24],\n [0, 0, 0, 10, -3, 12, -16, 24, -8],\n [0, 0, 0, 0, 3, 8, 2, -4, -21],\n [0, 0, 0, 0, 0, 1, -13, 14, -25],\n [0, 0, 0, 0, 0, 0, 8, 23,... | 520 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -15, 3, -24, -14, -10, 23, 19, 10],\n [0, 24, 23, 25, 22, 14, 22, -13, -21],\n [0, 0, -13, -1, -15, 12, 19, -2, 12],\n [0, 0, 0, 15, 16, -7, 12, -5, 20],\n [0, 0, 0, 0, 10, 5, -18, -3, -10],\n [0, 0, 0, 0, 0, 13, -3, -3, -1],\n [0, 0, 0, 0, 0, 0, -15, ... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-22, -6, 2, 17, -1, 16, 12, 17, -10],\n [-6, 6, 10, -5, 0, 14, 5, -7, 2],\n [2, 10, 5, 2, 2, 18, -6, 12, -9],\n [17, -5, 2, -13, 6, 4, 2, 12, 4],\n [-1, 0, 2, 6, 5, -6, 13, 8, -4],\n [16, 14... | 30 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[20, -19, 12, -12, -14, 17, 0, 14, -5],\n [-19, 13, 7, 6, 10, 9, -2, -4, -14],\n [12, 7, 10, -14, -13, 7, -16, 8, -8],\n [-12, 6, -14, -15, -20, -6, 0, 7, 8],\n [-14, 10, -13, -20, 5, 4, -8, -10, 8],\n [17, 9, 7, -6, 4, -24, 0, 3, -2],\n [0, -2, -16, 0, -8, 0, -18,... | 807 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[19, -19, 17, 13, -23, -18, 9, 2, -10],\n [-25, -7, 3, 3, -17, 6, 20, 24, -17],\n [6, 2, 19, -11, -24, -16, -22, 18, -5],\n [24, 4, -9, 21, 7, -4, -18, -20, 9],\n [9, 20, -16, -21, -23, 2, 16, 16, 8],\n [-11, -9, -23, -9, 22, -14, 5, 16, 0],\n [17, -14, 17,... | 298 | MATH |
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