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[[-10, 6, 6, 8, -15, -16, -11, -9, 14],\n [0, -17, -1, 14, -12, -1, 24, -4, 4],\n [0, 0, 18, 6, 25, 20, 23, -5, 9],\n [0, 0, 0, 23, -14, 15, 21, -8, -5],\n [0, 0, 0, 0, 14, 20, -19, -3, 18],\n... | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -24, 21, 18, 18, -17, -5, -2, 8],\n [-4, -23, -14, 2, 4, 0, 22, -5, 2],\n [0, 7, -5, 9, 8, 15, 25, 21, -8],\n [-15, -3, 22, -4, -9, -21, 18, -15, 4],\n [-11, 1, 9, 7, -6, -10, 8, -24, 9],\n [14, 2, 21, 13, -20, -17, -6, -25, -18],\n [-3, -23, -22, -1, 21, 12,... | 21 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[25, 4, -15, 2, 18, -14, 13, 0, -13],\n [-18, 2, 4, -17, 13, 5, -5, 21, 8],\n [5, -1, -14, -25, -4, 14, 11, 21, -25],\n [-25, 16, 16, -5, -11, -9, -4, 12, 9],\n [19, -10, -18, 21, -9, -... | 568 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -13, -7, 3, -23, 0, 14, -14, -24],\n [-15, 18, 2, -8, -13, 11, -4, -14, -24],\n [11, -19, 0, 0, -2, -14, -10, -3, 14],\n [-17, 6, -11, 11, -13, -21, -15, -16, -13],\n [15, 20, 24, -11, 16... | 976 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-23, 18, 5, 21, 16, -6, -7, 22, -15],\n [0, -23, -3, -19, -3, -19, 20, 8, 16],\n [0, 0, 22, 25, -8, 15, 22, 19, 16],\n [0, 0, 0, -1, -7, 13, -11, -10, 1],\n [0, 0, 0, 0, -7, 2, -5, 21, -12],\n [0, 0, 0, 0, 0, -4, -23, 11, 15],\n [0, 0, 0, 0, 0, 0, 17, 14,... | 576 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, 19, 9, -11, -25, 0, 9, -1, 16],\n [-11, -4, -20, -11, -2, -5, -19, 3, 6],\n [6, -21, -22, -4, -8, 9, -9, 24, 24],\n [-2, -24, -13, -11, -21, -23, 11, 11, 11],\n [-23, 9, -3, 2, 4, -8, 10, 7, 0],\n [22, 14, -9, 14, -19, -18, 5, -14, 22],\n [5, 18, -7,... | 224 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -16, 0, -18, 6, -3, -8, 14, -2],\n [-16, 10, -8, 16, -16, -6, 19, -2, 12],\n [0, -8, -7, 17, 0, -2, -8, 16, 1],\n [-18, 16, 17, 6, 2, 8, 14, -2, 14],\n [6, -16, 0, 2, 18, 16, -7, -2, 14],... | 660 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 9, 5, 19, -18, -6, 16, 8, -22],\n [-8, 25, -22, -6, -17, -10, 0, 12, -1],\n [-22, 15, 19, 15, 12, -7, -12, -5, -11],\n [-23, 11, 24, 20, -10, -12, -17, 21, -19],\n [-12, -20, -5, -11, -18... | 684 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-23, -21, -14, 18, -13, -2, 18, 6, -10],\n [6, 19, 11, 10, -5, 21, -14, 25, -5],\n [25, -5, 17, -20, -17, -25, -14, -12, -20],\n [-25, -4, 8, -15, -23, 16, -20, -20, -6],\n [-5, -24, 0... | 322 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, -14, 22, 4, 7, 21, -19, 2],\n [0, -23, 17, -20, 5, 12, -11, -19, 17],\n [0, 0, -9, -8, -4, 0, 25, 1, 14],\n [0, 0, 0, 3, 17, -5, -23, 5, 1],\n [0, 0, 0, 0, 7, 0, 2, 18, 17],\n [0, 0, 0, 0, 0, -11, 8, 24, -10],\n [0, 0, 0, 0, 0, 0, 2, -17, -24],\n [... | 720 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[22, -5, -22, -25, 0, 25, -24, -17, 19],\n [-8, 22, 22, 16, 15, -15, -1, 0, 10],\n [16, 9, 12, -23, 15, 9, 24, 14, -4],\n [-18, -11, 19, -19, -7, 14, 16, -9, -25],\n [19, 3, -13, 22, 3, 15, 16, -20, -21],\n [8, -15, -17, 12, 14, 15, -17, -18, 18],\n [14, -... | 591 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[18, -12, -21, 16, -24, -22, -14, -15, -22],\n [17, -17, -16, 1, -20, -11, 16, 5, -4],\n [-20, 7, 3, -5, 4, -5, 10, -4, 20],\n [-6, -4, 14, -15, 21, 5, 25, 14, -13],\n [-8, -4, -9, 12, -1, 6, -11, -13, 0],\n [24, -15, -13, 7, 24, 11, 12, -25, 13],\n [1, 10... | 18 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 17, -8, 0, -5, 4, -18, 3, -11],\n [17, 8, -13, 6, -6, 1, -2, 0, 16],\n [-8, -13, 16, 14, 1, -1, 3, -2, -4],\n [0, 6, 14, -25, -4, -16, -4, -2, -2],\n [-5, -6, 1, -4, 15, -4, -8, -2... | 324 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[15, 2, -3, 0, -4, -10, 4, -4, -2],\n [2, -9, 2, -2, 11, -14, -9, -10, 4],\n [-3, 2, 9, -10, 5, 15, -4, -3, -4],\n [0, -2, -10, 7, 6, -12, 14, -4, -24],\n [-4, 11, 5, 6, 25, -11, -22, 17, -5],\n [-10, -14, 15, -12, -11, -17, 3, -2, 6],\n [4, -9, -4, 14, -2... | 641 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 13, -4, 14, 1, 22, 4, -7, 6],\n [13, -24, 11, 16, -9, 8, -18, 6, 16],\n [-4, 11, -4, -8, -10, 18, 3, 2, 0],\n [14, 16, -8, 9, -3, -23, 4, 2, 0],\n [1, -9, -10, -3, -4, 2, -8, -4, -1],\n [... | 659 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, -23, 17, -15, -21, 12, -22, 6, -16],\n [-16, 18, -8, 21, -3, -8, 9, -23, -25],\n [-9, 16, -20, -15, -12, 23, 2, 13, 10],\n [-15, 25, 15, 14, -22, 22, -20, 12, -7],\n [5, -24, 17, -1, 24, 15, 22, -15, 20],\n [14, 19, 16, 18, -5, -23, -24, -15, -2],\n [... | 458 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 19, 3, 11, 4, 0, -7, -18, -8],\n [19, 5, -6, -11, -12, -10, -14, 10, 22],\n [3, -6, 6, 14, -10, 18, -11, 8, 2],\n [11, -11, 14, -2, -7, 7, 8, -1, 0],\n [4, -12, -10, -7, -1, -4, 4, 1, 4],\n [0, -10, 18, 7, -4, 23, 8, -20, -2],\n [-7, -14, -11, 8, 4, 8, -22, 1, ... | 316 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -23, 15, 5, -23, 12, -2, 0, 15],\n [21, 2, -17, 11, 1, 22, -23, 15, 23],\n [2, 6, 9, -19, -19, -5, 6, 12, -6],\n [-18, -22, 0, -11, -20, 22, 6, -21, 18],\n [20, -20, -23, 3, -7, -16... | 897 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -11, -12, -8, -14, -16, 6, 0, 4],\n [-11, 2, 8, 17, 21, -8, 4, 11, -10],\n [-12, 8, -25, -10, 0, 15, -8, 4, -2],\n [-8, 17, -10, 3, 4, -24, -11, 0, 0],\n [-14, 21, 0, 4, 24, -2, 5, -14, 4... | 220 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 11, -22, 9, -19, 0, 6, 17, 7],\n [-2, 24, -25, 3, 22, 19, 12, 12, -5],\n [-3, 20, -21, 4, 14, -8, -20, -21, 16],\n [-8, -13, -6, 12, -5, -22, -13, -8, -13],\n [-13, 13, 11, 9, 12, 14, 1, 0, -14],\n [-24, 17, -6, 9, -16, -18, 14, 20, 10],\n [5, -11, 16, ... | 860 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 7, -4, -25, 15, 20, 9, 18, 23],\n [-9, 8, 3, -20, -25, 1, -14, -22, -10],\n [-15, -6, 0, 2, 16, -18, -24, 14, 0],\n [1, 7, -19, 20, 10, -5, 23, 8, -3],\n [8, 14, -19, 0, 14, 23, -9, 5, 13],\n [-1, 11, -11, -24, -15, 6, 4, -9, -2],\n [19, -22, 24, 20, 6, -7, -23... | 894 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 6, 0, 11, -6, 0, -10, -10, -1],\n [6, 14, 14, 6, -12, 14, 1, 4, -8],\n [0, 14, -4, 6, 6, 9, -10, 7, -5],\n [11, 6, 6, 2, -5, 11, 10, 2, 14],\n [-6, -12, 6, -5, 21, -4, 6, 4, 9],\n [0, 14, 9, 11, -4, -11, 2, -17, 4],\n [-10, 1, -10, 10, 6, 2, -5, 11, 4]... | 705 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[23, -4, 3, -7, -9, 2, -8, -1, -10],\n [-4, 14, -8, 8, -13, -12, -8, -6, 20],\n [3, -8, -8, -10, 10, 0, 15, -3, 14],\n [-7, 8, -10, -3, -22, -4, -9, -4, 13],\n [-9, -13, 10, -22, -20, 8, 12, ... | 870 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -25, 14, -8, 18, 5, -6, 18, -1],\n [0, -16, 3, -7, 2, 1, -7, 17, 5],\n [0, 0, 24, -20, -17, 15, 1, -9, 10],\n [0, 0, 0, -10, -9, -23, 13, 11, -23],\n [0, 0, 0, 0, -23, -10, -6, 19, -20],\n [0, 0, 0, 0, 0, 9, -8, 4, 17],\n [0, 0, 0, 0, 0, 0, -14, 23, -... | 760 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 14, -11, 13, -20, 6, 22, -18, 9],\n [0, 16, 0, 16, -2, 25, -24, 15, -25],\n [0, 0, -3, 7, 18, 11, -15, -6, 0],\n [0, 0, 0, -1, -22, -7, -13, -7, -13],\n [0, 0, 0, 0, -3, -7, -23, -2, -3],... | 456 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-21, -6, -4, -2, -3, 4, 10, -6, 6],\n [-6, -3, 4, -14, 12, -2, -17, 2, -6],\n [-4, 4, 7, -10, 4, -8, -4, -22, -12],\n [-2, -14, -10, 8, -4, 12, -11, -14, -22],\n [-3, 12, 4, -4, -5, -11, 6, ... | 597 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[22, 3, 16, -2, -18, 8, -4, 13, 7],\n [0, -20, -13, 18, -7, 0, -9, 11, 1],\n [0, 0, -12, -23, -21, -12, -18, 17, -1],\n [0, 0, 0, 19, -23, 19, -15, -17, -22],\n [0, 0, 0, 0, 24, -10, 6, 8, -20],\n [0, 0, 0, 0, 0, 4, -14, -21, 2],\n [0, 0, 0, 0, 0, 0, 11, -10, -17],... | 720 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 12, 18, -8, -17, -13, 25, 19, 25],\n [0, -16, 12, -23, 22, 15, -9, -3, 1],\n [0, 0, -7, 3, -11, 16, 10, -14, -12],\n [0, 0, 0, -21, 18, -23, 21, 4, 21],\n [0, 0, 0, 0, 23, -3, 21, -11, -15],\n [0, 0, 0, 0, 0, -10, -15, 5, 7],\n [0, 0, 0, 0, 0, 0, -9, ... | 360 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, 11, -16, -9, 1, -19, -12, -4],\n [-2, 14, 0, 16, 0, 18, -2, -14, 18],\n [11, 0, 22, 8, -18, -8, 20, 14, 13],\n [-16, 16, 8, -18, 14, -14, 18, 6, 18],\n [-9, 0, -18, 14, 11, 14, -13, -14, -8],\n [1, 18, -8, -14, 14, 3, 1, -2, 3],\n [-19, -2, 20, 18... | 864 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[24, -16, 4, 19, 15, -1, -23, -4, 14],\n [20, -2, 1, 0, -10, 12, 15, -22, -3],\n [-7, -11, 5, -2, -15, -16, -18, -23, -7],\n [-22, 3, 19, 15, -5, 19, -17, 25, 22],\n [-8, -7, -9, 18, 17, -2, ... | 44 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-25, -6, 9, -16, -1, 21, 2, 9, 7],\n [19, -11, -5, 16, 9, 24, 25, 11, -16],\n [-10, -6, 24, -18, 19, 5, -18, -13, -2],\n [-14, 19, -9, 21, 15, 10, -14, 10, -13],\n [9, -21, -13, 20, -1... | 344 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, 18, -6, 4, -8, 6, 10, -12],\n [-1, -5, 18, -21, -15, -4, 2, -4, 8],\n [18, 18, 6, 4, 0, 1, 18, -5, -10],\n [-6, -21, 4, 7, 2, 9, -2, 1, 8],\n [4, -15, 0, 2, -21, 3, -4, -6, -14],\n [-... | 811 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-16, 5, -18, 15, 13, 2, 5, -13, -19],\n [25, -25, 19, 23, 18, 0, 20, -10, -14],\n [-10, 8, 1, -1, -7, -19, -14, 20, -2],\n [24, 13, -21, -25, -19, 22, 0, -2, 22],\n [-9, -22, -10, 10, -21, -... | 483 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[23, -19, 7, 12, -10, 6, 6, -6, -12],\n [-19, -2, 22, 0, -14, -1, 0, -3, -6],\n [7, 22, 4, 7, -8, 12, 14, -2, -12],\n [12, 0, 7, -20, 4, 0, -10, -5, 9],\n [-10, -14, -8, 4, 22, 12, 19, 9, 4],\n [6, -1, 12, 0, 12, -21, 18, -10, 16],\n [6, 0, 14, -10, 19, 18, -4, -2,... | 751 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 10, -5, 3, -12, -6, 2, 6, 12],\n [10, -10, -2, 12, -4, 11, -13, -6, 2],\n [-5, -2, 22, -6, 21, 3, 10, -4, 16],\n [3, 12, -6, 24, 2, -8, 2, 4, 1],\n [-12, -4, 21, 2, -15, 22, 10, 2, 0],\n [-6, 11, 3, -8, 22, 0, -1, 12, -12],\n [2, -13, 10, 2, 10, -1, -7, -6, 8]... | 758 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -14, 22, 11, -8, -16, -20, 3, 3],\n [3, 20, 20, -17, 6, 22, -13, 20, -15],\n [8, 3, 25, -14, 23, 5, 15, -4, 0],\n [17, -14, 9, 23, 12, -22, 19, 23, -16],\n [-8, 20, 22, -7, -11, -3, -3, -5, 0],\n [19, 8, 15, -13, -1, 18, 7, 2, -13],\n [1, -18, 10, 17, -20, -13... | 944 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[21, -5, 10, -4, 4, 6, 3, 9, 0],\n [-5, 6, 8, -1, -6, 6, -13, -4, -2],\n [10, 8, -12, 2, 2, -16, 0, 9, -14],\n [-4, -1, 2, -6, 13, 22, 6, 14, 2],\n [4, -6, 2, 13, 24, 2, -16, -10, 14],\... | 803 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -24, 5, 11, 16, 3, -25, 18, -12],\n [0, 23, -15, 6, -6, -24, 5, -21, 6],\n [0, 0, 15, -16, 10, 23, 0, 18, -23],\n [0, 0, 0, 13, -3, -3, 17, 10, -1],\n [0, 0, 0, 0, 12, -25, 21, 7, 12],\n [0, 0, 0, 0, 0, 2, -3, 4, -8],\n [0, 0, 0, 0, 0, 0, 13, 20, 21],\n [0, 0,... | 760 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[20, -10, 25, 1, 17, 11, 7, -6, -1],\n [0, -12, 11, -21, 11, -16, -16, -17, -12],\n [0, 0, -2, -20, 0, 13, 18, 21, 22],\n [0, 0, 0, 20, 6, 0, -23, -14, -12],\n [0, 0, 0, 0, -3, 22, -23, -23, ... | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-24, -2, -20, 20, -9, 0, 21, 11, -24],\n [0, 18, 11, -25, -24, 7, -15, 4, 8],\n [0, 0, 8, -19, 13, 13, -24, 4, 22],\n [0, 0, 0, 11, 3, 9, 12, -4, 11],\n [0, 0, 0, 0, 19, 23, 12, 4, -24... | 792 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -20, 7, 24, -11, -6, -14, -2, 14],\n [0, 15, 7, 22, 20, -14, -11, -18, -22],\n [0, 0, -12, 13, -11, -7, -12, -19, -20],\n [0, 0, 0, 15, -1, 24, 21, -11, 16],\n [0, 0, 0, 0, 2, 6, ... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 16, 12, -24, -25, -21, 4, 5, 17],\n [6, -23, -23, 16, -21, 9, -4, 6, -3],\n [12, 16, -18, -22, -20, 1, 19, -7, 16],\n [18, 18, 3, 12, 18, -20, -23, 6, 22],\n [-10, 7, -24, 17, 0, 9, 2, 17, 23],\n [-15, 20, -2, -10, -1, -3, 13, 9, -1],\n [15, 13, 19, 7... | 261 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-25, -1, -6, 10, -12, 1, -4, 12, 0],\n [-1, -18, 9, -8, 3, 9, -3, 12, -2],\n [-6, 9, -25, 18, 0, 6, -8, -4, 12],\n [10, -8, 18, -16, 8, -8, 2, -2, -6],\n [-12, 3, 0, 8, 1, -2, 0, 16, 2],\n [1, 9, 6, -8, -2, 6, -16, -4, -5],\n [-4, -3, -8, 2, 0, -16, 6, -21, -12],\... | 712 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 15, 5, -2, -16, 16, 17, -8, -23],\n [0, 9, 18, -3, -4, -15, 20, 23, -3],\n [0, 0, -1, -2, -22, 11, 3, -23, 5],\n [0, 0, 0, -3, 23, -4, 3, 10, 25],\n [0, 0, 0, 0, 23, 10, -16, -17, -7],\n [0, 0, 0, 0, 0, 5, -7, 24, 20],\n [0, 0, 0, 0, 0, 0, -7, 13, 0]... | 640 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-19, -8, 20, 14, -25, 23, -20, -12, -2],\n [-9, -9, 18, -5, 22, 9, 23, 8, -13],\n [-12, -22, -2, -20, -6, 6, -3, 15, -12],\n [-4, -9, 14, 25, -24, 23, -19, 9, 10],\n [24, -12, -6, 2, -13, 23, 18, -19, -23],\n [-21, 7, 20, -17, 1, -11, 8, -8, -22],\n [8, 19, -5, -8... | 428 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-19, 8, 21, -16, 15, 22, -20, -1, -14],\n [14, 15, 13, -12, -15, -14, -7, 16, 2],\n [-7, 3, 19, 9, -3, -10, 11, -5, 14],\n [-25, 20, 11, -1, -10, 7, -1, -4, -23],\n [-23, -15, 17, -21,... | 180 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 19, -14, 1, -9, -7, -16, 17, 0],\n [-18, 13, -24, -14, 13, 14, 5, 3, -18],\n [-11, 0, 22, 10, 15, -22, 24, 7, -14],\n [24, -15, 4, 19, 0, 24, 4, 10, 7],\n [19, 5, -24, -11, -24, -14, -8, -18, -23],\n [9, 7, 5, -22, -3, 11, 19, 19, 9],\n [14, 12, -25, -23, -16, ... | 871 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -4, -16, -8, -5, -1, -16, 4, -22],\n [-4, 1, -20, -22, -1, 7, 0, -12, -12],\n [-16, -20, -6, 6, -5, 2, 7, 4, 17],\n [-8, -22, 6, 12, 16, 6, 2, -4, 11],\n [-5, -1, -5, 16, -18, -12, -14, 8, 18],\n [-1, 7, 2, 6, -12, 4, -6, -10, 12],\n [-16, 0, 7, 2, -14, -6, -15... | 554 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[19, 9, 11, -25, 21, 8, -5, 0, -12],\n [-8, -2, 9, -25, 21, 17, -10, 20, 13],\n [12, -5, -2, 0, 21, 20, 13, -8, 15],\n [-2, 18, 2, -6, 13, -9, -5, 24, -8],\n [24, -24, 11, 10, -9, 17, -... | 734 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-21, -3, -10, 15, 20, 1, -17, -12, 3],\n [0, 5, -19, 15, 18, -17, -12, -7, 8],\n [0, 0, -10, 21, 11, -3, 11, 5, -24],\n [0, 0, 0, 7, -4, 5, -14, 7, -6],\n [0, 0, 0, 0, 7, -7, 7, -21, 25],\n [0, 0, 0, 0, 0, -4, -8, 10, -1],\n [0, 0, 0, 0, 0, 0, 24, 10, 11],\n [0, 0... | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, -14, -14, 20, -8, -9, 14, 11, 5],\n [-17, 13, 6, 11, -7, 16, 10, -23, -2],\n [10, 0, -6, -12, 6, -18, 11, 11, -15],\n [-20, 11, 6, 7, 20, -9, 8, 9, 12],\n [24, -4, 18, 12, -24, 6, 24, -3, -13],\n [2, -10, -13, 23, -2, -22, 12, 6, 20],\n [25, 19, 0, 17,... | 944 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-24, 2, 6, -4, 12, -21, -8, -7, -12],\n [2, -15, 2, 1, 16, 17, 0, 4, 3],\n [6, 2, 16, -8, -18, -8, -11, 2, -4],\n [-4, 1, -8, 17, 0, -14, 0, -11, -7],\n [12, 16, -18, 0, -6, 19, -3, -17, 9],\n [-21, 17, -8, -14, 19, -24, -11, -15, 14],\n [-8, 0, -11, 0, -3... | 752 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -1, -6, 20, -5, 14, 14, -24, 22],\n [23, 16, 20, 18, -6, -15, -24, 21, -11],\n [0, -23, -8, -6, -2, -10, 15, -3, 24],\n [13, -16, -4, -6, 23, 22, -16, 0, 23],\n [-4, -14, -19, 7, 18, -8, 22, 18, 16],\n [-15, -14, 6, 10, 10, -16, 12, 11, 19],\n [17, 15, 5, -23,... | 440 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-21, 13, 15, 18, 12, -4, -9, -5, 1],\n [19, -13, 4, 20, -11, -8, 17, -15, 12],\n [-19, 15, 8, 6, -13, -10, 0, 14, 15],\n [8, -5, -8, -6, -14, -5, 14, 6, 16],\n [-17, 21, -15, -15, 12, ... | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -12, 2, -18, 24, 2, 18, 4, 15],\n [0, -14, 9, -7, 20, -21, -14, -20, -21],\n [0, 0, -8, -1, 2, 23, -2, -3, -25],\n [0, 0, 0, 7, 11, -20, 8, -3, 1],\n [0, 0, 0, 0, -4, 19, -17, -15, 18],\n [0, 0, 0, 0, 0, 19, 9, 6, -12],\n [0, 0, 0, 0, 0, 0, 8, 17, -4]... | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-21, -13, 4, -16, -12, -19, 5, -22, 20],\n [0, 16, -22, -12, -11, 9, 8, -12, -13],\n [0, 0, 25, -10, 9, 1, 8, -5, -18],\n [0, 0, 0, -9, 18, -12, 4, 20, -9],\n [0, 0, 0, 0, -20, 10, 13, 10, 24],\n [0, 0, 0, 0, 0, -11, 11, 6, 5],\n [0, 0, 0, 0, 0, 0, 13, -18, 1],\n ... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -25, -4, -9, 22, 21, -7, -24, -10],\n [0, -5, 19, -25, -3, 16, -3, -16, -6],\n [0, 0, 15, -12, -20, 11, 18, 0, -11],\n [0, 0, 0, -23, -23, 3, -4, -12, -14],\n [0, 0, 0, 0, -20, 11, 12, -4, 13],\n [0, 0, 0, 0, 0, -6, 16, -16, -6],\n [0, 0, 0, 0, 0, 0,... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 0, 4, -14, -1, -10, 22, 2, 5],\n [0, -15, 6, 18, 0, -13, -8, 10, 19],\n [4, 6, -8, 11, 6, 14, -9, 20, -14],\n [-14, 18, 11, 12, 7, 4, -18, 9, 13],\n [-1, 0, 6, 7, -5, -6, -6, -8, -7],\n [-10, -13, 14, 4, -6, -19, 15, 0, 22],\n [22, -8, -9, -18, -6, 15,... | 825 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-25, -24, -21, 1, -6, -8, -2, -2, -5],\n [-24, 4, 4, -10, -6, 16, 6, 8, -6],\n [-21, 4, 15, -7, 2, 6, -13, -4, 10],\n [1, -10, -7, 19, 0, 14, 8, 11, 18],\n [-6, -6, 2, 0, -5, 16, -12, -10, 10],\n [-8, 16, 6, 14, 16, -19, -7, 0, 8],\n [-2, 6, -13, 8, -12, -7, -1, -... | 364 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -21, -10, 21, -6, 22, -6, -9, -21],\n [-6, -21, -23, 6, -1, 8, 24, -25, -24],\n [-16, -8, -13, -4, -19, 5, 6, -24, 17],\n [21, 11, 23, -22, 21, 5, -18, -13, -24],\n [-22, 18, 4, 18,... | 401 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-18, -11, 13, -23, 2, 2, -13, -20, -22],\n [0, 8, -21, 14, 4, 15, 22, -15, 5],\n [0, 0, -14, -2, -7, 9, -25, -20, -24],\n [0, 0, 0, -16, 22, 13, -18, 8, -23],\n [0, 0, 0, 0, 20, 13, -23, -20, 21],\n [0, 0, 0, 0, 0, -24, -2, -19, -19],\n [0, 0, 0, 0, 0, 0, ... | 440 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, -23, 7, 2, -4, 14, -9, -3],\n [9, 9, 6, -1, -8, 23, -13, 21, -8],\n [17, -16, 5, 15, -7, -18, 22, -18, -9],\n [-20, -11, 9, -25, 11, 24, -1, -20, -3],\n [20, -4, 19, 12, 7, -2, 4, 25... | 390 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -15, -17, 1, -13, -14, -15, 9, 18],\n [-3, -5, 2, -19, -13, 5, 9, -9, 25],\n [-2, -4, -16, -10, 11, -20, -14, -25, 24],\n [-10, 25, 8, 11, 1, -21, -7, -15, 11],\n [17, -15, -18, -1... | 496 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[18, 22, 16, 0, 18, -22, -4, 25, -10],\n [0, -24, 11, -8, -7, 4, -17, 5, -8],\n [0, 0, -16, 12, -4, 23, 14, -10, -3],\n [0, 0, 0, 2, 4, 11, -1, 1, -18],\n [0, 0, 0, 0, 3, -9, 1, 24, -3]... | 40 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, -12, -13, -1, 5, 3, -20, 18, 19],\n [0, -25, -9, 4, 4, -9, 6, -24, 19],\n [0, 0, 20, 12, -3, -16, 2, -23, 4],\n [0, 0, 0, 11, 17, -9, -8, -3, -23],\n [0, 0, 0, 0, 20, -11, -20, -25, 25],\n [0, 0, 0, 0, 0, 10, -8, -22, -21],\n [0, 0, 0, 0, 0, 0, -17, -... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 18, -25, 2, -13, 17, -12, 20, -1],\n [0, 9, 20, 7, -17, 15, 25, -20, -23],\n [0, 0, 15, -23, -11, 19, 2, 10, 21],\n [0, 0, 0, -12, 5, 16, 24, -5, 5],\n [0, 0, 0, 0, -12, 2, 18, -19, 20],... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -22, 0, 3, -8, -8, -14, 1, -22],\n [-22, -2, -4, -10, 10, 10, 6, -9, 16],\n [0, -4, -24, 15, 7, -21, -14, 5, -4],\n [3, -10, 15, 4, -2, 7, 5, 15, 9],\n [-8, 10, 7, -2, -8, 16, 4, -9, 7],\n [-8, 10, -21, 7, 16, 0, 8, 2, 13],\n [-14, 6, -14, 5, 4, 8, 13... | 584 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 16, 5, 0, -3, 19, 5, 7, -2],\n [0, -22, 9, 9, -16, 21, -13, 21, 1],\n [0, 0, 8, 13, 18, 2, 6, 2, -6],\n [0, 0, 0, -24, -23, -10, 14, 1, -10],\n [0, 0, 0, 0, -5, -23, -2, 2, -5],\n [0, 0, 0, 0, 0, 11, -6, 4, 22],\n [0, 0, 0, 0, 0, 0, -14, 5, -6],\n [0, 0... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 12, 0, -12, 22, 7, 16, 25, -11],\n [0, -5, -8, -19, -8, -8, -25, -3, -19],\n [0, 0, -21, 18, -4, 6, 16, -19, -19],\n [0, 0, 0, -17, 18, 20, 18, 21, -11],\n [0, 0, 0, 0, -17, 10, -8, -2, -23],\n [0, 0, 0, 0, 0, 18, 23, -20, -19],\n [0, 0, 0, 0, 0, 0, 25, -12, 1... | 250 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 24, -17, -12, -10, 21, -10, -11, -23],\n [0, -21, 19, -1, 10, 1, 1, 0, 25],\n [0, 0, -25, 0, 18, 19, 10, -8, -3],\n [0, 0, 0, 18, -6, -9, 18, -25, -11],\n [0, 0, 0, 0, 2, -16, -17, -19, ... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -19, -10, -8, -20, 24, 25, -25, -3],\n [0, 12, -18, -14, -21, 17, 1, 19, 24],\n [0, 0, 17, 11, -13, -7, -13, -4, 20],\n [0, 0, 0, 12, 22, -3, 23, 0, -19],\n [0, 0, 0, 0, 24, -1, 13, 12, ... | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[16, 7, -1, -5, -6, -10, -24, 21, 10],\n [0, -15, 23, -19, -6, 15, -19, -15, 24],\n [0, 0, 7, -18, -18, -25, 6, 5, -23],\n [0, 0, 0, 12, -12, 24, -2, 6, -10],\n [0, 0, 0, 0, 23, -10, 17, 18, 19],\n [0, 0, 0, 0, 0, -13, 18, -5, 12],\n [0, 0, 0, 0, 0, 0, -7,... | 680 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -14, 2, -2, -12, 1, -1, 19, -13],\n [-14, -11, 14, 22, -9, -3, 10, 4, 6],\n [2, 14, 14, -4, 6, 2, -4, 5, -5],\n [-2, 22, -4, -20, -5, -12, 8, -10, -2],\n [-12, -9, 6, -5, 0, -8, 18, 20, 6],\n [1, -3, 2, -12, -8, -25, 10, 2, -20],\n [-1, 10, -4, 8, 18, 10, 1, -... | 242 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -12, 16, 11, 9, 7, -21, 12, -15],\n [24, 14, -7, 24, -20, 5, -9, 14, 11],\n [-15, 23, 15, -10, -19, 7, 19, 13, 9],\n [-8, 20, 16, -23, 6, 3, 5, 9, -13],\n [15, -22, 16, -16, 22, -6, 4, 0, 3],\n [19, 8, -1, 7, -17, -10, -17, -11, -17],\n [24, -4, -11, 1, -25, 14... | 470 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[17, -8, 2, 4, -4, -16, 6, -10, 0],\n [-8, -6, 8, -6, 0, 3, -12, 16, 0],\n [2, 8, -24, 0, 8, 7, -19, 0, 0],\n [4, -6, 0, -6, 5, -20, -22, -6, 0],\n [-4, 0, 8, 5, -1, 3, 5, -10, 8],\n [-... | 64 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 2, 2, -7, 0, 22, 2, -2, 10],\n [2, -9, -4, -8, 24, 4, 21, 6, -6],\n [2, -4, 23, -11, -2, 15, 5, 10, -16],\n [-7, -8, -11, 5, 7, 0, 16, 6, -7],\n [0, 24, -2, 7, 20, 8, 8, 0, 16],\n [22, ... | 984 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 14, 24, 0, 3, 1, -14, 0, -25],\n [0, 23, -22, -11, 22, 16, 7, 4, 7],\n [0, 0, 24, -13, -24, -19, -23, 23, 13],\n [0, 0, 0, 5, -14, -6, 15, 7, -7],\n [0, 0, 0, 0, 2, -22, 5, 21, 24],\n [0, 0, 0, 0, 0, -22, -9, -22, 13],\n [0, 0, 0, 0, 0, 0, -1, -20, 21],\n [0, 0... | 320 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -16, -13, -2, -21, -9, -1, -13, 12],\n [0, -14, 3, 21, -14, -1, 3, -23, 6],\n [0, 0, 15, -19, -23, -18, -19, -10, -5],\n [0, 0, 0, 20, 2, -19, 3, 6, -5],\n [0, 0, 0, 0, 4, -23, -11,... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 17, 14, 3, 22, 1, 21, 1, 23],\n [0, -13, 23, 9, -14, 11, 11, 12, 11],\n [0, 0, 17, -4, 1, -5, -12, 1, -3],\n [0, 0, 0, 3, -9, -17, 14, -2, 24],\n [0, 0, 0, 0, -5, 24, -7, -21, 15],\n [0,... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 12, -21, -20, -11, 5, 10, 7, -19],\n [0, -24, 8, 22, 25, 10, 9, 11, 10],\n [0, 0, -5, -1, 19, 23, -1, -14, 12],\n [0, 0, 0, -18, 4, -6, 15, 24, -13],\n [0, 0, 0, 0, 10, -6, -14, -5, 12],\n [0, 0, 0, 0, 0, -20, 23, -21, 3],\n [0, 0, 0, 0, 0, 0, -13, 16, -12],\n... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -11, -13, -25, -2, -11, 17, -8, -9],\n [0, -14, -9, 11, -12, 10, 15, 16, -12],\n [0, 0, -18, -18, -14, 2, -20, 11, -7],\n [0, 0, 0, 22, 1, 7, -13, 19, -2],\n [0, 0, 0, 0, 9, 9, -4, -11, -17],\n [0, 0, 0, 0, 0, -6, 7, -18, 22],\n [0, 0, 0, 0, 0, 0, 18,... | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-24, 22, 9, -4, -2, 7, -24, -19, 4],\n [0, -19, -17, -2, -2, 17, -1, 17, -22],\n [0, 0, 20, -13, 8, 9, -17, -14, 9],\n [0, 0, 0, 8, 11, -10, 16, 2, -4],\n [0, 0, 0, 0, -17, 18, 1, 4, -... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -25, 10, 16, 17, -20, -22, -22, -25],\n [7, -23, -19, -10, -3, -10, -25, 19, -24],\n [18, 18, -15, 16, -25, -12, -24, 6, 4],\n [6, -10, 17, 1, 11, 4, -25, -15, 7],\n [25, 3, 2, 3, 20, -8, 12, -15, -8],\n [0, 18, -3, 9, 10, -16, -1, -3, -12],\n [20, -8, 6, -19,... | 394 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, -7, -21, -12, 4, 12, -22, -6, 6],\n [18, -7, 16, -18, -2, -11, -2, 6, 23],\n [12, 18, 7, 22, -18, -4, 20, -18, 21],\n [18, 0, -10, -25, 12, -21, -25, 1, -16],\n [8, -25, -4, -5, 8, -9, -15, -1, -25],\n [-3, -23, -1, -9, 3, -24, 11, 19, 17],\n [-20, -1... | 216 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -9, -11, 15, 5, 4, 16, 13, -21],\n [0, 10, -22, -22, -25, 24, -2, 6, 25],\n [0, 0, -3, -15, 0, -20, -5, 16, 21],\n [0, 0, 0, -24, 14, 9, -2, -8, -19],\n [0, 0, 0, 0, -15, 24, 3, -4, -23]... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-24, -15, -25, -24, -18, 8, -13, -9, -11],\n [0, 20, -19, 3, 1, -23, -8, 19, 6],\n [0, 0, -22, 0, 20, 24, 13, 15, -22],\n [0, 0, 0, 4, -5, 8, -20, 6, 2],\n [0, 0, 0, 0, -21, -3, -22, 24, 2],\n [0, 0, 0, 0, 0, 21, 10, 11, -6],\n [0, 0, 0, 0, 0, 0, 24, 6, -16],\n [0... | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, -24, -12, 16, 13, 5, 8, 0, -4],\n [-24, 20, -6, 8, -9, -4, -14, 16, 16],\n [-12, -6, -7, 0, -9, -16, 6, -3, -9],\n [16, 8, 0, -23, 11, -10, 9, 10, -10],\n [13, -9, -9, 11, -20, 3, 8, 13... | 151 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 12, 4, -14, 18, 7, -13, -5, -6],\n [3, 16, 3, -9, -2, 9, 7, -17, -5],\n [-20, 18, 10, 4, -8, -16, -9, -2, 9],\n [-6, -12, -22, 19, -11, 9, 16, 25, 3],\n [-21, 22, -3, -7, -23, -4, -11, -18, -10],\n [23, 18, 12, 4, -23, -1, -11, -9, -18],\n [-14, 0, -12, -19, -1... | 718 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[23, 4, 15, -4, 4, 22, 2, 20, -15],\n [4, 7, 16, -4, -4, -13, -6, -7, -8],\n [15, 16, 18, -15, 4, 6, 10, 8, -14],\n [-4, -4, -15, 4, -12, -13, 0, 8, 4],\n [4, -4, 4, -12, -16, 10, -6, -... | 484 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 8, -8, 21, 12, -25, 21, -7, -15],\n [-9, 15, -3, -24, 25, 4, -5, 23, -1],\n [11, 11, -13, 11, 0, -24, 25, -3, -15],\n [-24, -20, 22, -16, -18, 23, -13, -21, -3],\n [-4, 4, 12, 8, -... | 682 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 20, 3, -6, -10, -15, 4, 23, -23],\n [0, -2, 7, 0, 12, 1, 11, 19, -20],\n [0, 0, 9, 16, -8, 16, 25, 1, -1],\n [0, 0, 0, 12, 15, 6, 22, -17, -2],\n [0, 0, 0, 0, -17, -16, -6, 16, -14],\n [... | 64 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 25, -16, -1, -13, 7, 23, -3, 6],\n [0, -7, -21, 11, -10, 19, 13, -13, 3],\n [2, 15, 14, 12, -16, 11, -8, -20, 7],\n [18, 12, 2, -10, 1, -18, 0, 18, 12],\n [-5, 20, 7, 2, 25, 5, -19, -16, 10],\n [17, 21, 18, -15, -5, -2, 14, -12, 6],\n [18, -9, -8, -22,... | 900 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -16, 11, -13, 9, 18, 23, 11, 18],\n [9, 6, 12, 10, 23, -17, -13, 7, 12],\n [-17, -13, -20, -17, -21, 21, -11, 7, -1],\n [19, -4, -1, 8, 2, -15, 25, 11, 7],\n [19, -15, 7, -24, 5, 5, 11, -6, 10],\n [1, -7, 14, -6, -11, 15, 3, 23, -4],\n [-11, -14, 15,... | 806 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, 16, 20, 8, -23, 22, 21, -1],\n [10, -2, -1, 23, -21, -4, 20, 13, 3],\n [9, 21, 10, 1, -17, -8, 24, 18, 16],\n [10, -20, 20, -9, -21, -15, 17, 4, -13],\n [-22, 25, -11, -25, 9, 9... | 283 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, -8, 5, 2, -13, -15, -1, -10, -7],\n [0, 10, 3, -15, -25, 14, -14, -1, -10],\n [0, 0, -15, -17, 6, 24, -3, 17, -9],\n [0, 0, 0, -13, -13, 18, 11, 6, 1],\n [0, 0, 0, 0, 7, -8, 10, -5, -2],\n [0, 0, 0, 0, 0, -10, 8, 20, -13],\n [0, 0, 0, 0, 0, 0, 20, 3, -... | 0 | MATH |
[
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"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[25, 11, -1, 25, -11, -14, 10, 10, 20],\n [0, 25, -19, 22, -12, 11, 24, -25, 15],\n [0, 0, -20, -9, 22, 14, 22, 6, -15],\n [0, 0, 0, -20, 23, -25, -14, 23, 12],\n [0, 0, 0, 0, 17, -9, -... | 0 | MATH |
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"content": "Determine the value of det(A) where A =\n[[-15, 1, -10, 8, -5, -1, 15, 8, 9],\n [1, -4, 15, -11, -6, -6, -15, -14, -2],\n [-10, 15, 25, 18, 14, 5, -17, -12, 14],\n [8, -11, 18, 12, 1, -16, -2, 20, -8],\n [-5, -6, 14, 1, 23, 10, -7, -8, 6],\n [-1, -6, 5, -16, 10, -21, 2, 23, -4],\n [15, -15, -17, -... | 430 | MATH |
[
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"content": "What is the determinant of the matrix:\n[[-7, 25, 23, 23, 1, 15, -10, -13, -15],\n [0, 1, 14, -9, -4, 2, -25, -16, -11],\n [0, 0, 16, -4, 19, -20, -12, 11, 3],\n [0, 0, 0, -8, -6, 7, -14, -20, 19],\n [0, 0, 0, 0, 1, 15, -13, 12, 14],\n [0, 0, 0, 0, 0, 7, 22, -3, 5],\n [0, 0, 0, 0, 0, 0, -11, 10, 6... | 984 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[20, -20, -21, -15, 23, -17, 4, -15, -20],\n [25, 1, 25, -11, -5, 25, -5, 18, -11],\n [0, -7, 21, 10, 16, 18, 6, -25, -12],\n [-9, -11, 18, -18, -19, -17, 13, 3, -8],\n [11, -5, -1, 6, -16, -14, -25, 0, -7],\n [-4, 13, -18, 12, 12, 9, 20, -5, -18],\n [15, ... | 488 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 10, -16, 11, 18, 10, 19, 2, -16],\n [0, 15, 3, -3, -6, -16, -6, 3, -13],\n [0, 0, -24, -1, -6, 0, -19, -14, 12],\n [0, 0, 0, -23, -19, -24, 17, 6, 6],\n [0, 0, 0, 0, 19, -3, 14, -... | 320 | MATH |
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