messages listlengths 1 1 | ground_truth stringclasses 140
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[6, -4, 9, -14, 23, -25, -16, 1, -2, 9, -9, 12],\n [-18, -25, 9, 19, -10, 6, 8, 6, 5, -7, 3, -5],\n [26, -2, 18, 19, 17, -16, 23, 7, 1, 8, -23, -18],\n [16, -5, -2, -6, -2, 14, -10, -1... | 518 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-7, -17, -3, 20, -20, 21, 22, -7, -14, 2, -17, -18],\n [-20, 17, 6, -3, -11, 5, -23, -13, 2, -5, -4, -1],\n [-1, 22, 17, 20, -5, 17, -24, 15, 25, -10, -13, 18],\n [3, -14, -1, 13,... | 93 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, 13, -3, 10, -11, -5, 20, -10, -26, 4, -2, -15],\n [-7, -8, -22, -12, 14, -2, 8, 17, 24, 20, -24, 25],\n [-9, -5, -11, -12, -22, 15, 15, -14, 23, 1, -17, -11],\n [-25, 23, 9, 24, -2, -22, 1, -10, -... | 98 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[5, -11, 3, -13, 23, 14, -9, -5, 25, -11, 22, 22],\n [-11, -1, 24, 16, -21, 24, -20, -18, 17, -1, -25, 9],\n [-24, -6, 17, -24, -18, -15, -19, 24, 10, -6, 10, 13],\n [-24, 24, 14, -6, -1, -3, 19, 26, 25, 7, 5, 0],\n [20, 3, -23, -... | 576 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[18, 0, -3, -7, 17, -12, -21, -9, -5, 22, -6, -3],\n [-10, -16, -9, 8, 4, 1, -3, 9, 18, -3, 6, 24],\n [3, 25, 10, -14, -11, 21, 16, -18, 23, 20, -14, -20],\n [8, 17, -1, 23, -18, 8, -3... | 527 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[2, 6, -25, -9, 25, -13, 13, 3, 2, 2, -8, 19],\n [-1, 19, 25, 13, -18, 19, 17, -14, 11, 4, -13, 4],\n [-12, 7, 23, -17, -6, 12, -2, 10, 13, -7, 18, -20],\n [-9, 14, 17, -1, -10, 15... | 84 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -12, -4, -20, 16, 7, 11, 14, 22, 24, 17, -21],\n [-11, -25, 5, 16, 20, 11, 1, 14, -18, -2, 23, -1],\n [18, -1, -22, -10, -1, -1, 26, 16, -18, -4, 25, -3],\n [14, -18, -17, 25... | 87 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[16, 16, -16, -15, 17, 7, 8, 12, 25, 19, -11, -3],\n [4, -13, 22, 20, 5, 16, -14, 11, -10, 17, 9, 26],\n [15, -9, -8, -20, 3, -15, -16, 2, -24, 7, 7, 4],\n [-5, -25, 0, 20, 9, 5, 8, -10, 7, -1, -17, 1... | 81 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-4, 15, 0, 14, -11, 5, 9, -10, -9, 0, -20, 14],\n [11, -7, 8, 20, 6, -1, -3, -3, 4, 0, 22, -18],\n [-25, -21, 4, -2, -11, 18, -21, -4, 20, -22, -10, -18],\n [-1, -14, -20, 21, 13, -9, 10, 18, -3, 5, -20, -7],\n [18, 7, -8, 19, -1... | 497 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-4, -7, 18, 2, -1, 14, -15, 21, 2, -8, 7, 21],\n [0, 3, 10, 4, 1, -2, 22, -21, -20, -21, 8, -2],\n [-6, 20, 21, -10, 14, -1, 14, -10, -20, -2, 7, -1],\n [-21, -17, -10, -13, -24, 21, -11, -22, 21, -4... | 86 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[7, 7, 10, -24, 8, 6, -8, 4, 25, 17, -5, 0],\n [11, 1, -6, -7, 11, -14, 2, -6, 15, 6, 5, 21],\n [19, 1, 23, -13, 15, 25, -5, 10, 7, -10, 6, 6],\n [11, -1, 12, -20, -2, 21, 24, 3, 14, 6, 23, 12],\n [1, -9, -17, 25, -25, 16, 23, 16, -13... | 89 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-15, 18, -25, 13, -23, 5, 14, 7, -22, -22, -23, 24],\n [14, -15, 8, 10, 7, 18, 1, -20, 26, 13, 25, -16],\n [17, 5, 23, 23, 5, 4, 21, -7, -21, 23, 22, ... | 105 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-4, 26, 17, 9, 1, 21, -8, 16, 16, -14, -14, -19],\n [16, 21, -14, 8, 0, -16, -6, -19, 15, -1, 3, -5],\n [23, 22, 12, 23, -17, -1, 25, 0, -5, -14, 12, -20],\n [25, 16, 15, -15, -14, -15, -15, 11, -24, -19, 22, 4],\n [... | 102 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[22, -9, 15, -1, 17, -7, -19, 24, 6, -23, 11, -5],\n [9, 21, 4, -19, -18, 20, -9, 8, -3, -10, -26, 12],\n [15, -12, -14, -4, 2, 4, 10, 1, 5, -20, -13, -13],\n [5, -18, -21, 24, -12, 3, 3, -11, -4, 4, -15, -6],\n [-24, -24, 11, -5, -6,... | 97 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-26, -14, -13, -4, 12, 1, 2, 13, 6, -25, 16, 6],\n [-3, -15, 13, 1, 8, -17, 20, 17, 7, -22, 14, -9],\n [-21, -16, 19, -26, -4, -23, -20, 14, 22, -10, -16, 0],\n [-15, 20, 7, -19, 25, -4, -1, 7, 5,... | 100 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[2, 2, -20, 17, -21, 8, 10, -23, -13, -21, -10, 22],\n [-3, -14, -15, 2, -3, 7, -13, 0, -22, 13, 20, -18],\n [-11, -14, -12, 9, -2, -11, 17, 25, 17, 4, 20, 10],\n [6, -7, -1, 8, 13, -20, 18, 15, 4, -10, 16, -19],\n [-4, 20, 17, -9, 15... | 86 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-7, 0, -22, 18, -16, 22, 15, 17, -21, -22, -5, -26],\n [-7, -3, -7, 20, 21, 2, 15, -3, -19, 7, -5, 12],\n [6, 25, 3, -21, -14, 17, -8, -1, -10, 10, 0, -3],\n [20, -13, -24, -22, -13, -19, 16, -2, ... | 87 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, -8, -8, -8, 2, 12, 18, 7, -19, -21, 5, 1],\n [-16, 1, 5, 14, -19, -7, -3, 25, 0, 20, 26, -16],\n [20, -4, -5, -22, 21, 7, 4, 20, 10, 20, -1, -4],\n [16, 11, 11, 5, -22, -2, 6, 25, -20, -11, 22, 2],\n [-12, -7, -... | 92 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-22, -8, 2, -12, 15, 9, -15, -13, -12, 24, 4, -22],\n [17, -24, 20, 3, 20, -15, -12, 11, 1, 22, -4, 20],\n [-12, -16, 3, -15, -8, 5, -26, -11, -16, 4, 6, 9],\n [3, 11, -23, -2, 7, -10, 6,... | 107 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, 21, 18, 8, 9, 2, 6, -1, -19, -18, -5, -22],\n [17, 14, 9, 5, 3, 22, 17, 18, 16, -10, 3, 20],\n [-18, -23, -15, 8, -7, -10, -5, -20, 12, 26, 17, 26],\n [15, -19, -18, 19, -21, -8, -5, 20, -7, -7, 0, 0],\n [-20, -3, -19, -24, -1... | 529 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-1, -12, 9, 18, -15, 14, 18, 16, -15, -23, -24, 10],\n [11, 5, -1, -23, -26, -22, -25, 19, -16, -18, -19, 12],\n [-12, -18, 15, 23, 3, 2, 24, -2, -5, 7, -5, 19],\n [3, 26, -17, -22, -22, -25, 3, -5, -14, 12, -2, 26],... | 93 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-6, -1, -3, -5, 10, 16, -1, -5, 19, 6, -3, -22],\n [-3, 8, -5, 6, -10, 25, -15, 3, -1, -14, -21, -24],\n [-16, 16, 26, -17, -16, -11, -7, 15, 17, -8, -18, 9],\n [-12, -4, -6, 12, -22, 24,... | 94 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-9, -13, 4, 23, -9, 20, -2, -16, -1, -22, -11, -19],\n [-14, 5, 0, 22, -1, -18, 20, -20, 23, 19, -19, -25],\n [-9, 9, -3, 7, 15, 11, -16, 25, -17, 2, ... | 105 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-16, -4, 18, -17, 15, -3, 26, 19, 25, -11, -15, 23],\n [5, -3, -23, 15, 6, -9, 20, -10, -6, -26, 19, 17],\n [-2, 4, 16, -7, -1, -8, 3, -2, 9, 22, -9, -23],\n [0, 6, -21, -20, -26, 11, 8, ... | 90 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-5, 14, -12, 18, 26, 8, -8, 7, -9, -13, -5, -3],\n [-14, -19, 15, -25, 15, 0, 7, 2, -1, -4, 9, -18],\n [-6, 15, 9, -24, -20, -4, 5, -4, -11, -22, -14, -17],\n [-25, -11, 25, -26, -21, -8, 6, 1, -22, -15, 3, -10],\n [-8, 13, 15, -... | 485 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-14, 4, -14, -4, 13, 5, 10, -23, -10, -7, 19, -16],\n [15, 6, 12, -21, 12, 20, 11, -9, -25, 14, 11, -10],\n [-3, 3, 16, -3, -23, -20, -12, 3, 2, 22, 17, 18],\n [26, -14, 13, 12, 2... | 91 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, 12, -8, 14, 7, 1, -15, 12, -17, 25, 20, -2],\n [-4, -1, -8, 11, -7, 18, 25, 17, -9, 21, -16, -2],\n [16, -26, 5, 6, -20, 4, -1, -20, 9, 19, -3, -22],\n [-5, 17, 9, -24, 23, 10, 11, 19, -21, 25, -2, -4],\n [-15, 1, 17, 13, 5, 25,... | 105 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, -13, 26, -1, 3, 15, 18, 5, 3, -15, 9, -8],\n [17, -2, 6, 15, -6, -25, 10, -6, -1, 5, 0, -10],\n [-23, 12, -12, 6, -13, -1, 20, -25, -7, -1, -25, 21],\n [-25, 21, -10, -9, 24, 21,... | 562 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-2, -18, -2, -9, -20, 19, -1, 22, -9, -26, -18, -17],\n [21, -16, 5, -6, 9, 5, -8, -19, 8, -5, -23, 2],\n [4, -19, -15, -22, 3, 8, 10, -23, 16, -6, -11, 26],\n [-9, 4, 11, 5, 21, 6, -8, -7, 21, -17, ... | 81 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-20, 25, -8, -5, 19, 11, -14, -1, 17, -5, -20, 25],\n [8, -24, 8, 20, -11, 18, -11, -25, 11, -10, 11, -3],\n [-5, 23, -4, 17, -8, 17, -5, -10, -25, -1... | 88 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[15, 22, 3, 23, -20, -14, -5, 18, -25, -19, -6, -7],\n [-16, 7, 17, -22, 26, 21, 3, 6, -15, -22, -26, 8],\n [-2, -23, -18, 22, 17, 24, -24, 3, -7, -17,... | 92 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[10, 1, -24, -4, 6, 12, -2, -2, 12, -6, 4, 22],\n [3, 12, 18, 18, 15, 25, 7, 11, -20, 0, -14, 2],\n [-4, -19, -6, -14, -1, 16, -17, 2, 0, -23, 15, 4],\n [-10, -19, 25, 10, -7, 20, -17, 24, 23, 17,... | 539 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-20, -8, 0, 23, 0, -9, 3, 1, 2, -18, 12, 12],\n [-6, 18, 11, -20, 18, -2, -1, 25, -21, 22, -7, -9],\n [-7, 13, -9, 20, -26, 6, 12, 21, -4, 25, -13, 1],\n [-6, 17, 10, -20, -15, 24, 10... | 561 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[21, 14, -13, 26, 6, 6, 9, -4, -26, 0, 24, 5],\n [-6, 17, -7, 0, 9, 14, 5, 12, 2, 19, -4, 8],\n [-12, 16, -17, 25, -12, -2, -10, 24, 4, -16, -7, 4],\n [-11, 9, 12, -16, -7, -1, 22, 24, -1, 15, 20, -21],\n [18, 8, -19, -20, 10, 23,... | 559 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-8, -18, 6, -19, 11, 5, -4, 7, -4, 19, 5, -26],\n [-20, 16, 21, -3, -25, -9, -8, 15, 9, 1, 8, 5],\n [-14, -21, 2, -17, 13, -17, 7, -7, 20, 6, -16, -3]... | 89 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-11, 7, 0, 16, -24, -18, 17, 7, -8, 11, -1, -4],\n [-9, 18, 19, 13, 14, 18, 22, 11, 25, -17, 16, -17],\n [-6, 11, 11, 20, -20, -15, 25, 14, 6, -2, 1, -3],\n [21, 4, -9, -4, -20, 2... | 95 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[8, 5, -8, -12, -17, -1, -21, 21, 20, -1, -25, 22],\n [21, 5, -24, -8, 9, -7, 3, 10, 18, -7, 7, 17],\n [-10, 15, -4, 14, -18, 0, -10, 14, 19, -10, 22, -25],\n [-12, -16, 10, 14, -18, -... | 527 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-11, -5, -16, 14, -16, -22, 15, 11, 21, -15, 13, -2],\n [18, -14, 21, -1, -16, 13, -4, -14, 6, 25, 25, 1],\n [24, -23, 1, 7, 24, 24, -17, 22, 25, -19, -18, -9],\n [-25, -9, 13, -25, -5, -11, 10, 5, -... | 90 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, 14, 23, -16, 17, -19, -26, -19, -22, -26, -24, 0],\n [18, 21, -4, 17, 12, 13, -16, 18, -16, 9, 11, 4],\n [-3, -8, 26, 5, 13, 11, -10, 23, 8, -15, -12, 12],\n [-14, 3, 15, -8, -18, 1, 17, 16, -... | 575 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[17, 20, -18, -25, 25, 20, 23, 18, 21, 20, -16, -24],\n [15, 22, 3, -19, 10, -6, -19, 20, -16, 14, 7, 12],\n [-11, -20, -23, 5, 10, 19, -5, -20, -14, -... | 87 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, -25, 20, -13, -20, 2, -23, -23, -3, 15, -6, 24],\n [18, 1, 11, -19, 15, -10, -18, 19, -7, -22, 8, 14],\n [2, -15, 5, 4, 4, -26, 16, -22, 24, 9, -15, -11],\n [-11, -6, 6, -1, -24, -4, -2, -7,... | 494 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-8, -14, 16, -18, -8, 24, 5, -6, 5, 19, -15, 2],\n [6, -26, 22, -23, -14, -4, 1, 16, 23, -15, -8, 25],\n [6, -9, 7, 3, 16, 20, 20, -21, -23, -15, -4, 1],\n [-16, 1, 13, 7, 21, 7, -6, 9, 1... | 87 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[14, 23, -4, 22, 7, 3, -2, -3, -2, 3, 12, 17],\n [-11, -17, 4, -16, -18, 9, 21, -8, 25, -22, -15, -17],\n [-13, -7, -7, 17, 9, 25, -2, 14, 19, -22, 14, 0],\n [-25, -15, 1, 17, -14, -6, 16, -19, 26, -15, 14, 17],\n [-16, -8, -19, 0... | 480 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-21, -17, 24, -16, 2, -11, -7, -6, 2, -13, 14, -11],\n [-18, -21, 11, 2, -9, -3, 24, -10, 9, -6, -8, -4],\n [0, 26, -16, -1, 26, -16, 16, -5, -8, -19, -4, 21],\n [26, -4, 13, -18, -3, -15, -15, 5, -25, -21, -23, -14],\n [9, 14, 12, 1... | 86 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-6, -13, 13, -13, 26, 24, 5, -1, -24, -12, -6, 3],\n [21, 20, -13, 20, 12, 10, 14, 21, 1, -25, -5, -20],\n [17, 5, -11, 9, -25, -10, 22, -24, 21, -4, 10, 12],\n [1, 18, 14, -19, 6, -23, 26, -20, -16, 13, -19, -7]... | 570 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[19, 15, 22, -11, 25, 22, 21, -17, -9, 11, -10, 14],\n [13, 4, -1, -1, 13, -15, -9, 7, 8, -16, 26, 3],\n [18, 23, -16, 19, 25, -23, 9, -17, 7, 4, 5, 23],\n [1, 16, 10, 5, 5, -10, 7, 8, 12, -6, 5, 7],\n [7, -19, -1... | 525 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-3, -25, -11, -25, -6, -17, 15, -10, -15, -20, -18, 19],\n [23, -17, -11, -26, -18, -14, 21, -11, 7, 14, 3, -14],\n [-19, -16, 22, 25, 4, 16, -16, 21, -20, -26, -4, 5],\n [-12, -9, 1, -13, -14, 7... | 496 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[9, 26, -11, -15, 1, -20, 6, -3, -16, -12, -8, -12],\n [-18, -14, 23, 2, -1, -4, -10, -22, -11, 12, 3, -6],\n [-22, -1, 16, 21, 3, -5, 18, -25, 17, -15, 15, 0],\n [-1, 18, 17, -2, -8, 22, ... | 98 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[1, 8, -12, -20, 8, 21, 4, 11, -19, 21, 11, -11],\n [7, -26, -8, -13, -8, -4, -23, 7, -25, -15, -4, 16],\n [26, -9, 5, 24, -10, 4, 9, -1, -15, 8, -11, -23],\n [1, 11, 6, 10, -17, 4, -13, -22, -17, ... | 97 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-19, 17, 3, -19, 0, 12, -4, -19, -12, 26, -20, -15],\n [23, 9, 11, 16, 3, -17, -8, -9, 17, 22, -7, -25],\n [3, 24, 17, 16, 20, 16, -16, -5, 15, -8, -24, -23],\n [8, 20, 11, -18, -19, 7, 24, 20, 4... | 557 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-26, -15, -11, -13, 3, 16, 25, -8, -8, -14, 17, -17],\n [20, 2, 1, -14, 18, -12, -10, -4, 16, -17, 9, 22],\n [-13, 5, 7, 4, 12, 5, -11, -1, -10, -5, 9, 8],\n [-4, -2, -22, -21, -1, 11, -21, -8, 16, -... | 88 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-7, 5, -15, -23, -18, -16, 22, 3, 18, -1, 5, 1],\n [24, 13, 10, 15, 20, 24, 14, -11, 21, -19, -24, -24],\n [-17, -15, -12, 20, 0, 24, 19, -16, -21, -15, -9, -2],\n [7, -1, -3, -11, 9, 9, -6, 3, 2... | 519 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[24, 7, 21, -11, 1, -13, 25, -26, 14, -12, -12, -2],\n [16, -22, -19, -5, 12, 11, 12, 24, 19, 16, 24, -13],\n [-8, -1, 11, 6, 19, -15, 2, -15, 2, 14, 14, 19],\n [-7, 7, 19, 3, 2, 12, 20, 13, 24, -... | 527 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-24, -17, 22, -12, -3, -17, 25, -6, 19, 21, 11, 12],\n [15, 24, 23, 1, 14, -25, 14, -23, 16, 22, -24, 5],\n [20, 7, -11, -23, -9, 1, 15, -21, 16, 15, ... | 97 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[0, 0, -14, -18, -19, 18, 0, 5, 2, 19, 6, -22],\n [11, -18, 25, -14, 6, 3, -2, -21, 12, -17, 9, 23],\n [21, -8, -16, -10, -25, -20, 14, 4, 4, 19, -10, -12],\n [-20, 3, 12, -13, 4, -18, -18, 22, 26... | 555 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -9, 9, -15, 1, 21, -16, 16, -21, -1, -11, 11],\n [-18, -9, 6, 23, -8, -18, 19, 17, 15, -18, 17, -22],\n [-4, 24, 15, 7, 11, -5, -22, -26, -1, -9, -1, -12],\n [-25, 26, -12, -16, 18, -7, 20, 15, -10, -22, 6, 2... | 549 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-11, -10, 2, -7, 9, 20, -3, 16, 21, 25, 26, -23],\n [-22, -8, 21, 24, -3, 21, -26, 8, -25, -17, -21, 13],\n [11, -7, -8, 21, 9, 21, 2, 14, -3, -18, 5, 13],\n [-22, -6, -10, -3, 0, 21, -9, -5, -21, 1, 15, -7],\n [-11, -8, -19, -9,... | 544 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[1, -24, -20, 7, 21, 5, -18, 8, -8, 19, -12, 4],\n [-11, 24, 20, 19, 10, -20, 8, 2, -25, 21, 7, 8],\n [4, -15, -26, 20, 2, -26, -26, -12, -24, -13, -17, -24],\n [-... | 101 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[13, -1, 11, -24, 10, 9, 11, -25, -5, -24, 13, 20],\n [15, 20, -1, 0, 11, 17, -19, -4, -21, -2, -11, -1],\n [-12, 25, 20, 5, 13, -8, -13, 26, 21, 17, 8, -1],\n [25, 10, -14, 20, -19, -13, ... | 88 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-20, -9, -17, 4, -1, 20, 18, -1, -2, 25, -9, -3],\n [17, -12, -19, 16, -2, 8, -3, 19, 13, 26, 11, -6],\n [-26, -1, -17, -1, -25, 13, -13, 6, 12, -26, 3, 10],\n [-9, 3, 0, 22, 22, 3, 18, 2... | 89 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-10, 2, -25, -16, -11, 24, -10, -6, -6, -21, 19, 18],\n [-4, 5, 12, 18, 11, 2, 4, -2, -25, -5, 10, 17],\n [-12, -21, 6, -16, 26, -15, -3, -24, 3, -8, 18, 16],\n [-20, -15, 23, 2, 21, ... | 538 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-13, -7, -13, -25, -2, -23, 14, 21, 6, -25, -4, 17],\n [21, -6, -12, 24, -3, -7, 11, -2, -5, 25, 24, 20],\n [-23, -11, 16, -20, -3, 7, 12, 2, 17, -1, -13, 20],\n [-7, -20, -9, 16,... | 108 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-20, 4, 7, -16, 15, -8, -22, -4, 20, -25, 16, -23],\n [-10, 4, 3, -25, -3, -17, 1, 16, 5, 6, -9, -3],\n [10, 3, -22, -4, 3, -23, 14, 24, -3, -24, -12, 19],\n [-26, -17, 18, -1, -15, -26, ... | 92 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-18, -11, -3, 7, 16, -3, 22, 11, 11, -2, 14, 26],\n [6, 17, 16, -10, -20, 0, 9, 14, -8, -12, -21, 9],\n [-22, 26, 18, -22, -25, 16, -9, 5, 20, 22, 2, 22],\n [-7, -8, 25, -11, -16,... | 83 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[20, 22, 10, -22, -16, 13, 16, -5, 25, -12, -18, 23],\n [-21, -1, -21, 5, 16, -7, 8, 16, -24, -9, 8, 25],\n [-17, 9, 3, -1, 3, 4, -23, -3, -26, -1, 22,... | 80 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-1, 21, 16, 3, -13, 20, 26, 10, 11, 3, -12, -8],\n [-16, -7, -2, 11, 16, 3, 13, -4, 17, -10, -26, 15],\n [-13, 12, -9, 14, -11, -17, 17, -18, -13, -25, 15, -6],\n [15, -25, -21, -16, 14, -24, 24, -16, -23, -12, -... | 533 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[25, -14, 5, 2, -9, -25, 0, 23, 15, -24, 26, 3],\n [-17, -18, -24, -5, 11, -16, -21, -22, 3, -13, -25, 6],\n [10, -19, -17, -6, -8, 8, -9, -20, -14, 19, 23, -15],\... | 89 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[6, -12, -7, 16, 15, 5, -3, -24, -23, 17, -21, 25],\n [-8, -1, 21, -2, -2, -17, 11, -7, -22, 15, 17, 23],\n [8, -22, 8, -24, 14, 5, 9, 3, 25, 22, 12, 2... | 90 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[20, -26, 5, 2, -7, 19, -14, -15, -19, 12, -19, -9],\n [-6, 1, 4, -12, 12, 6, 11, -4, -11, -3, -6, 19],\n [-19, 15, -10, -12, -13, -7, 5, -16, 11, 5, -23, 2],\n [-22, 16, -15, 16, 23, 12, -4, 6, -11, 23, 17, -16],... | 526 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-26, 8, 20, -12, 26, 1, -15, -26, -16, 24, 10, 22],\n [-25, 18, 8, 18, -19, 4, -6, 26, 18, -24, -2, 14],\n [1, 1, -25, -19, -26, -6, -12, -19, 13, -5, 12, -7],\n [-14, -1, 12, -20, -1... | 540 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[15, -25, 14, 5, -5, -1, 14, 18, -17, 12, 18, -22],\n [-15, 14, 14, 5, 23, 13, -9, -17, -4, -26, 26, 26],\n [15, 10, -9, 3, -8, 18, 11, -10, 1, -5, 19, 11],\n [5, -2, 21, -18, 9, 23, 10, -26, 2, -1... | 99 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[26, 15, 1, -18, 0, -8, -20, -2, 3, -14, -25, -9],\n [26, 13, 26, -19, -7, -18, -14, 25, -6, 1, 17, -20],\n [4, 26, -4, -14, 18, 9, -25, 7, -22, -25, 20, 7],\n [-25, -7, -19, -4, 10, -11, -5, 19, -19,... | 94 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[0, -6, 18, 5, 5, -15, 17, -18, -7, 22, -12, -14],\n [19, -19, -6, 18, -2, 8, 13, 3, 4, -21, -16, 15],\n [-19, -19, 12, 24, -15, -24, 16, 18, -11, 14, 0, -11],\n [-22, 13, -15, -24, 8, 18,... | 93 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[5, 3, 13, -15, 2, -26, -1, -11, -9, 6, 25, 23],\n [15, 16, -4, 21, -22, -6, -26, 4, -9, -6, -20, -26],\n [-4, 0, -25, 7, -11, 13, -17, -7, 21, 10, -2, -23],\n [5, 18, 1, 13, -14, -22, -10, 20, -20, -17, 0, 8],\n ... | 531 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-12, 7, 26, -16, -18, -3, 10, 8, -5, 13, 11, -20],\n [17, 3, 2, 12, 14, -18, -26, -24, -22, -16, -23, 17],\n [6, 6, 18, -7, 10, -7, 7, -6, 24, -20, -11, 5],\n [9, 23, -16, 21, 2, 15, 7, -17, -24, -5, 5, 17],\n [-7, -... | 89 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[25, 14, 16, -3, 22, -1, 5, 16, 0, 14, -8, -19],\n [10, -21, -8, 16, -4, -25, -24, -25, -14, 5, 16, -2],\n [16, -14, 3, -8, -3, 18, 6, -14, 4, 11, -19, 3],\n [-8, 5, 3, 19, 11, -10, 7, -11, 10, 25,... | 94 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[12, 1, 6, -25, 14, -12, 12, -20, -7, -14, 5, 2],\n [-23, -8, -17, 9, -15, -5, 0, 8, 13, -10, -21, 18],\n [23, 21, 16, -13, 6, 17, 25, 1, 11, -20, -16, 6],\n [-24, -5, -14, 2, -21, 15,... | 524 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, -7, 21, -10, 25, -21, 9, 14, -7, -1, 13, 23],\n [-15, -20, 13, 3, -5, 15, 2, -5, -3, -24, 23, 14],\n [-3, -1, -22, -14, 10, -5, 7, 12, -24, 5, -3, -18],\n [-24, -5, -3, 11, -1... | 82 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[16, 12, -2, -12, 24, -7, -10, -26, 2, 17, -8, 3],\n [-2, 1, 10, 15, -16, -11, -9, 14, -18, 1, 0, 19],\n [25, 11, 17, -4, 16, -5, -23, 5, -3, 11, 23, 1],\n [-21, 6, 4, -17, -15, -20, -3, 1, -16, 5, -7, 1],\n [-26, 0, -11, 9, -21, -17,... | 86 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[24, 13, 25, 15, 22, 24, -26, -6, -1, -12, 16, -2],\n [12, -11, 8, -4, -15, 21, 25, -8, 7, -19, 24, -4],\n [-16, 16, 7, -22, 10, -2, -3, -3, 15, 7, 20, -9],\n [-15, 15, 12, -12, 20, -15, 2, 2, -7, -12, -24, -11],\... | 529 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-13, -13, -25, 1, -6, -12, 17, 19, -4, -17, -1, 8],\n [7, -25, 4, 16, 17, 20, 17, 16, 25, 25, 19, -22],\n [-8, 3, 22, 20, 25, -10, 2, -15, -19, -12, 26, 7],\n [1, -6, 26, -10, 26, 15, -9, -3, -3, -15, -26, 9],\n ... | 537 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-5, 13, 24, 20, 4, 24, -21, -23, -20, 7, 0, -25],\n [-13, 14, 2, 12, -5, -22, 17, -9, 24, -11, 17, -21],\n [-26, -15, -3, -16, 16, 14, 7, 2, 5, -6, 13, 6],\n [6, 1, 17, 9, -26, -15, 19, 6, 17, -22, -25, 9],\n [-3, 16, 23, 24, 23, 25,... | 87 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-3, 1, -9, 17, -1, -17, 22, 17, 7, 19, 11, -16],\n [-13, 19, 11, -26, -10, 22, -10, -17, 3, 15, 19, 6],\n [-25, 23, -7, 5, -24, 9, -22, -7, -24, -24, 9, -21],\n [12, 9, -3, 20, 11, 10, -19, 11, 22, -... | 92 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[26, 0, -22, -22, 21, 13, -12, 20, -18, 20, -2, -19],\n [-13, 12, 5, 4, -4, 17, -26, 20, 4, -20, -12, 15],\n [-21, -11, -13, 17, -10, -17, 2, 15, -19, -16, -9, 18],\n [-7, -11, 0, -4, -13, -15, 18, 0, -14, -11, 6, -3],\n [-15, -18, -1... | 100 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-13, -20, -18, 6, -3, 25, 15, 16, -6, 17, -26, -6],\n [13, -3, 11, 17, 14, -23, -21, -24, 7, -2, 26, 0],\n [-9, -22, -3, 5, -6, 17, 7, 2, -22, 23, 1, ... | 84 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-10, -17, 10, 10, -25, -15, 10, 3, -12, -4, 25, -9],\n [4, 26, 11, 2, -13, 16, 13, -4, -2, 14, 11, 1],\n [8, 3, 0, -19, 21, -8, -26, 18, 17, -7, 3, 2],\n [-19, -13, 11, -24, -24, -13, -6, 8, 17, 17, 22, 16],\n [14, 0, 1, 1, -22, 16, ... | 88 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-23, 22, -3, -18, -8, -19, 14, 1, -14, -19, -13, 23],\n [23, -17, -7, -26, -15, 8, -7, -15, 23, -15, 12, 2],\n [-24, -20, -4, -14, -16, -2, 25, -7, 22, 20, 0, -21],\n [-21, 12, 14, -18, -6, -9, -... | 524 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[19, -8, -26, 8, -11, -19, -20, -6, -16, -1, -12, 18],\n [25, -21, 10, -23, -8, 20, -6, 10, 16, -9, 15, 21],\n [9, 24, 10, -12, 11, -25, 15, 25, 4, -21, -8, 11],\n [-12, 6, 13, -1, 26, 3, -16, 19, -26, -13, -17, -... | 558 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[23, -22, -12, 21, 23, -21, -23, -4, 18, -26, 7, -12],\n [-23, 0, -14, 19, 20, 13, 5, -18, 10, -2, -24, 12],\n [13, -11, -10, 0, -17, 26, -26, 24, 23, 2, -9, 25],\n [5, 10, 16, 6, -5, 16, -16, 10, 2, -7, -5, 5],\n [23... | 103 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[21, -15, -26, 22, -13, -1, -20, -11, -12, -23, 3, -4],\n [-5, -12, -10, -25, -19, -21, 12, 1, 21, -22, -6, 23],\n [-7, 16, 7, -20, 3, 3, -12, 0, -18, 0, -25, 9],\n [0, 20, 13, -2, 9, 13, -20, -14, 10, -7, -5, -9]... | 553 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[10, 1, -23, -7, 23, -5, -15, -26, -19, 14, 0, -6],\n [18, 6, 11, 6, 19, 10, 18, -22, -12, 3, -24, 1],\n [3, 9, -24, 25, 17, 4, -13, -21, -8, -22, 22, ... | 92 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[20, -8, -17, -8, -18, -20, -13, -25, -5, 18, -7, -1],\n [-23, 12, 13, -4, -11, -2, 25, -18, 26, -16, -2, 4],\n [19, 0, 9, 24, 20, -13, -4, -11, -7, 26, -24, -21],\n [2, -23, -26, 23, -19, 21, -7, -11, 20, 4, 5, 7],\n [2, -15, -23, 16... | 91 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[3, -18, 3, 2, 11, 19, 15, 22, 7, -1, -25, 9],\n [-20, 25, 9, 13, -13, 0, -1, -7, 8, -16, -1, 8],\n [-22, -11, -16, 6, -18, -5, -22, -7, 16, 7, 3, -17],\n [10, 5, -3, -10, 17, -24, 12, 16,... | 89 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[14, -25, -25, 11, 11, 16, -4, -17, 18, 26, 1, -8],\n [1, 4, -25, 2, 25, -13, 1, -26, 17, 23, -11, 10],\n [-6, 24, -13, 16, -10, -12, 21, 4, 19, 22, 9,... | 99 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-21, -26, -18, 25, -11, 2, 2, -22, -8, -5, 22, -19],\n [24, -9, 17, 21, -13, -23, 13, 0, -3, 3, -15, 16],\n [-14, 13, 23, 18, -23, -1, -26, 0, -4, 15, 11, -16],\n [12, 15, 17, -6, -5, 1, 11, -21,... | 548 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[7, 9, -9, 6, -26, 21, -2, 18, -13, -16, 25, -19],\n [15, -11, 12, 10, 4, 15, -9, -20, -23, 5, 4, -17],\n [3, 23, 23, 8, 18, 4, 4, 19, 19, 6, -22, -17],\n [19, 24,... | 87 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[9, -22, 10, -18, 5, 10, 7, 12, 20, 13, 2, 4],\n [-24, 16, -2, 15, 9, 17, -14, 12, -8, -11, 15, 3],\n [12, 8, -25, -26, 21, 18, -24, -1, 1, 0, -13, 23],\n [16, 24, -3, 8, 25, 7, -3, -21, 4, 2, 9, ... | 558 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-10, 3, -3, 4, 24, 25, -14, -12, -1, 5, 18, 8],\n [-11, -18, -8, 13, 13, 19, 24, 18, -24, -1, 10, -19],\n [-21, -22, -6, 0, 17, 11, -19, -5, -4, -2, -20, -13],\n [14, 2, -10, 24, -21, 5, -8, 0, 3, 23, 26, 6],\n [... | 509 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[7, -7, 3, -11, 17, -23, 4, -1, 14, -15, -25, -19],\n [-13, -3, 16, 13, 14, -2, -20, 5, 26, -4, 19, 12],\n [-1, 15, -20, 20, 23, 18, -23, 17, -2, 25, -9, -20],\n [-5, -23, 2, -3, 13, 25, 2... | 88 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-14, -23, -6, -13, 9, 23, -20, -14, 8, 22, 6, -16],\n [24, 12, -2, 19, 12, -3, -5, 16, 24, 21, 22, 19],\n [-5, -12, -9, 17, 18, 5, 9, -17, -18, 17, -2, -23],\n [11, 19, 9, 15, 10, 12, -20, 15, -1... | 510 | MATH |
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