messages listlengths 1 1 | ground_truth stringclasses 112
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-16, 1, 11, -22, 6, 3, -13, -22, 22, -6],\n [18, 13, -14, 16, 0, 6, -21, -5, 5, 19],\n [-16, -12, -16, 20, 1, -8, 8, -4, -13, -15],\n [-22, -21, 6, 19, -13, 19, -14, 8, 9, -21],\n [1, 14, 20, -17, -15, 17, 2, 19, 20, 2],\n [-12, ... | 397 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[0, -7, 21, -15, -19, 9, -20, -7, 11, -10],\n [10, -1, 8, 1, -20, 10, 7, 3, 11, -1],\n [7, 12, 2, 5, 10, 0, 3, -14, -15, 14],\n [10, -8, -15, -2, -20, -14, -9, 15, 4, -3],\n [-19, 1, 4... | 317 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-15, 6, 14, 4, 14, 1, 22, -7, 3, 8],\n [4, 3, 20, -8, -8, 0, 2, 21, -19, 13],\n [-7, 17, -2, 17, 20, -6, -20, -16, -11, -22],\n [20, 14, -17, 0, 2, 2, -20, -19, 7, 10],\n [6, -19, -9, -2, -16, -2, -16, -22, 11, 0],\n... | 73 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-21, -21, -18, -9, 0, 12, -22, 18, 17, -8],\n [7, -2, -15, -16, 18, 11, 19, 14, 9, 10],\n [-17, 19, -13, 3, 22, 3, -4, 12, 22, -19],\n [2, -15, -11, 1, 1, -6, 2, 10, 4, -21],\n [-14, 10, -4, -18, -3,... | 77 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-7, -6, -8, 3, 22, -21, -6, -22, 7, 9],\n [7, 19, -19, 19, 21, 9, 12, -22, -4, 10],\n [-4, 13, 4, -10, 4, -9, 1, 12, -4, 2],\n [-12, -14, -17, 13, 14, 6, -14, 10, 0, -8],\n [-12, 0, 3, -22, 7, -6, 18... | 73 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-3, 13, 17, -18, -1, -21, 2, 17, 1, -18],\n [-7, -8, -10, -12, -7, -5, 2, 15, 17, -19],\n [-2, -12, 11, 7, -19, -9, -12, -19, 3, -20],\n [14, 15, 18, -19, 3, 16, 22, 19, 21, 19],\n [-12, -12, 15, 15, -3, 3, 15, -11, 6, -9],\n [2, 19,... | 77 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, -19, 18, -4, -16, 12, 3, 21, 0, 11],\n [-16, -12, -15, -10, 9, 18, 11, -5, -8, 20],\n [1, -2, -5, -9, -4, -10, -7, -21, 11, 3],\n [-1, -3, 6, -5, 6, 19, 21, 4, 12, 6],\n [-17, 14, 2, -2, 8, 17, -7, -9, -17, -12],\n [4, 15, -18... | 304 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, -21, -5, 15, 10, -14, -8, 5, -15, 13],\n [16, -15, 19, -4, -19, 4, -10, 15, -2, 3],\n [22, 0, 7, 8, 8, -7, 19, 18, -16, -6],\n [1, -3, 16, 4, -21, -22, 11, 4, 14, -17],\n [15, 4, -7, 12, 4, 12, 1... | 68 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-22, -10, -15, -1, -19, 11, 22, 14, 0, -3],\n [1, 4, -10, -18, -7, 15, 6, 3, -1, 1],\n [-10, 20, -2, -22, -19, -20, 0, -7, 22, -10],\n [16, 8, 1, -8, -18, -1, -1, -12, 1, 22],\n [-13, 11, -12, 20, 6, -1, 10, -15,... | 390 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[11, 19, 20, 5, 12, -9, -5, -4, -4, 10],\n [12, -3, 6, -15, 2, -6, -22, 15, 7, 5],\n [10, -10, 1, 21, 14, -1, -10, 17, -11, 18],\n [-16, 13, 6, 6, 3, 4, 1, 8, -16,... | 66 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-3, 9, 8, -1, -18, 8, -8, 21, -6, 14],\n [-4, -13, 21, 11, 2, 14, 5, -8, -3, -10],\n [-3, 20, 8, -5, 18, 5, -19, 1, 21, 22],\n [-14, 9, 9, 16, -2, 21,... | 63 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, -3, 19, 4, 5, 8, -16, -15, 9, -12],\n [3, 2, -16, -3, 18, 7, -22, -5, -15, 6],\n [17, -1, 9, 17, -9, -21, 12, -16, -20, -8],\n [20, 11, -1, -5, -5, 11, 13, 16, 15, 14],\n [-5, 20, 17, 6, -11, ... | 336 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-1, -12, 3, -22, 13, -2, -15, -3, 22, -6],\n [-8, -2, -22, -20, 8, 8, -2, 0, -6, -1],\n [-1, 13, -15, -15, -9, 15, 1, -1, -8, -3],\n [4, 5, -1, 8, -14, 0, -18, 22, 16, -6],\n [17, -18, -16, -15, ... | 346 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[5, 5, 2, -12, 17, 20, -21, -11, 18, 15],\n [-11, 2, 14, 8, -6, -11, 7, -21, -7, -22],\n [11, 22, -22, 13, -20, 11, -11, 22, 4, 14],\n [2, -11, 10, -14... | 77 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-11, -3, -17, -15, -9, -18, 13, 15, -20, 13],\n [-1, -15, -9, -16, -19, -4, 20, 1, -7, -17],\n [21, -15, 2, 9, 2, -13, 20, 18, -6, -20],\n [-14, -5, 7... | 65 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[-9, 6, -6, -22, -3, 10, -21, -6, 0, -1],\n [-22, -11, -10, -9, -13, -11, -1, -5, 16, -4],\n [7, -8, 16, -9, -14, -18, 10, -18, 1, -15],\n [-4, -11, -15, -15, 15, -3, 6, 18, 11, -5],\n [-22, -12, 21, 12, 9, 19, -7, -1... | 72 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-14, -3, -14, 8, 5, 12, 17, 15, 21, -21],\n [-20, -9, -6, 12, -19, 7, 16, -9, 4, -10],\n [-3, 1, -13, -16, -6, -1, 21, -12, 19, 0],\n [-1, 17, -5, 22, 3, 7, -10, -19, 20, 4],\n [17, -13, ... | 70 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-22, 3, -12, -8, 16, 17, -5, 1, 5, 2],\n [0, -12, 10, -7, 13, 0, -17, 20, 1, 15],\n [19, -17, -13, -1, 0, -18, 5, -14, 16, 21],\n [5, 2, 20, 15, 4, 1, 20, 20, -7, -21],\n [-21, -18, -... | 349 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-18, -12, 6, 5, 5, -18, -3, 14, 16, -13],\n [9, 6, -21, -22, -3, -22, -19, -8, 7, -17],\n [15, -22, -16, -18, -16, 13, -20, -11, -8, -3],\n [18, -2, 9... | 61 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-22, -16, -19, -13, 17, 12, 16, -7, 4, -3],\n [-13, 22, 10, -16, 19, 21, -1, 20, -6, -14],\n [17, -13, 13, 8, 8, -18, -5, -17, 19, 5],\n [20, 1, -18, 5, -20, -5, -19, 17, 19, 9],\n [9, -4, 6, 10, -21, -12, 10, 18, 17, -22],\n [19... | 349 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, 17, -6, 12, -17, -11, -8, 9, 0, -16],\n [15, 8, 6, 21, 5, -11, 4, -19, -2, -14],\n [11, 14, -2, 0, 1, -13, 15, -17, -2, 14],\n [6, 17, -2, -1, 12, -18, -8, 18, -4, -7],\n [17... | 64 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-11, 4, 6, -21, 6, 17, -14, 21, 5, 14],\n [0, -10, -18, 9, 5, -8, 1, 9, -2, -18],\n [14, 13, 5, 9, 0, -7, -13, 6, 4, 12],\n [19, 22, 1, 0, -20, 13, 22, -9, -19, 21],\n [19, 9, -3, -6, 6, ... | 76 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-12, -7, -1, -12, 14, 3, 3, 19, -2, 3],\n [-8, 16, 12, -12, -14, 19, 0, -19, 7, 5],\n [2, -1, 2, 3, 6, 18, 9, 3, 5, -3],\n [-21, 0, 16, -18, -2, -1, -12, 7, 5, 13],\n [-6, -2, 14, 13,... | 296 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[4, 17, -8, 0, -15, 2, -12, -2, -13, -14],\n [-22, -1, -17, 7, 11, -10, -1, -17, 18, 1],\n [-2, 16, 0, -18, -16, -20, -10, -11, -17, 11],\n [-8, -5, -20, -1, 12, 5, 18, 19, -11, -22],\n [13, 7, 0, 14, 5, -18, 13, ... | 359 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[20, 1, -15, 17, 2, -19, -8, -7, -12, 5],\n [-16, 15, 1, 8, -19, 14, 12, -17, 10, 9],\n [15, 12, -6, 9, -9, -4, 1, 16, -12, -16],\n [22, 1, 1, -9, 1, -12, -15, 21, -8, 19],\n [-21, 1, 22, -13, 9, ... | 356 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-4, -3, 19, -16, -14, -16, 4, -2, 12, 1],\n [9, -11, 0, 13, 6, -20, 20, -15, 11, -9],\n [13, 9, -16, -13, -11, 17, 0, -12, -10, -11],\n [-16, 21, -13, -16, 4, -16, 1, 0, 2, 21],\n [13, 10, 14, 19, 16, -16, 7, 8, 22, 14],\n [-2, 11, -... | 67 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[10, 19, -20, 15, -6, -11, -12, -6, 12, 18],\n [-17, 12, -17, 9, -12, 20, 16, -10, -10, 16],\n [11, -20, 9, -19, 17, -22, -14, -16, 4, -20],\n [-1, -7, -15, -18, 7... | 73 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-10, 14, 15, -9, -17, 6, -14, 13, 0, -8],\n [-16, 2, 14, 0, -12, -15, 13, 19, 16, -22],\n [21, -10, -7, -10, 14, -9, -10, -11, 5, -1],\n [-3, -4, -12, 7, 3, -8, 7, 6, 9, 7],\n [21, -7, 13, -5, 18,... | 65 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-15, 20, 0, 22, 7, 5, -10, 14, -11, -13],\n [-6, -22, -1, -8, -7, -3, -13, 19, 3, 0],\n [-6, 11, 18, -1, -19, -16, -18, 8, -4, -19],\n [-1, -20, 0, -19, 1, -9, 18, -20, -2, 3],\n [-22, 7, -19, -9, -5, -11, 15, 19, 13, -7],\n [-22, -2... | 66 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[12, -2, -22, -21, 19, 20, 3, -20, 1, 3],\n [-15, 14, -15, -5, -5, -11, 13, 17, -21, -3],\n [-20, 17, 21, 11, -17, 17, -13, 1, -5, 10],\n [16, -16, 22, 21, 6, -4, 15, 16, 2, -6],\n [14, -20, 1, -5, 3,... | 71 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, 21, 1, 18, -8, 17, -11, -9, 4, 14],\n [-10, 15, 15, -20, -7, -11, -9, 11, 8, 16],\n [-18, -11, 3, -6, 21, -12, 10, 18, 17, -19],\n [9, 8, -12, -6, 4, -15, -2, 10, -18, 9],\n [2, -15, 4, 3, 17... | 75 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[9, -12, -21, 9, -18, 8, -10, -1, 12, -4],\n [6, 0, -4, -7, 8, -7, 3, -20, 0, -14],\n [1, 10, -9, 5, 1, 20, -16, 15, 21, 2],\n [-21, 22, -22, 0, 17, -5, -15, 11, 20, -15],\n [6, -10, -22, 6, 14, -22, 21, -18, -21, -1],\n [7, -12, ... | 366 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[4, -11, -6, -2, 20, -1, 3, 16, -10, 19],\n [19, 22, 0, 7, -6, 4, -3, -16, -19, 8],\n [7, 8, -19, -5, -3, 17, 17, 0, 15, -14],\n [-7, -2, -14, 2, 13, 20, -9, -6, 5, 22],\n [18, -15, -9, -8, 16, 2, -12... | 79 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -21, -21, -18, -10, -4, -4, -22, 12, -5],\n [9, 9, -15, -12, -3, -15, 5, -2, 15, 15],\n [-17, -21, -13, 19, -14, -20, -21, 13, -15, -14],\n [3, 11, 7, 15, -15, -20, -12, 2, -... | 72 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-14, -1, 2, 8, -2, 15, -4, -13, 14, -11],\n [-4, -21, -8, 15, -15, 12, 15, 20, 7, -14],\n [7, -4, 6, -21, 5, -15, 2, -13, -1, 12],\n [19, 1, 3, 8, 0, -21, 16, 10, 1, -11],\n [14, -14, 21, 20, 21, -20, 21, 0, 1, 1... | 343 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[2, 10, 13, 3, 13, -12, 7, 10, -13, 6],\n [2, 9, -19, 16, 11, -1, -10, 13, -17, -6],\n [3, 1, -14, -21, -3, 4, -17, 4, 1, -8],\n [10, 19, -13, -2, -17,... | 67 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[1, -13, 12, -17, -3, 15, -11, -20, -5, -2],\n [12, 14, -4, 2, -5, 17, 7, 19, 19, 11],\n [-13, -1, -19, -20, 5, -1, -11, -10, 18, 10],\n [-4, 18, -6, 11, -19, 16, -15, 10, -22, -18],\n [9, 17, -22, 12, -1, 6, -6, ... | 354 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-22, -19, 17, -6, 3, -9, 9, 13, -3, -7],\n [-4, 22, 16, 1, -9, 6, 19, -9, -12, -12],\n [17, 1, -1, -2, -17, -9, -14, 12, 21, 13],\n [2, -8, 22, 5, -9, -10, 18, 8, -18, -4],\n [-15, -10, 18, -6, 9,... | 80 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-18, -4, -2, -20, 3, 10, 7, -1, -18, -4],\n [-14, 1, 16, -11, 22, 4, 19, -2, 15, 12],\n [9, 13, 10, 20, -6, -18, 21, -3, 0, 16],\n [-19, 3, 7, 6, 11, -13, -3, 1, 11, 14],\n [-10, 0, -13, -1, 22, -9, ... | 66 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-21, 2, -18, 11, 16, -18, 20, -15, -9, 6],\n [7, 14, -19, 12, -16, 3, 9, 20, 10, 1],\n [-22, 6, 22, 15, 15, -2, 0, -18, 7, 17],\n [-5, -17, -18, 19, -5, -10, -3, 15, -2, -19],\n [-10, -5, -10, -10, 16, 14, 12, 15... | 350 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-18, -20, -12, 22, 9, -1, -12, 15, -1, -19],\n [16, -20, -13, 14, -4, -5, 5, 8, -6, 1],\n [-22, -18, 9, -6, -2, 18, 20, -1, 16, 16],\n [11, -9, -7, -18, -5, -19, ... | 73 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-21, -15, -5, -16, 20, 8, -1, 5, 2, -22],\n [9, 2, -7, 6, 19, 1, -6, 19, -17, -9],\n [3, 5, 13, 8, 4, -21, -4, 5, 22, 21],\n [-2, 22, -8, 11, 17, -20, -22, 1, 20, 4],\n [-14, 1, -... | 79 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-9, 0, 6, 19, 12, 4, 4, 7, -20, -11],\n [8, 14, 4, 1, 18, 17, -12, 4, -14, -7],\n [-9, 7, 1, 19, -10, 10, -14, 3, 19, 22],\n [-10, -2, 6, 5, 1, -10, 19, -3, 16, -16],\n [18, -8, 2, 12, -10, 20, -15, -2, -17, -13]... | 340 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -6, 3, -5, -1, -17, -4, 14, 11, -12],\n [1, 22, 14, 0, 17, 20, -19, -5, 7, -8],\n [14, 0, -11, -19, -19, 18, 18, -9, -15, 0],\n [-22, -12, 4, -19, 6, -6, -4, 22, 1, 21],\n [18, 21, 9, 8, -7, 9, 21... | 72 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-1, 22, 10, 0, 0, 15, 3, 9, 5, 7],\n [17, -6, -5, 2, -19, 3, 8, -11, -5, -13],\n [13, -21, 2, -14, 9, -18, -20, -6, -10, -20],\n [5, -19, -5, 12, -9, -7, -11, -12, -21, 10],\n [-10, 7... | 321 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[14, 15, -5, -3, -18, 20, -14, 6, -6, -11],\n [3, 10, 10, 13, 6, -1, -5, -6, 21, 1],\n [-1, 21, -18, -22, -4, 7, 16, -8, 12, -18],\n [-17, 2, -12, -1, 11, 21, -9, -14, -3, -7],\n [-6, -6, 11, 19, -12,... | 66 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-2, 11, 0, 11, 17, -16, 3, 17, -6, 8],\n [16, 2, 14, -8, -21, -12, 9, 7, -6, 1],\n [22, -19, 9, -4, -20, -19, 2, -14, -2, 0],\n [6, 7, 2, 6, 11, -9, -1, -7, -12, -9],\n [-16, -18,... | 64 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, 17, 8, 5, -13, -17, -8, 4, -13, -2],\n [-4, -19, -1, 15, -8, -17, -12, 21, 7, 17],\n [1, -1, 7, -19, -17, 15, 3, -4, -21, -19],\n [-18, 12, 6, -7, 22, -11, -2, -14, -12, -15],... | 72 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-18, 10, 22, 13, -15, -17, -8, -8, -14, -18],\n [3, 0, -7, 16, 12, -13, 4, -7, -2, -11],\n [-14, -7, -14, 6, 0, 16, 20, 1, -1, 8],\n [-13, 19, 4, 11, 16, 1, -2, -8, -6, 22],\n [-4... | 61 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[22, 2, -8, -3, 11, -9, 7, 21, -10, -9],\n [6, 3, -20, 2, 4, 22, 17, -7, 15, -12],\n [6, 1, 6, 11, -12, -3, -3, -14, 0, 13],\n [4, 1, 17, 2, 2, 10, 8, -13, 16, -8],\n [-22, -7, -2, -21, -20, -8, 9, 4,... | 65 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[-2, -9, 2, -16, 20, -1, 9, 18, 9, 19],\n [7, -6, 17, 15, -2, 3, 20, -20, 15, -6],\n [16, -17, -2, 22, 17, -10, -14, -18, 20, -16],\n [15, 21, 21, 15, 8, -19, -10, 21, -8, 17],\n [-10,... | 384 | 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, -19, 8, -19, 6, -14, -8, 21, 18, -20],\n [-8, -12, -17, -16, -19, -2, -22, 0, -10, 20],\n [5, 6, -5, 0, 5, -14, 20, -17, -7, 14],\n [-22, -1, 0, ... | 62 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-7, 21, -21, -16, -2, 8, 0, 2, 12, 12],\n [22, -16, -18, 9, -18, 2, 8, -3, -1, 15],\n [-10, 16, -21, -1, -14, -21, 22, 9, -15, -7],\n [10, -12, 9, -15, 9, -2, 2, ... | 69 | MATH |
[
{
"content": "Calculate the rounded sum of all singular values from the SVD of:\n[[-10, -3, -2, -1, -22, 17, 18, -6, 22, -19],\n [-17, 22, -4, 7, 0, 9, 6, -15, -2, -6],\n [-6, -2, -8, 4, 2, 10, -21, 19, -7, 13],\n [-15, -7, -16, -18, 0, -15, -20, 12, 13, 13],\n [-8, 7, -8, 6, -19, 11, 0, 12, 5, 8],\n [19, 10, -... | 344 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-16, -3, -4, -15, -20, 4, -8, -15, -5, 6],\n [13, -20, -14, -13, 17, -3, -21, -22, 4, -19],\n [14, 9, -5, -9, 22, -8, -19, -4, 1, 7],\n [-10, -12, 5, -12, -22, 19, -19, 15, 11, -1... | 61 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-8, -7, 22, -9, -8, -11, 20, 12, 2, -9],\n [-21, -5, 12, -14, -12, 3, -20, -18, 9, 18],\n [-13, 15, -17, -12, -6, -21, 18, 1, -18, -2],\n [-17, -19, -14, -18, -19, -14, -5, 20, -7, -21],\n [6, 19, 13, -11, 18, 22, 14, 11, 12, 17],\n ... | 77 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, 6, 3, -22, -6, 16, -21, -8, -1, -3],\n [6, 2, 20, 1, 11, 20, -2, -21, -7, 17],\n [-2, 14, -15, -9, -1, -5, -18, 19, 22, 7],\n [8, -14, 8, 8, 18, -14, 14, -17, 19, 3],\n [-13, ... | 70 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[17, 22, 13, 5, 0, 8, -12, -3, 9, -6],\n [19, 15, -17, -22, 14, -19, 8, -12, -6, -16],\n [12, -21, 17, 14, 14, -13, -11, -6, 3, -18],\n [-18, 15, 4, -18, -15, 8, 10, -2, 12, -2],\n [-8, 13, -21, 7,... | 64 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[1, 13, -14, 17, -7, 4, 22, 14, -10, -21],\n [-11, 18, 10, 0, -9, 16, 7, 11, -14, -8],\n [1, 18, 2, 13, 9, -2, 19, 16, -17, 2],\n [-21, 8, 7, -8, -5, 9... | 66 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[3, 9, -2, -14, 20, -4, -2, -5, -17, 12],\n [-9, -14, 12, -21, -17, 12, 2, -14, 8, -16],\n [5, -21, -22, 14, 1, 12, -16, 15, 6, -22],\n [7, 9, -13, 11,... | 71 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-19, -5, -15, -1, 18, -1, -4, 5, -21, -14],\n [12, -1, 3, 11, -16, 7, 2, -14, 4, -22],\n [10, -15, 9, 17, -4, 13, 22, -1, 16, 3],\n [-20, -14, 12, -16, -8, -19, 14, 5, -14, 12],\n [2, -14, 10, -6... | 359 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 0, 0, 6, -17, 16, -18, 9, 17, 3],\n [-9, -5, -2, 2, -3, 1, -20, -1, -15, 6],\n [-16, -17, -17, -11, -1, 3, 2, -4, 13, 12],\n [-10, 2, 22, 9, 7, -2, 19, 22, 17, 21],\n [-15, 18, 19, -16, -20, 14, -20, -5, 19, -14]... | 73 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[6, -11, 17, -3, 14, -21, -3, -11, 15, 7],\n [-5, -13, -16, 19, -18, 6, 12, 16, -11, -13],\n [14, -21, -20, -9, -3, 22, -19, 3, -8, -14],\n [-20, -21, 16, 18, 7, 14, -6, -20, -14, -15],\n [-14, -6,... | 70 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[18, 9, 20, -12, -20, -2, 20, -9, -17, 6],\n [8, 5, 20, 13, 5, -4, -20, -11, 13, 1],\n [-11, 1, -22, 5, -7, -2, 7, 11, 3, 12],\n [8, -7, 19, 6, 6, -14, -9, -15, -21, -12],\n [-21, -5, -18, -16, 0, -4, -4, -4, 22, 17],... | 77 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-22, 12, 1, 11, -3, -7, 7, 16, 2, -18],\n [6, 14, 5, 18, 0, 9, -5, 18, 12, 20],\n [1, 5, 13, -2, -18, 3, 0, 21, 10, 3],\n [-1, -3, -21, 18, -5, -18, 9, -12, -2, -1],\n [-20, -14, -21, 5, 11, -13,... | 340 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[18, -8, -16, -16, -15, -4, -5, -6, -5, -4],\n [17, -10, -12, -16, 4, 14, -18, -15, -13, 14],\n [3, -8, -7, 6, 5, -13, 17, -19, 17, -9],\n [21, 10, -5, -11, -13, -2, 10, -9, -14, 3],\n [-8, -2, -1, 18, 20, -18, 21, -7, 12, -18],\n [3,... | 81 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[16, -14, -4, -10, 14, -4, -17, -11, -8, -20],\n [-19, 14, 15, -17, 5, -15, 8, -2, 22, 6],\n [-8, 1, -2, 0, 8, 11, 5, 9, -1, -20],\n [-14, -17, -22, -1, -19, 22, -15, 14, 19, -4],\n [21, -22, 18, 1, -6, 9, -9, -6, 9, ... | 72 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[9, -17, 8, -14, 20, -7, 2, 17, 5, -6],\n [8, 0, 8, 3, -19, 16, 20, 20, 20, -8],\n [14, 15, 0, -18, 18, 20, 2, 7, 3, -20],\n [-19, -5, 14, -12, -12, 13, -7, 20, 2, -22],\n [3, 22, ... | 75 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[21, -14, 9, 3, 6, 19, -4, 6, 12, -11],\n [-15, 2, 4, 20, 22, -17, -10, -12, 15, -17],\n [-18, -16, -4, 20, -17, 2, -14, -3, 2, -15],\n [14, 15, -21, -1, 13, -19, -22, 10, 1, -18],\n [12, 19, 3, 20, 18, 20, 3, 18, -18... | 70 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[-3, 18, 20, -18, -8, -21, -11, -16, -21, -15],\n [-14, 4, 5, 14, -8, -4, 7, -10, 22, -17],\n [7, -22, 19, 15, 2, 12, 3, -10, -4, -13],\n [22, -16, -8, 0, 13, 20, 8, -15, 7, 11],\n [10, -22, -7, -12, 4, -1, 17, -4... | 341 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-13, -7, 1, -2, 17, 18, 13, 19, 22, 0],\n [-2, 9, -6, -6, -2, -19, 0, 2, 9, -17],\n [-9, 18, 15, 19, 15, 18, 22, -7, 9, -7],\n [-4, 14, 20, -2, -8, 3, 7, 17, -8, 20],\n [-10, 4, 0... | 66 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[1, -20, -9, -12, 22, 15, 5, 0, -5, -3],\n [10, -21, 16, 14, 3, -21, -20, -3, -13, 19],\n [-2, 17, -14, -21, 5, -20, -7, -19, 0, 7],\n [15, -10, -17, -13, -6, -15, -14, 11, -6, 20],\n [-1, -20, 18, 17... | 76 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[9, 6, 22, 5, 17, -12, -4, -22, -14, -21],\n [-19, 6, -19, -22, 5, -5, -10, 17, -17, 20],\n [16, -1, 7, 4, -15, 20, 5, -21, -3, -12],\n [-9, 1, -10, -15, 21, -2, -1, -14, 19, 20],\n [-12, -7, -14, -20, 13, 19, -10, -22, 21, -12],\n [1... | 74 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[-19, -18, -17, -10, 1, 5, -10, 19, -5, -16],\n [-19, 8, 1, -1, -2, 19, 3, 7, 12, 0],\n [22, 17, 7, -4, 9, -4, -1, -19, 22, -11],\n [-8, -8, -13, -4, -15, 8, -14, 6, -16, -15],\n [18, -6, -8, -7, -16,... | 70 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-15, 12, 16, 13, -17, -16, -11, 16, -22, 20],\n [20, 2, -11, 4, 0, -4, -2, -2, 1, -10],\n [19, 13, -8, -22, 11, 19, 8, 9, 13, 6],\n [-13, -2, 13, 1, 4, -2, -5, -19, -5, -14],\n [7... | 80 | MATH |
[
{
"content": "Compute the rounded largest singular value from the singular value decomposition of the matrix:\n[[17, -21, 4, 22, 21, -15, 15, -7, 1, 0],\n [-9, 4, -13, 5, 2, -21, 22, 10, 12, 18],\n [-10, -18, -18, -1, 11, -22, -6, -14, -13, -8],\n [22, 6, 2, -2, -6, 4, 5, 0, 16, 13],\n [-20, 10, -16, -18, 3, -6... | 73 | MATH |
[
{
"content": "What is the rounded largest singular value in the SVD of the following matrix?\n[[8, -13, 14, -17, -17, 5, 15, -9, -10, -10],\n [-13, -7, 16, 12, -8, 0, 14, -15, 3, -1],\n [-18, 11, 4, -4, 20, 20, 12, 22, -3, 15],\n [-10, -5, -5, -22, 9, 2, -2, 4, -12, -22],\n [-4, 9, -15, -4, -7, 12, -21, -11, 6,... | 71 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-4, -10, 19, 10, -22, 5, 17, -17, -20, 22],\n [2, 21, -7, 20, -19, -15, 16, -7, 21, 15],\n [0, -17, 20, 21, -7, -7, 0, -7, 13, -11],\n [14, -14, -5, -... | 70 | MATH |
[
{
"content": "What is the rounded sum of all singular values in the SVD of the following matrix?\n[[10, -20, -17, 5, -21, 9, 3, -18, -12, -13],\n [-8, -5, -9, 5, 7, -10, -3, -21, 2, 21],\n [20, -11, 2, -19, 19, -11, -16, 15, 17, 9],\n [20, -17, 4, 12, -2, -3, -4, 10, -19, -4],\n [5, -1, 1, 7, 6, -13, 9, -14, 2,... | 353 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[0, -1, -21, -18, 19, -8, 9, -17, -9, 1],\n [-2, -9, -11, -19, 21, -2, -6, 6, -7, -5],\n [15, 18, 21, -12, 9, 5, -7, 11, 7, 15],\n [-1, -18, -14, -10, 16, 0, 4, 9, 8, 10],\n [19, 3... | 67 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[6, -10, 0, -8, 1, 20, 0, -13, 15, -18],\n [-18, 8, 17, -22, -21, 6, -16, 6, -14, 13],\n [-16, 5, -13, -7, -13, 16, 3, 11, 11, 17],\n [-9, -5, -22, -6, -1, 14, -7,... | 87 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-21, 3, 9, 0, 17, -5, -4, 1, -19, -21],\n [7, 15, 8, 17, -7, 10, -20, -5, -13, -21],\n [7, 7, 2, 20, 1, 12, -13, 7, 3, 12],\n [1, -3, 16, 17, 12, 16, -13, 4, -8, -8],\n [14, 12, -... | 76 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-8, -3, 17, -21, 2, -10, 4, -10, 5, -8],\n [6, -2, 21, 8, 0, 14, -20, 12, -9, -21],\n [-10, -21, -11, 4, 11, 17, -18, 2, -12, -10],\n [5, -2, 3, 4, 3, -8, -17, -19, -19, 7],\n [-10, -14, 19, -9, 5, 17, -20, 18, 6, 10],\n [-8, 16, -8,... | 72 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[4, -6, 22, -6, -18, 1, -15, 21, -14, -5],\n [-7, 9, 17, 16, 18, 21, 9, 19, -21, 15],\n [20, -19, -18, 14, 14, 3, 20, -14, -8, 1],\n [1, 12, 18, 2, 3, 0, -17, 18, 4, -4],\n [8, 15, 20,... | 358 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[-8, -13, -21, -21, -2, -11, -13, -11, 16, -21],\n [-22, -21, 0, 5, -6, 17, -2, 21, 11, -14],\n [-6, 19, 22, 9, -18, -9, 2, -1, -18, 15],\n [-14, 8, 18, -2, 13, -22, -1, 0, 0, -8],... | 71 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[17, -4, 10, 0, -14, 15, 22, 22, -5, -21],\n [-6, -7, 22, 1, 8, -22, 5, 10, 19, 14],\n [16, -19, -22, 10, -13, -20, 14, 22, -2, -14],\n [17, 20, 1, -15, 1, 1, -13, 12, -19, 21],\n [-14, -12, 20, -1... | 74 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded difference between the largest and smallest singular values:\n[[-19, 21, 15, 8, -18, 2, 5, -4, 14, 19],\n [0, 13, 22, -10, -6, 7, 0, -20, -10, 9],\n [22, 12, -21, -20, 6, -13, -3, 11, -8, 17],\n [22, -22, 3, 9, -21... | 68 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-20, -2, -11, -9, 0, -10, -7, -6, -5, -10],\n [3, 22, 17, 16, 8, 17, -6, 9, -22, 12],\n [13, -4, 5, -21, 6, 20, 6, 20, -4, 5],\n [11, 8, 14, -4, 9, 6, -14, -16, -... | 67 | MATH |
[
{
"content": "What is the rounded difference between the largest and smallest singular values in the SVD of the following matrix?\n[[19, 13, -19, 19, -13, -10, -17, -16, 5, 14],\n [-8, 7, 17, -13, -11, -6, 7, -22, 13, 17],\n [1, 15, -2, 19, 9, -5, -10, 14, 21, -2],\n [-5, 17, 3, -18, -18, 8, 5, -10, -12, -22],\... | 65 | MATH |
[
{
"content": "Compute the rounded difference between the largest and smallest singular values from the singular value decomposition of the matrix:\n[[-20, -7, -15, 22, -18, 15, 12, -15, 13, 2],\n [-15, -2, -14, 9, 21, -10, 0, -15, 12, 5],\n [-8, 6, -19, 11, 14, 1, -2, -21, -16, -12],\n [-11, -19, 12, 17, 3, -5,... | 67 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[0, -2, -4, 2, 0, -4, -18, -4, 12, -11],\n [16, 2, -18, -11, 4, -19, -4, 22, 1, 19],\n [5, 10, 12, -7, -11, -7, -12, 20, 5, 0],\n [-6, -4, -12, -19, -13, -4, 13, 20, 16, 18],\n [-1, -21, 10, 17, 4, -4, -19, -4, 2, -17],\n [-10, -1, -1... | 78 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[-21, 0, 21, 7, 15, 16, -14, -16, 21, -8],\n [-8, -2, -9, -12, -12, -3, -10, 22, 7, 17],\n [16, -3, 22, 20, 15, -15, 14, 19, 10, 3],\n [21, 16, -15, -5, 16, -9, -5, -2, 0, -19],\n [-13, 20... | 79 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[14, 19, 6, 5, -2, 10, 3, 15, -8, -21],\n [-11, 10, -8, 22, -22, 10, -19, 5, -9, 22],\n [-11, -17, -3, -2, -7, -11, -3, 22, 10, -21],\n [11, 3, 10, 19, 7, -22, -15, -22, -13, 9],\n [17, -21, 8, -1... | 349 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded largest singular value:\n[[6, -12, -1, 16, -17, 7, 20, 2, 13, -22],\n [-1, -14, 22, -15, 11, -7, -4, -15, -11, 20],\n [18, 8, 19, 10, -4, 4, 1, 5, -19, -11],\n [0, -3, 17, 5, -22, 18, -12, 21, 8, 18],\n [15, -14, -... | 69 | MATH |
[
{
"content": "Calculate the rounded largest singular value from the SVD of:\n[[-11, -13, 6, -2, -10, 0, -17, 8, -14, 1],\n [-7, -12, 13, -22, -2, 21, 13, 14, -17, -9],\n [6, -22, -15, 21, -4, 0, 16, 18, -12, 4],\n [17, 13, 19, -3, 19, -15, 13, 3, 12, -20],\n [-19, 21, 6, 5, -4, 20, 5, -5, -9, 20],\n [-9, 6, -20... | 76 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[5, 16, 20, 6, 12, -1, -14, 13, -15, 7],\n [7, 8, -1, 21, 8, 17, 5, -18, -6, -12],\n [-1, 2, -10, 13, 22, 22, -12, -18, -9, -1],\n [-20, 12, 9, 15, 17, 1, 5, -2, 10, 5],\n [16, 13, -13, 14, 17, 2,... | 363 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[8, -6, -7, -13, 12, 10, 15, 12, 4, -16],\n [4, 18, -11, 10, -10, -21, -20, -12, -18, -21],\n [5, -10, 12, 17, -10, -11, -5, -5, -6, 16],\n [-1, -10, 22, 15, -4, 1, -4, -2, 1, 7],\n [5, 12, 15, -6... | 333 | MATH |
[
{
"content": "Calculate the rounded difference between the largest and smallest singular values from the SVD of:\n[[-17, 6, -21, 2, 9, 3, 3, 15, -1, -13],\n [0, -19, -7, 19, 10, -10, 21, -10, 10, -9],\n [-15, 3, -1, -22, -7, 21, 6, 0, -18, -2],\n [13, -3, 20, -15, 3, 18, 2, 19, -16, -1],\n [10, -18, 15, -11, 21... | 69 | MATH |
[
{
"content": "Find the Singular Value Decomposition (SVD) of the matrix and determine the rounded sum of all singular values:\n[[9, -20, -10, 5, -1, -4, 8, -3, 1, 9],\n [-14, -4, 0, 2, 10, 21, -21, -20, 5, 14],\n [12, -9, 1, 14, -20, 0, 11, -14, -5, -21],\n [-1, 12, 8, 3, -9, 22, 5, -12, 9, -2],\n [0, 1, -11, -... | 347 | MATH |
[
{
"content": "Compute the rounded sum of all singular values from the singular value decomposition of the matrix:\n[[-2, 1, 7, -7, 18, -1, -21, -4, 14, -21],\n [-12, 10, -14, 2, -17, -12, 4, -15, 22, 8],\n [4, 21, 18, -18, -8, -21, -8, 8, -3, -20],\n [19, 16, -13, 3, -13, 17, -10, -2, 11, 21],\n [9, -14, 7, -22... | 367 | MATH |
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