messages listlengths 1 1 | ground_truth stringlengths 5 12 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^6 and find the value at position (3, 8) of the result:\nA =\n[[-10, 12, 7, -9, -1, 0, -11, 6],\n [-9, 10, 0, 6, -5, -5, 3, -2],\n [5, -9, 11, -12, -12, 1, -9, -2],\n [5, 3, 4, 11, -11, -9, -10, 2],\n [-11, 11, 6, -4, -3, 8, 12, 6],\n [-8, 1, -3, 3, -7, 12, -5, -11],\n ... | -6097947 | MATH |
[
{
"content": "Find the value at position (3, 7) of the 6th power of the matrix:\n[[11, -8, -4, 4, 1, -2, 2, 0],\n [-8, -3, 0, 0, -4, -4, -1, -6],\n [-4, 0, -9, 6, 0, 3, 2, -2],\n [4, 0, 6, 9, 4, -7, 6, 2],\n [1, -4, 0, 4, -6, -2, 4, -4],\n [-2, -4, 3, -7, -2, -1, -4, -6],\n [2, -1, 2, 6, 4, -4, 10, 2],\n [0, -6... | 3926280 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 0, 12, -11, 8, 5, 0, -2],\n [0, 1, -2, 10, -7, -2, 3, 8],\n [12, -2, -9, -1, 0, 9, 3, 0],\n [-11, 10, -1, -2, 0, 2, -6, 2],\n [8, -7, 0, 0, 8, 2, 3, -2],\n [5, -2, 9, 2, 2, 6, 2, -2],\n [0, ... | 127767777 | MATH |
[
{
"content": "Find the sum of all entries of the 6th power of the matrix:\n[[1, 2, -8, 0, 2, 10, 2, 0],\n [2, 6, 1, 0, -6, 0, -2, 0],\n [-8, 1, -12, 4, -2, 0, 8, 4],\n [0, 0, 4, 9, -4, -2, 9, -4],\n [2, -6, -2, -4, 2, 4, 8, 0],\n [10, 0, 0, -2, 4, -8, -4, 2],\n [2, -2, 8, 9, 8, -4, 12, -2],\n [0, 0, 4, -4, 0, 2... | 283349654 | MATH |
[
{
"content": "Calculate the matrix power A^6 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 11, 4, 4, 8, 3, -4, -11],\n [-2, 2, -10, 11, 3, 8, 6, 9],\n [-7, 1, -8, -8, -7, 5, 9, 5],\n [6, -11, 4, -12, -4, 0, -9, -8],\n [10, 5, -3, 12, -9, 0, 0, 4],\n [-5, -9, 10, -10, -2, -1, -4, 2... | 764832179 | MATH |
[
{
"content": "Find the value at position (4, 8) of the 5th power of the matrix:\n[[0, 9, -4, 11, -3, 6, -7, -6],\n [2, 9, 6, 1, 3, 1, 12, 7],\n [-11, -4, -10, -7, -8, 1, 2, 5],\n [4, -4, 6, 10, 12, -4, 3, -7],\n [-5, 12, -10, 9, -8, -6, 10, 12],\n [-12, 9, 8, -9, 3, 1, -12, -9],\n [-3, -2, -6, -9, -12, -12, 4, ... | -2075986 | MATH |
[
{
"content": "Find the sum of all entries of the 6th power of the matrix:\n[[-2, -2, -5, 10, 1, -4, 2, -8],\n [-2, -9, -6, -8, 10, 2, -6, -4],\n [-5, -6, -4, 6, -4, -5, 1, -4],\n [10, -8, 6, -6, -6, -1, -8, -1],\n [1, 10, -4, -6, 3, 5, 4, -6],\n [-4, 2, -5, -1, 5, 9, -6, -7],\n [2, -6, 1, -8, 4, -6, 10, -8],\n ... | 1332335199 | MATH |
[
{
"content": "For the matrix power A^7 where A =\n[[9, 9, 9, -11, -2, -3, 10, 0],\n [-6, -3, -9, 9, 7, 3, 7, -7],\n [-4, 0, -6, 5, 1, 9, -8, 9],\n [0, 11, -5, 2, 6, -4, -7, 10],\n [12, 1, 10, -3, -4, 4, 0, 4],\n [6, 0, -4, -12, -12, -8, -5, 5],\n [-9, 9, -12, 2, 7, -9, 12, -4],\n [9, 11, 7, -3, 11, 2, -10, -11]... | 2987082498 | MATH |
[
{
"content": "Find the value at position (4, 7) of the 7th power of the matrix:\n[[9, -8, 11, -12, -2, -1, -10, 10],\n [3, 1, -1, 7, 3, 8, -5, 4],\n [4, -6, 2, -4, -9, -5, -3, 2],\n [10, 5, 1, -8, -4, 0, 12, 6],\n [-2, -1, -10, -11, 10, 9, 2, -8],\n [-6, -9, -8, 12, 3, 2, 3, 12],\n [-9, -7, 5, -10, 12, 9, 11, -... | 58643866 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[11, -6, -2, 7, 0, 0, -2, -4],\n [-6, -7, -4, 0, 3, 1, -5, -2],\n [-2, -4, 9, -10, -6, -2, 0, -2],\n [7, 0, -10, 3, 2, 3, -2, -4],\n [0, 3, -6, 2, 9, 1, 0, 4],\n [0, 1, -2, 3, 1, 6, 2, 4],\n [-2, -5, 0, -2, 0, 2, 8, 8],\n [-4, -2, -2, -4, 4, 4, 8, 12]], determi... | 1392875159 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^6 where A is:\n[[7, -2, -2, 6, -1, -4, 2, -6],\n [-2, -12, -4, -2, 2, -8, 9, 2],\n [-2, -4, 5, -6, -7, 6, 0, -4],\n [6, -2, -6, 5, 0, 4, 8, -2],\n [-1, 2, -7, 0, -9, -3, -2, 8],\n [-4, -8, 6, 4, -3, 5, 0, -3],\n [2, 9, 0, 8, -2, 0, ... | 1080489830 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-12, 4, 6, 10, -5, -4, 9, 0],\n [4, 9, -1, -3, -8, -1, -4, 0],\n [6, -1, -1, 2, 0, 4, -4, 0],\n [10, -3, 2, -4, 4, 8, 2, -8],\n [-5, -8, 0, 4, -2, -6, 8, -4],\n [-4, -1, 4, 8, -6, 4, 0, -4],\n [9, -4, -4, 2, 8, 0, -1, -10],\n [0, 0, 0, -8, -4, -4, -10, 2]], de... | 67877906 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[7, 0, 8, -6, 8, -6, -5, -2],\n [0, -11, 1, 9, -2, -2, -4, 3],\n [8, 1, 10, 0, 2, -2, -5, 8],\n [-6, 9, 0, -7, 1, 0, 12, -10],\n [8, -2, 2, 1, 1, -4, -7, -5],\n [-6, -2, -2, 0, -4, 11, 7, -6],\n [-5, -4, -5, 12, -7, ... | 259959960 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 3) of the result:\nA =\n[[1, 4, -6, 3, 9, -1, 3, 4],\n [4, 6, -4, 0, -7, 4, 0, 6],\n [-6, -4, 6, -4, -1, -10, -5, -8],\n [3, 0, -4, 2, -6, -4, -8, 8],\n [9, -7, -1, -6, 4, -2, 2, -2],\n [-1, 4, -10, -4, -2, 3, -8, 1],\n [3, 0, -5, -... | -2547859 | MATH |
[
{
"content": "Find the value at position (7, 5) of the 7th power of the matrix:\n[[-8, 10, 0, -1, -6, -4, 2, 2],\n [10, -4, -6, 6, 0, -1, -8, -11],\n [0, -6, -7, -8, 4, -8, -2, -2],\n [-1, 6, -8, 10, 1, 2, 1, 2],\n [-6, 0, 4, 1, -8, 7, 6, -2],\n [-4, -1, -8, 2, 7, 2, -8, 5],\n [2, -8, -2, 1, 6, -8, -4, -5],\n [... | 2509292624 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[11, -8, 11, -6, -6, 10, 12, 9],\n [9, -4, 2, -7, 3, -6, 2, 10],\n [-11, -5, -1, -2, -7, 7, 0, 10],\n [3, -5, 4, 0, -9, 7, -3, 12],\n [9, 7, 3, 4, -5, -2, 12, -8],\n [8, 3, 11, -5, 8, 3, -9, -7],\n [8, -5, -4, 0, 4, -4, 0, -4],\n [-7, -3, -8, -6, -2, 11, -4, 12... | -88087700 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-3, -2, -10, -5, 4, -6, -1, 3],\n [2, 8, 0, 5, 5, 11, -8, 1],\n [-2, -10, 4, 10, -1, -10, 10, -11],\n [-9, 5, 7, 8, 1, -5, -11, 6],\n [-3, -8, -2, -4, 3, -8, 2, 1],\n [-4, 7, -8, 2, -4, -9, 8, 8],\n [-9, 7, 8, 9, -6, 2, 9, 4],\n [5, -6, 6, -3, 0, -11, 9, 7]], ... | -1532429 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^6 where A is:\n[[-2, -8, -4, -10, -9, -6, -7, 10],\n [-8, -6, -2, 2, 6, -5, 0, 10],\n [-4, -2, 6, 0, 2, -2, -4, -2],\n [-10, 2, 0, -5, -4, -4, 4, 0],\n [-9, 6, 2, -4, 7, -2, 4, 2],\n [-6, -5, -2, -4, -2, 11, 3, 1],\n [-7, 0, -4, 4, 4, 3, 8, 4],\n [10,... | 888239873 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (8, 3) of the result:\nA =\n[[-11, -11, 5, 4, -4, -5, -11, -11],\n [-8, -1, 3, 1, 7, -11, 11, -5],\n [-9, 7, -4, 7, 12, 6, -11, 3],\n [-2, -5, -1, -10, 0, -11, 0, -5],\n [2, 11, 8, -4, -2, 9, 8, -10],\n [-6, 1, 2, -4, 7, -2, -6, -1],\n ... | 1271066 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[12, -5, 10, 1, 11, 3, -9, 5],\n [1, -4, 2, -10, -9, 10, 5, 1],\n [2, -5, -3, 11, -1, 8, -4, -5],\n [4, -4, 0, 1, -8, -4, 12, 3],\n [6, 11, 10, -6, -1, -11, 5, 5],\n [3, -2, -11, 1, -9, -6, -11, 8],\n [1, -6, -4, -5, -4, -6, 6, 4],\n [10, 0, -2, 9, 5, 4, 3, -3]... | 2163942 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-9, -9, 9, -2, 8, 12, -5, -4],\n [3, -3, 10, -4, -10, 12, -11, -4],\n [0, -7, -9, 1, -2, -11, -10, -8],\n [12, -6, -2, -1, -2, 6, 0, -9],\n [1, -1, -11, -5, 9, 6, 0, 8],\n [8, -12, -8, 9, -2, -2, 0, -11],\n [6, 3... | -801144016 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-10, 4, 0, -4, 0, 3, 6, 1],\n [-5, 9, 6, 12, 11, -10, 10, 8],\n [5, 3, 1, 3, 11, 4, 7, -2],\n [0, -2, -9, 1, -8, -9, -12, 1],\n [-6, -3, -11, -3, -10, 8, -5, -3],\n [-5, 1, 5, -4, 9, -4, -9, -10],\n [1, 1, 8, 3, -8, 7, 10, 11],\n [2, 8, -4, -6, 0, 10, -5, -1]]... | 1063017 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (8, 8) of the result:\nA =\n[[-9, -2, -8, -6, -8, -5, -6, -2],\n [-2, 2, 6, -4, 8, -10, 4, -4],\n [-8, 6, -12, -9, 2, 8, -2, -4],\n [-6, -4, -9, -1, -8, 5, 10, -6],\n [-8, 8, 2, -8, -6, -6, 4, 10],\n [-5, -10, 8, 5, -6, 7, 4, 6],\n [-6,... | -66164 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the value at position (7, 1) of the result:\nA =\n[[-8, 9, -4, -12, 2, 11, -9, -6],\n [-7, 2, -7, -6, 7, 9, -10, 8],\n [0, -11, -10, 0, -4, 9, 6, 5],\n [-8, -3, 1, 8, 4, -10, -6, -4],\n [-8, -9, -10, 0, -4, 10, -6, -5],\n [-3, -12, 7, 8, 8, -12, 6, -11],\n [... | 73669825 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-9, -7, -1, 6, 6, 0, 5, -1],\n [-7, -7, 4, -2, 0, 6, -4, 7],\n [-1, 4, -9, -2, 0, -3, 6, -2],\n [6, -2, -2, -1, -10, 2, 4, -3],\n [6, 0, 0, -10, -8, 5, 2, 5],\n [0, 6, -3, 2, 5, 12, 4, -3],\n [... | 17380896468 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[10, 0, -2, 8, 5, -4, -5, -6],\n [0, -2, 5, 2, 4, -3, -2, -4],\n [-2, 5, 0, -2, 2, 0, -10, 4],\n [8, 2, -2, 3, 6, -4, 0, 10],\n [5, 4, 2, 6, -8, 0, 2, 11],\n [-4, -3, 0, -4, 0, -10, 4, 4],\n [-5, -2, -10, 0, 2, 4,... | 5998473 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[11, -12, -9, -4, -11, -10, -7, 0],\n [2, -2, -3, -10, 7, -4, 12, -3],\n [8, 10, 12, 11, 10, -1, -5, 8],\n [8, 8, 4, 9, -8, 11, -5, 5],\n [-2, 9, -3, 2, -7, 6, 4, 10],\n [-3, -8, 3, -1, 8, 11, -8, 8],\n [-12, -11, -8, 10, 6, 2, -12, -2... | -10341720 | MATH |
[
{
"content": "Calculate the matrix power A^6 and find the sum of absolute values of all entries of the result:\nA =\n[[-10, 8, 8, -4, -6, 8, 10, -4],\n [8, 3, 0, 6, 4, -4, -2, -8],\n [8, 0, -8, 2, -3, 4, 0, 3],\n [-4, 6, 2, -10, 2, 1, -8, 4],\n [-6, 4, -3, 2, 0, 0, 10, -3],\n [8, -4, 4, 1, 0, 8, -3, 4],\n [10, ... | 1810522431 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 6th power of the matrix:\n[[2, 3, -8, 4, -2, -4, 4, 4],\n [3, -3, 6, 0, -3, 8, -9, 7],\n [-8, 6, 1, 4, 0, -8, -4, -8],\n [4, 0, 4, -6, 12, 2, -2, 0],\n [-2, -3, 0, 12, 10, 7, -5, 4],\n [-4, 8, -8, 2, 7, 0, -2, -9],\n [4, -9, -4, -2, -5, -2, -5,... | 1881292592 | MATH |
[
{
"content": "Calculate the matrix power A^6 and find the value at position (2, 1) of the result:\nA =\n[[12, 12, 12, -10, 2, -3, -3, 11],\n [-10, -7, -8, 11, 6, 1, 4, -1],\n [-4, 12, -10, 5, -9, 1, 11, -7],\n [2, 4, 11, -8, -7, 8, -8, 6],\n [1, -9, -8, -2, -11, 9, -11, 7],\n [-1, 3, 4, -9, 1, -6, 2, 3],\n [-5,... | 4396600 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-1, 3, -4, 8, -4, 4, 1, -4],\n [3, 7, -6, -12, -2, -3, 0, 0],\n [-4, -6, 11, -6, -2, 4, -4, -2],\n [8, -12, -6, 12, 0, -4, -2, -4],\n [-4, -2, -2, 0, 7, 5, 0, 4],\n [4, -3, 4, -4, 5, -10, 1, -8],\n [1, 0, -4, -2, 0, 1, -9, 10],\n [-4, 0, -2, -4, 4, -8, 10, -10... | 1564056996 | MATH |
[
{
"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-1, 5, 2, 12, 1, -4, -8, 2],\n [-5, 10, -10, -1, -8, -4, 7, -10],\n [10, -5, 8, 0, -5, -8, 12, -6],\n [-8, -4, -8, -5, -1, -9, -4, 9],\n [9, 1, 6, 0, -10, -9, -12, 9],\n [-12, -2, 3, -9, -6, -1, -7, 11],\n [7, -4, -5, 1, 2, 8, 9, -8],\... | 2862085399 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^6 where A is:\n[[-11, -10, -6, 7, 4, -4, 9, -4],\n [6, -8, 12, -7, 5, -12, 12, 4],\n [1, 2, -8, 4, 8, 8, 10, 10],\n [-2, -3, 4, 12, -12, -8, 3, -6],\n [-1, -5, 5, -12, 7, -1, -9, -1],\n [9, -12, -12, -10, 8, -1, 9, 8],\n [0, 0, 8, -... | 1264512556 | MATH |
[
{
"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-9, 12, 7, -12, -9, 10, -10, -3],\n [9, -12, -9, 6, -12, 3, 6, 7],\n [8, 9, 5, -11, -7, 8, -12, 6],\n [-8, -11, -12, 3, 12, 8, -11, -9],\n [-10, 10, 4, 2, -3, -1, -1, 7],\n [-6, -3, -8, 7, 7, -2, -11, 11],\n [3, -1, 3, -9, -11, 12, -3,... | 3073033347 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the value at position (8, 5) of the result:\nA =\n[[7, -4, -7, -10, 9, -11, 5, 10],\n [6, -6, -10, 5, 7, 7, 6, -4],\n [3, -7, 8, -1, -7, 0, 11, -8],\n [0, 7, -6, -1, 8, -9, -8, 3],\n [-9, -5, 3, -5, 4, 1, -1, -10],\n [7, -11, 0, 8, -2, 11, -1, 5],\n [-4, -6,... | 10099753 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-8, 7, -7, -1, 8, -10, 1, 8],\n [-9, 4, 4, 1, 2, -6, -9, 4],\n [-7, -2, -1, 2, -1, -2, 4, -5],\n [-1, -4, -2, -10, -6, 8, -10, 8],\n [3, -3, 10, -6, 12, 11, 7, 2],\n [8, 8, -3, -1, 5, 10, 10, -... | 9393921410 | MATH |
[
{
"content": "Find the sum of all entries of the 6th power of the matrix:\n[[4, 8, 10, -8, 0, -10, 10, 4],\n [-2, -12, 5, 4, -4, 7, -6, -8],\n [3, -6, 0, 0, 2, 10, 4, 4],\n [6, -3, -11, 1, 10, -10, -6, 12],\n [-2, 4, 2, 6, -2, 2, 2, -7],\n [2, -4, -8, 6, 11, -8, 9, 0],\n [5, 7, 4, 2, 1, 3, -9, 4],\n [7, 1, 5, -... | -4742481 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-12, 0, -10, -7, 4, -5, -7, 3],\n [-12, -3, 5, 9, 1, 11, -8, 4],\n [1, 5, -9, 7, 10, -11, -6, -6],\n [-6, 0, 6, 9, -7, 7, 4, 12],\n [5, 12, 11, -12, 10, 0, 6, 3],\n [-3, 0, -3, 1, -4, 8, -2, -1... | 50128274462 | MATH |
[
{
"content": "What is the value at position (4, 7) of the matrix A^5 where A is:\n[[10, 6, -2, -6, -2, -2, 10, -4],\n [6, -1, 0, 2, 0, -2, -2, -6],\n [-2, 0, 12, 0, -2, -2, 9, -2],\n [-6, 2, 0, -6, -4, 4, 2, 2],\n [-2, 0, -2, -4, 12, 3, 4, 5],\n [-2, -2, -2, 4, 3, 4, 6, -1],\n [10, -2, 9, 2, 4, 6, -6, -11],\n [... | 1146996 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-1, -10, 8, -10, 6, 3, -6, -4],\n [-10, 0, 1, 0, 4, 2, -2, 6],\n [8, 1, -1, -7, -6, 3, 0, -6],\n [-10, 0, -7, -4, -7, 8, 9, 1],\n [6, 4, -6, -7, 0, -9, 2, 2],\n [3, 2, 3, 8, -9, 5, 4, 0],\n [-6, -2, 0, 9, 2, 4, 1... | 1000645654 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, 6, -8, -8, 4, 5, 10, -7],\n [6, -3, -4, 4, 8, -7, 4, 6],\n [-8, -4, 8, 0, -3, 6, 0, 1],\n [-8, 4, 0, -7, 4, -6, -3, 0],\n [4, 8, -3, 4, 7, 0, 4, -1],\n [5, -7, 6, -6, 0, 12, -2, -10],\n [10, 4, 0, -3, 4, -2, -8, 2],\n [-7, 6, 1, 0, -1, -10, 2, 4]], determin... | 4474129 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-11, 9, -1, 4, -7, 4, -11, -5],\n [1, -7, -4, -12, -8, -6, -4, 1],\n [-4, -9, 7, 2, -9, -10, 11, 8],\n [10, 9, 1, -4, 6, -7, -10, 5],\n [3, -10, -11, -11, 10, -3, 2, -10],\n [-5, 5, -2, -6, 6, 12, -6, 12],\n [-11, -7, -8, 1, 5, -9, -9, 11],\n [0, 10, 8, 12, -1... | 140032885 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-10, -2, 3, 3, -4, 4, -5, 6],\n [-2, -6, -4, 6, 4, -2, -3, 2],\n [3, -4, -8, 0, 9, -1, 0, -5],\n [3, 6, 0, -12, -6, -4, -2, -8],\n [-4, 4, 9, -6, -12, 9, 0, 10],\n [4, -2, -1, -4, 9, -6, 7, 8],\n [-5, -3, 0, -2, 0, 7, 0, -6],\n [6, 2, -5, -8, 10, 8, -6, 10]], ... | 4004631 | MATH |
[
{
"content": "Find the value at position (7, 7) of the 6th power of the matrix:\n[[3, -1, 4, 12, 2, 12, -10, -8],\n [0, 11, -7, -4, 6, -6, 0, 9],\n [-8, 3, -9, -8, 7, 6, 10, -7],\n [-9, 12, -12, 4, -4, 3, 10, -11],\n [-2, -8, 0, 7, 4, 12, 2, 9],\n [-1, -7, 7, 0, 5, 11, 2, 2],\n [-5, 6, 10, 1, -6, 1, -8, 2],\n [... | 77921244 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (5, 4) of the result:\nA =\n[[-12, 0, 0, 8, 0, 3, 2, 0],\n [0, 1, 6, -4, 0, 10, 0, 0],\n [0, 6, -10, -10, 4, -2, 12, -6],\n [8, -4, -10, 10, 0, -4, 5, 0],\n [0, 0, 4, 0, -7, 4, -2, -2],\n [3, 10, -2, -4, 4, 11, 3, 0],\n [2, 0, 12, 5, -2... | 457516 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-4, -10, -7, -10, -12, 9, 8, -10],\n [1, 7, -11, -1, -3, 0, 7, -9],\n [6, 9, -12, 12, -2, 3, 6, 6],\n [-1, -10, 10, 11, 5, 4, -8, 3],\n [11, 1, 6, -7, -10, -7, -1, 7],\n [-2, -6, -12, 3, 3, 4, 2, 8],\n [-4, -8, 7, -5, 8, -12, -6, -2],\n [7, 8, 0, 9, 0, -6, -2,... | 62443373 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-12, -1, -10, -12, -9, -7, -8, -2],\n [7, 10, 0, -2, -7, 6, 12, 2],\n [8, 0, -3, -12, 0, -7, 8, 11],\n [7, -1, 4, 5, 11, -5, 1, -8],\n [9, -11, 12, 9, 12, -2, -10, 9],\n [3, 8, 3, -4, 0, -3, 4, 12],\n [8, 4, -3, -5,... | 124407228620 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[0, 7, 9, 0, 10, -4, 8, -6],\n [7, -4, 0, 8, -10, -8, -1, 2],\n [9, 0, 1, 2, 11, -2, -2, -4],\n [0, 8, 2, 2, 8, 2, 9, -2],\n [10, -10, 11, 8, -3, -2, -9, -10],\n [-4, -8, -2, 2, -2, 9, 6, -6],\n [8, -1, -2, 9, -9,... | -5068042 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^6 where A is:\n[[-5, -1, -2, 7, -2, 0, 0, -8],\n [-1, 7, 2, 0, 10, -8, 0, 2],\n [-2, 2, -7, -8, 0, 1, -3, -2],\n [7, 0, -8, 6, -2, 2, -4, 2],\n [-2, 10, 0, -2, 0, 1, -6, 11],\n [0, -8, 1, 2, 1, -4, 2, 0],\n [0, 0, -3, -4, -6, 2, 7, ... | 867299204 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-10, 11, -7, -6, -4, -8, 3, -11],\n [-10, -10, 7, 10, -3, 9, -10, 2],\n [1, 10, -9, -3, -2, -2, -5, 10],\n [10, -4, -5, -1, 4, 10, 2, 6],\n [7, -7, -8, -5, 5, 8, 8, 2],\n [-10, 1, 2, 0, 8, 7, 8, -4],\n [10, 4, 6, 12, -9, 7, -3, 9],\n [... | 15636887 | MATH |
[
{
"content": "Calculate the matrix power A^6 and find the value at position (7, 2) of the result:\nA =\n[[11, 1, -6, 6, 4, 3, -2, 0],\n [1, 9, 2, -1, 10, 2, -2, -4],\n [-6, 2, -8, -4, -4, 2, -8, 4],\n [6, -1, -4, 10, -1, 6, -4, -4],\n [4, 10, -4, -1, -4, -2, 6, 6],\n [3, 2, 2, 6, -2, 3, -4, 8],\n [-2, -2, -8, -... | -1380592 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-12, -8, 7, 1, 5, 0, 10, -1],\n [2, 11, -9, -4, -10, 9, -2, 2],\n [3, -6, -6, 9, -4, 4, 0, -4],\n [-4, 7, -1, 8, 6, 10, 2, 5],\n [-5, 12, -7, 12, -7, -10, -10, -11],\n [-8, 7, -1, -7, 3, -8, -7, -9],\n [1, -10, 4, -8, 9, 8, 8, -7],\n [7, -9, 0, -5, -2, 11, 6, ... | -15674754 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-8, -8, -10, -11, -10, 2, -6, -10],\n [2, -2, 3, 0, -11, 7, -1, 8],\n [-6, -12, 1, 11, -3, -10, -2, 9],\n [7, 8, 2, -7, 5, 0, 2, -10],\n [2, 11, 11, -12, -3, 11, 5, -5],\n [-1, -8, -12, -5, -8, 4, 2, -9],\n [0, 4, 0, 12, -11, 11, -9, 12],\n [-11, -1, 6, 5, -3,... | 2715040250 | MATH |
[
{
"content": "For the matrix power A^7 where A =\n[[-10, 4, 2, 1, 11, 2, 3, -9],\n [6, 11, 12, -5, -7, 3, -10, -5],\n [-8, -8, -1, 12, -12, -6, 11, -2],\n [-3, -10, -5, -12, -5, 10, 7, -2],\n [-6, 3, -6, 0, -3, 4, -10, -6],\n [-2, 0, -8, 12, 10, 6, 2, -12],\n [-8, 0, -3, -8, 10, -12, -3, 5],\n [9, -5, 7, -10, 6... | -53394370 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 8, -3, 8, 3, -8, 7, -10],\n [-10, -11, 8, -9, 9, 5, -11, 11],\n [-7, -10, 8, -10, -11, -10, 4, 1],\n [-6, 9, 8, -7, -5, 6, 6, -1],\n [-8, -8, 1, 4, 3, -9, 12, -5],\n [-10, 8, -8, 10, 11, 12, -6, 5],\n [11, -5, -2... | 94550169 | MATH |
[
{
"content": "Calculate the matrix power A^6 and find the sum of all entries of the result:\nA =\n[[10, -2, 7, -5, -4, 3, -1, -8],\n [-2, -5, 6, 7, -2, -2, 10, -4],\n [7, 6, 3, 6, 4, 5, 6, 2],\n [-5, 7, 6, 4, 6, 1, -10, 2],\n [-4, -2, 4, 6, 9, -4, 0, 4],\n [3, -2, 5, 1, -4, -8, -6, 6],\n [-1, 10, 6, -10, 0, -6,... | 333067725 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[0, 0, 11, 4, -7, -11, 4, -1],\n [10, -7, -8, -8, 12, -4, 9, -10],\n [10, 7, -8, -6, -1, -6, -3, -5],\n [4, -8, 2, -4, 10, -2, 0, 5],\n [4, 11, -4, -3, -8, -2, 9, 2],\n [-11, 8, 7, 11, 11, 1, -8, 11],\n [-7, 9, 2, -9, -3, 6, -4, 8],\n [-3, -9, 9, -9, -7, -5, 3,... | 1460313921 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^6 where A is:\n[[3, -4, 0, -3, 4, 2, 4, 4],\n [-4, -1, -4, -6, 2, -6, 0, -2],\n [0, -4, 7, 4, -3, 2, -4, 4],\n [-3, -6, 4, -5, 2, -8, 7, -6],\n [4, 2, -3, 2, -6, 3, 12, 1],\n [2, -6, 2, -8, 3, 4, 5, 8],\n [4, 0, -4, 7, 12, 5, -12, 0],\n [4, -2, 4, -6,... | 416956912 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-9, 2, -4, 0, 6, -4, -2, 2],\n [2, 8, 2, 9, 0, 8, 0, -7],\n [-4, 2, -4, 6, 0, 3, 2, -1],\n [0, 9, 6, 9, -1, 4, 4, 2],\n [6, 0, 0, -1, 2, 6, 2, 2],\n [-4, 8, 3, 4, 6, -8, -1, 4],\n [-2, 0, 2, 4, 2, -1, 10, -3],\n [2, -7, -1, 2, 2, 4, -3, -1]], determine the val... | -475363 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-9, 10, 11, 1, 9, -10, 8, 4],\n [0, -5, -1, -1, -1, -11, -3, 10],\n [-4, -12, -9, 10, 1, 3, 12, 5],\n [-11, -7, -10, 7, 6, 0, 4, 1],\n [9, -2, 3, -2, 5, -11, 10, 8],\n [-5, 1, -11, 0, -3, -5, -... | 135352410 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[12, 0, 0, -4, 4, -2, -6, 5],\n [0, -11, 0, 5, -5, 2, 0, 10],\n [0, 0, -4, 4, 1, 0, -4, -7],\n [-4, 5, 4, 10, -1, -6, 1, 8],\n [4, -5, 1, -1, 12, -4, 3, 10],\n [-2, 2, 0, -6, -4, 5, -6, 2],\n [-6, 0, -4, 1, 3, -6, 11, 0],\n [5, 10, -7, 8, 10, 2, 0, -4]], determ... | -21547828 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^6 where A is:\n[[-5, 4, -3, 10, -1, 2, 2, -2],\n [4, -4, 0, -5, -3, 2, 2, -5],\n [-3, 0, -7, 0, 7, 2, 2, 2],\n [10, -5, 0, 1, -3, -6, -4, 0],\n [-1, -3, 7, -3, -11, 0, 1, 4],\n [2, 2, 2, -6, 0, 8, 0, 5],\n [2, 2, 2, -4, 1, 0, -9, -9],\n [-2, -5,... | -14905897 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 6th power of the matrix:\n[[1, -10, -2, -3, 4, 0, 12, -11],\n [0, 6, -8, 3, -3, -1, 7, 0],\n [8, 3, 9, 8, -12, 9, -4, 3],\n [6, 2, 5, 9, -1, 1, -10, -9],\n [-7, 3, 0, -1, 9, -1, -11, 0],\n [-10, 0, 12, -11, 6, -4, 7, -12],\n [0, -11, 2, 6, 12, ... | 1349737866 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-4, 2, 6, 2, -3, 4, -4, -4],\n [2, 5, 4, -2, -1, 2, 0, 0],\n [6, 4, -9, 2, 0, -2, 6, -2],\n [2, -2, 2, 12, -1, 2, 0, 0],\n [-3, -1, 0, -1, 9, 4, -2, -2],\n [4, 2, -2, 2, 4, 11, 0, -1],\n [-4, 0, 6, 0, -2, 0, -5, 0],\n [-4, 0, -2, 0, -2, -1, 0, -5]], determine ... | 198573262 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^6 where A is:\n[[6, -3, -1, 1, -7, 8, 11, -4],\n [-6, -7, 9, -12, 8, 1, 11, -7],\n [-1, 4, -8, -2, -8, -1, -10, 11],\n [-4, -7, 9, -11, -11, 9, -1, -5],\n [-11, -4, 3, 12, 2, 1, 7, -9],\n [-9, -2, 8, 11, 5, -8, -11, 2],\n [-2, 11, 4... | 2090572325 | MATH |
[
{
"content": "Find the sum of all entries of the 6th power of the matrix:\n[[3, -4, -8, 0, 0, 0, 6, 9],\n [-4, -1, 4, 6, 0, 3, -3, -6],\n [-8, 4, 5, -1, 0, 0, -8, -4],\n [0, 6, -1, 11, 6, 0, 4, -4],\n [0, 0, 0, 6, 2, 11, 5, -4],\n [0, 3, 0, 0, 11, -8, 7, -3],\n [6, -3, -8, 4, 5, 7, 1, 6],\n [9, -6, -4, -4, -4, ... | 331752815 | MATH |
[
{
"content": "Find the value at position (1, 8) of the 7th power of the matrix:\n[[11, 9, 10, 8, 9, 9, 3, 12],\n [-3, 7, -1, -8, 7, 4, -3, -7],\n [8, 7, -7, -1, 8, 6, -11, 0],\n [9, 7, -2, 2, 0, -10, 1, -5],\n [-4, 2, 10, 5, -5, -2, -8, 2],\n [2, -6, 8, 5, -1, -1, -9, -2],\n [8, -7, 8, -3, 2, -12, 4, -10],\n [1... | 708498764 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-5, -3, -2, -1, -1, 8, 3, 0],\n [-3, 12, -6, 4, -2, -8, -2, 2],\n [-2, -6, 8, 6, 2, 10, 5, 6],\n [-1, 4, 6, 4, -2, 6, 0, 6],\n [-1, -2, 2, -2, -1, 2, -2, 10],\n [8, -8, 10, 6, 2, 5, 0, 6],\n [3, -2, 5, 0, -2, 0, -4, -2],\n [0, 2, 6, 6, 10, 6, -2, -8]], determi... | -26227191 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[11, 2, -1, 12, -12, 1, 5, 5],\n [-7, -12, 4, 5, 2, -1, 0, 7],\n [-11, -9, -10, 6, 12, -5, -1, -1],\n [-3, 12, -12, -8, 7, -2, -4, 1],\n [-10, -8, 11, 8, -4, 5, -7, 8],\n [12, -6, 3, -5, 10, -3, -8, -2],\n [8, 0, 7, -... | 34183559972 | MATH |
[
{
"content": "For the matrix power A^7 where A =\n[[-12, 1, -5, 2, -6, 8, 1, 3],\n [1, -7, -4, 3, 5, -3, -2, 4],\n [-5, -4, 12, 4, 0, -2, 3, -2],\n [2, 3, 4, 3, 6, 2, -4, -2],\n [-6, 5, 0, 6, 7, 1, 0, -2],\n [8, -3, -2, 2, 1, -5, 8, -10],\n [1, -2, 3, -4, 0, 8, -3, 1],\n [3, 4, -2, -2, -2, -10, 1, -2]], determi... | 385442156 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, -2, 8, 0, -4, -12, 1, -4],\n [-2, 4, 1, -2, -6, -10, -9, 0],\n [8, 1, -5, -6, -8, -6, -6, 0],\n [0, -2, -6, -5, 2, -3, -2, 2],\n [-4, -6, -8, 2, -1, 10, 8, 1],\n [-12, -10, -6, -3, 10, -1, -8, -2],\n [1, -9, -6, -2, 8, -8, -9, 8],\n [-4, 0, 0, 2, 1, -2, 8, ... | 136218995 | MATH |
[
{
"content": "What is the value at position (7, 1) of the matrix A^7 where A is:\n[[11, 1, -4, 0, 2, 8, -12, 4],\n [1, -7, 6, -6, 2, -10, 3, -6],\n [-4, 6, -7, 5, -4, -6, -4, -7],\n [0, -6, 5, 12, 1, -6, 6, -11],\n [2, 2, -4, 1, 10, 10, 5, 0],\n [8, -10, -6, -6, 10, 1, -10, 8],\n [-12, 3, -4, 6, 5, -10, -4, 5],... | -6213436651 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[9, 7, -7, -10, -3, -1, -12, 9],\n [3, 4, -3, -1, 6, -5, 10, -5],\n [-3, -3, 5, -3, -6, -9, -12, -2],\n [6, -8, -5, -11, -11, 11, 1, -4],\n [-3, 0, -12, 1, -11, -9, 6, -12],\n [-9, -2, 0, 5, -3, -8, -12, 1],\n [3, 11, 5, -10, -10, -9, ... | -73290514 | MATH |
[
{
"content": "What is the value at position (1, 7) of the matrix A^7 where A is:\n[[8, -3, -6, -6, -10, -6, -4, -5],\n [-10, -8, 0, 0, -5, 5, -6, -3],\n [-3, 10, -2, -1, 0, -5, 4, 11],\n [1, 4, 6, 3, -4, 7, -3, -4],\n [-12, 11, -10, -2, -6, 5, 0, 10],\n [10, 12, 5, 3, 11, 3, 8, -3],\n [-4, -5, 6, -10, 11, -4, -... | -95192255 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-10, 8, -2, 3, 6, -4, 1, 0],\n [8, 8, 3, 1, -4, -4, 4, 2],\n [-2, 3, 10, 0, -6, -4, 0, -2],\n [3, 1, 0, -12, 2, 4, 1, 3],\n [6, -4, -6, 2, 3, 4, -4, -7],\n [-4, -4, -4, 4, 4, -1, 5, 0],\n [1, 4, 0, 1, -4, 5, 7, 7... | 5136380 | MATH |
[
{
"content": "What is the value at position (4, 8) of the matrix A^5 where A is:\n[[10, -8, 4, 9, 0, 4, -7, 2],\n [-8, 1, -12, 4, 0, 2, -9, 3],\n [4, -12, -8, 2, -6, 8, -5, 2],\n [9, 4, 2, 5, -5, 4, 1, 7],\n [0, 0, -6, -5, -9, 4, 2, 0],\n [4, 2, 8, 4, 4, 2, -2, 2],\n [-7, -9, -5, 1, 2, -2, 10, 0],\n [2, 3, 2, 7... | 800019 | MATH |
[
{
"content": "Calculate the matrix power A^6 and find the value at position (3, 6) of the result:\nA =\n[[9, -8, 6, 0, 2, -10, -9, 1],\n [-8, -11, -6, 1, 2, 1, -1, -3],\n [6, -6, 6, 4, -2, 10, 2, -2],\n [0, 1, 4, -3, -4, -2, 10, 0],\n [2, 2, -2, -4, -11, 8, 2, 7],\n [-10, 1, 10, -2, 8, -1, -3, -2],\n [-9, -1, 2... | -24517174 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[7, -4, 0, -1, -5, 2, -10, -3],\n [-4, 2, -7, -6, 6, -2, -2, 8],\n [0, -7, -9, -4, 6, -3, 8, 1],\n [-1, -6, -4, -4, -6, -2, 0, 4],\n [-5, 6, 6, -6, -10, -3, 1, 10],\n [2, -2, -3, -2, -3, 10, 0, 0],\n [-10, -2, 8, 0, 1, 0, -6, 1],\n [-3, 8, 1, 4, 10, 0, 1, -12]]... | 58877461 | MATH |
[
{
"content": "What is the value at position (3, 6) of the matrix A^5 where A is:\n[[-10, -1, -4, -11, 1, -8, -10, -1],\n [-1, 8, -6, -12, -10, -2, 0, 9],\n [10, -3, 6, -9, 9, -8, -2, -4],\n [0, 4, 2, 0, 8, -2, -12, -5],\n [10, -8, 9, 3, -9, 12, 6, 5],\n [10, -11, 0, 3, 9, -5, 6, -10],\n [6, 4, -4, 8, 12, 8, 10,... | -141176 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-1, 2, -4, 4, 4, 2, -1, 5],\n [2, -8, -6, -5, -6, 4, -2, 7],\n [-4, -6, 8, 5, -2, -5, 0, -6],\n [4, -5, 5, 0, -5, -5, -3, 4],\n [4, -6, -2, -5, -8, -4, 3, -1],\n [2, 4, -5, -5, -4, -5, -6, -10],\n [-1, -2, 0, -3, 3, -6, -12, 7],\n [5, 7, -6, 4, -1, -10, 7, -8]... | 242834814 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[4, 7, 3, -2, 2, -8, 0, 2],\n [7, 4, -4, 0, 8, 6, -3, 0],\n [3, -4, 10, 4, 2, 2, 0, -7],\n [-2, 0, 4, -1, 1, 6, 0, -9],\n [2, 8, 2, 1, -9, 2, -3, 2],\n [-8, 6, 2, 6, 2, 1, 4, 10],\n [0, -3, 0, 0, -3, 4, -7, -4],\n [2, 0, -7, -9, 2, 10, -4, -1]], determine the s... | 95885041 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^6 where A is:\n[[-8, 10, 6, 0, -8, -7, -6, 3],\n [10, -2, 0, -4, -2, -8, -4, -1],\n [6, 0, -11, 10, 6, -6, 4, 2],\n [0, -4, 10, -7, 2, -4, -9, 8],\n [-8, -2, 6, 2, 12, 8, -1, 0],\n [-7, -8, -6, -4, 8, 6, 0, 2],\n [-6, -4, 4, -9, -1, 0, 6, 5],\n [3, -1... | 259266807 | MATH |
[
{
"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[8, -10, -9, -6, -10, -4, -5, 5],\n [8, 1, 7, -8, -10, -3, -2, 4],\n [-5, -4, -5, 7, -11, -9, 3, -4],\n [-4, 8, -8, -10, 1, 2, -7, 3],\n [10, -3, 1, -1, -4, 10, 6, -1],\n [0, 10, 0, 4, -11, 7, 10, -4],\n [8, -5, -... | -2058106509 | MATH |
[
{
"content": "Find the sum of all entries of the 7th power of the matrix:\n[[2, 2, 4, 0, 0, -6, 7, 10],\n [2, 6, -2, 6, -4, 0, -6, -8],\n [4, -2, -6, 0, 8, -4, 6, -5],\n [0, 6, 0, -6, -3, 8, 5, 0],\n [0, -4, 8, -3, 5, -4, 2, -6],\n [-6, 0, -4, 8, -4, 6, -12, 5],\n [7, -6, 6, 5, 2, -12, -1, -10],\n [10, -8, -5, ... | -2324475539 | MATH |
[
{
"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-9, -1, -5, 10, 10, -3, 10, -12],\n [0, -6, 7, -10, 3, -1, -8, 5],\n [-5, -1, 12, 8, -10, 3, -3, 10],\n [4, -3, -10, 12, -11, 1, -4, 4],\n [-9, 9, 2, 0, 10, 6, -4, -9],\n [8, -5, 2, 1, -10, 11, 4, -5],\n [1, 0, 2, -2, 2, -1, 11, 9],\n ... | 954430306 | MATH |
[
{
"content": "For the matrix power A^7 where A =\n[[9, 0, 7, -3, -4, -2, -2, 0],\n [0, 2, 6, -11, 8, -2, -5, -2],\n [7, 6, -6, 0, 2, -4, -2, 0],\n [-3, -11, 0, 1, 0, 4, -1, 0],\n [-4, 8, 2, 0, 3, -11, -4, -4],\n [-2, -2, -4, 4, -11, -5, -2, 4],\n [-2, -5, -2, -1, -4, -2, 5, 2],\n [0, -2, 0, 0, -4, 4, 2, 0]], de... | 24607003015 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[9, -12, 12, 9, 9, -4, -8, -2],\n [9, 9, 10, 12, 8, 8, -9, 7],\n [3, 11, 5, -5, -11, 4, -3, 0],\n [2, -4, -5, -7, -9, 5, 11, -10],\n [-9, 8, 0, 7, -2, -5, 12, 1],\n [1, 3, 1, -12, -11, 7, -12, -2],\n [-7, 2, -1, -8, 10, -1, 9, 1],\n [1, 6, -8, -10, 12, 5, -7, -... | 34908029 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-6, 4, -4, 0, -2, -5, -3, -8],\n [4, -5, 6, -8, -10, 10, 2, -1],\n [-4, 6, -12, -5, -4, 4, -2, -6],\n [0, -8, -5, 12, 4, 6, 0, -8],\n [-2, -10, -4, 4, -5, 6, 6, -1],\n [-5, 10, 4, 6, 6, -5, 0, -6],\n [-3, 2, -2, 0, 6, 0, -9, -5],\n [-8, -1, -6, -8, -1, -6, -5,... | -1389564 | MATH |
[
{
"content": "What is the value at position (4, 4) of the matrix A^5 where A is:\n[[-11, -9, -3, 8, 8, -8, 0, 6],\n [-9, -12, 6, 4, -4, 2, -6, -4],\n [-3, 6, 3, 4, 4, -4, 6, -2],\n [8, 4, 4, -11, 0, 1, 1, -8],\n [8, -4, 4, 0, 12, 1, 2, -8],\n [-8, 2, -4, 1, 1, -3, -1, -6],\n [0, -6, 6, 1, 2, -1, -8, -3],\n [6, ... | -5916668 | MATH |
[
{
"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-11, 12, -5, -1, 9, -4, -2, 6],\n [7, 10, 4, 0, -12, -12, -5, 0],\n [-7, -10, 3, -3, -6, 9, 8, -10],\n [1, 3, -9, 0, -12, 12, -8, 5],\n [-1, -2, -4, -6, 1, 11, -10, 3],\n [-6, -12, -7, -7, -3, -1, 9, 6],\n [-7, 1, -10, -3, -4, 10, 7, 6... | -693662157 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[6, 6, 5, 1, 6, 0, -6, 4],\n [6, -8, -4, -4, 5, -4, 2, -10],\n [5, -4, 3, 10, 1, 4, 0, -3],\n [1, -4, 10, 2, 5, -2, 2, -4],\n [6, 5, 1, 5, -7, 4, -4, -3],\n [0, -4, 4, -2, 4, 12, 0, 5],\n [-6, 2, 0, 2, -4, 0, 8, -2],\n [4, -10, -3, -4, -3, 5, -2, -9]], determin... | 339774783 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-12, -3, 12, -8, -8, -4, 1, 8],\n [0, 0, 11, -12, 4, 7, -5, -10],\n [4, -1, 12, 12, 12, 12, 5, 1],\n [-2, 3, -9, 5, -6, -2, 3, 3],\n [-10, 12, 10, 11, -4, -5, -6, 12],\n [4, -2, -9, -9, -8, -5, -3, 4],\n [-7, -4, -3, -5, 2, 5, 10, -8],\n [5, -12, -11, -3, -7, ... | -15827539 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-2, 2, 8, -4, -10, 0, -2, 2],\n [2, 9, -6, -6, 6, 4, 2, -2],\n [8, -6, 8, -2, 11, -5, 6, 4],\n [-4, -6, -2, 5, 8, 0, 4, 2],\n [-10, 6, 11, 8, -7, 2, 4, 0],\n [0, 4, -5, 0, 2, 3, 4, 2],\n [-2, 2, 6, 4, 4, 4, -4, 2],\n [2, -2, 4, 2, 0, ... | 1308974089 | MATH |
[
{
"content": "Calculate the matrix power A^6 and find the value at position (3, 5) of the result:\nA =\n[[-1, 1, -3, -4, 6, 4, -8, -10],\n [1, 3, -2, -6, 5, 6, 2, -4],\n [-3, -2, -1, -6, -11, 4, 0, 0],\n [-4, -6, -6, -11, 2, 4, -8, -2],\n [6, 5, -11, 2, -6, 1, 10, -2],\n [4, 6, 4, 4, 1, 4, 0, 10],\n [-8, 2, 0, ... | 4729857 | MATH |
[
{
"content": "Find the sum of all entries of the 6th power of the matrix:\n[[1, 11, -8, 3, -8, 9, 0, 3],\n [2, -8, 8, 10, -7, 0, 3, -3],\n [-11, 0, 4, -12, -9, 5, -7, -1],\n [12, 11, 7, 0, -11, 4, 10, -3],\n [6, 9, -8, 8, -1, 5, -4, -2],\n [-9, -3, -12, -11, -4, 10, 5, 3],\n [10, 1, -9, -11, -1, 7, -8, -9],\n [... | 209447251 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[7, 8, -2, 7, -8, -6, 8, 0],\n [8, 5, -4, 2, -6, -1, 0, 6],\n [-2, -4, 1, 4, 10, 5, 2, -3],\n [7, 2, 4, -5, -2, 2, -2, 4],\n [-8, -6, 10, -2, -6, -6, 0, 4],\n [-6, -1, 5, 2, -6, 0, 1, 2],\n [8, 0, 2, -2, 0, 1, -8, -8],\n [0, 6, -3, 4, ... | 3105992 | MATH |
[
{
"content": "For the matrix power A^7 where A =\n[[4, 0, -9, 10, 5, 5, 9, -4],\n [-10, -6, 2, -4, -4, -9, 5, 4],\n [9, 8, -7, -6, 12, -3, -3, -7],\n [-7, 6, -5, -4, -12, 3, -7, 10],\n [-5, 2, -1, -3, 3, 2, -2, 11],\n [-6, -5, -2, -4, -6, 2, 2, 3],\n [-10, 3, 2, 12, -12, 1, 11, 9],\n [-2, -10, -4, -7, 10, 3, -2... | 7658843017 | MATH |
[
{
"content": "For the matrix power A^7 where A =\n[[4, 4, -10, 6, 11, 10, 2, -3],\n [-5, 4, -9, -5, -11, 10, -5, 12],\n [-6, -4, 5, 4, -12, -1, -9, 4],\n [-6, 11, -10, -12, 6, -11, -7, -2],\n [10, 12, 8, -9, -12, -2, 3, -7],\n [-2, -5, 7, -12, 1, 8, 8, -11],\n [-7, -4, 1, 9, -5, -10, -3, 5],\n [7, -4, -4, 6, 0,... | 11567363559 | MATH |
[
{
"content": "For the matrix power A^6 where A =\n[[-9, 3, 3, 2, -7, -8, 9, -3],\n [-6, -6, -3, -3, 12, 2, -7, 11],\n [-11, -5, 12, 7, 2, 8, 8, 5],\n [-8, 12, -9, -3, 6, 1, 10, 11],\n [0, -3, 9, -7, 0, 8, -2, 9],\n [12, 2, -11, 2, 6, 4, 7, 5],\n [-7, 2, 4, 11, 9, -4, -1, 9],\n [10, -8, 1, 11, -5, 12, 9, 4]], de... | -28636905 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 0, 6, -8, 4, 1, 3, -4],\n [0, 10, 0, 8, 2, -2, 2, 0],\n [6, 0, -3, -5, -3, 8, 0, 6],\n [-8, 8, -5, 0, -11, -8, -5, 7],\n [4, 2, -3, -11, 12, -2, 0, -10],\n [1, -2, 8, -8, -2, -9, 8, -2],\n [3, 2, 0, -5, 0, 8, -6, -4],\n [-4, 0, 6,... | -2628289 | MATH |
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