messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -4, 5, -3, 4],\n [5, 5, 3, -2, 3],\n [5, -3, -5, 5, -1],\n [4, 4, -4, -2, -4],\n [-4, -3, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 210941 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[5, 4, 0, 2, 0],\n [4, 0, -1, -2, 2],\n [0, -1, -5, 3, -2],\n [2, -2, 3, 5, -1],\n [0, 2, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -326 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[-1, 4, 1, 2, 0],\n [4, 4, 1, 0, -2],\n [1, 1, -3, 4, 0],\n [2, 0, 4, 3, -1],\n [0, -2, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 858 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 4, -1, 4, -1],\n [4, -3, 1, 1, 3],\n [-1, 1, -3, 0, 4],\n [4, 1, 0, 0, -2],\n [-1, 3, 4, -2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2439 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 1, 0, -4, 1],\n [1, -2, -4, -2, -2],\n [0, -4, -2, -2, 4],\n [-4, -2, -2, -3, -2],\n [1, -2, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 19929 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 5, 0, 5, 4],\n [-2, 2, 3, -4, 1],\n [3, 3, -1, -5, 0],\n [2, -5, -4, -5, -1],\n [-4, 4, 4, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10030 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, -1, -4, 2],\n [-5, 1, -5, 0, 0],\n [-1, -4, -4, 3, -1],\n [-1, 1, 0, -4, 5],\n [-5, -1, -2, -3, -4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 315 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, -2, -4, -2],\n [-3, 3, 1, 5, -3],\n [2, 3, 1, 0, -2],\n [-1, 2, -3, -4, -3],\n [1, 2, -5, 1, 3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, -3, 2, -2, 2],\n [-1, -3, -2, -2, 2],\n [0, 1, 3, 0, -3],\n [-3, 5, -3, 4, -4],\n [-5, 5, 4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6887 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-3, -1, 1, 1, -1],\n [-1, 2, -2, 1, -2],\n [1, -2, -1, 0, -2],\n [1, 1, 0, 4, 1],\n [-1, -2, -2, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, 2, 2, -2, 0],\n [2, -4, 2, 2, 0],\n [2, 2, 4, 0, 0],\n [-2, 2, 0, -5, -2],\n [0, 0, 0, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13389 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, -2, 5, -4, -3],\n [-1, 5, -4, -2, -5],\n [-2, 1, -3, 4, 2],\n [0, 0, -5, -1, -3],\n [4, -5, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2506 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 4, 4, -2, 5],\n [0, 3, -3, 3, -2],\n [-1, 1, 0, 4, 2],\n [2, 2, -3, 4, 0],\n [1, 3, 4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75280 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 2) of the result:\nA =\n[[-1, 2, -5, 0, -2],\n [-1, 5, -1, -4, 2],\n [-4, -2, -1, -5, 0],\n [-4, -1, 0, 5, 2],\n [3, 0, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9153 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 1, -1, 1, 5],\n [-5, -5, -1, -4, 2],\n [-3, -5, -4, 4, 4],\n [1, 0, 2, 1, 4],\n [2, -3, 0, 1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8429 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, -4, -4, 2, 2],\n [-4, -3, -2, 1, 0],\n [-4, -2, 0, 1, 2],\n [2, 1, 1, 0, 2],\n [2, 0, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 153471 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^5 where A is:\n[[-5, 5, 3, -1, -5],\n [2, 1, 1, -1, -5],\n [3, 5, 3, 2, -1],\n [-3, 2, -5, -3, 5],\n [1, -2, 1, 5, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6941 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 1, 4, 1, 1],\n [1, 5, 1, -3, -3],\n [1, -4, -4, -3, -2],\n [0, 2, 4, 4, 1],\n [-2, -4, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1163 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, 1, 1, 0, -4],\n [1, -1, 4, -4, 2],\n [1, 4, -5, -2, 0],\n [0, -4, -2, -2, -2],\n [-4, 2, 0, -2, -2]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3717 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 2, 0, -2, 0],\n [2, 2, 0, 0, 0],\n [0, 0, 3, -2, -4],\n [-2, 0, -2, 5, -4],\n [0, 0, -4, -4, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3344 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 3, -4, -4, -3],\n [1, 5, -3, -5, 0],\n [-3, -5, -2, -5, -5],\n [-4, 4, 2, -4, 5],\n [-4, 5, 5, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31759 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 5th power of the matrix:\n[[2, 0, 5, -2, -3],\n [-5, 5, -3, 3, -1],\n [0, -1, -5, 4, -5],\n [-2, -3, 5, 2, 1],\n [5, 1, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16910 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -4, -2, 2, -1],\n [-4, -3, -2, 0, -5],\n [-2, -2, 4, 3, -4],\n [2, 0, 3, -1, 1],\n [-1, -5, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45300 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, -4, 5, -5, 4],\n [-4, 0, -3, 4, -1],\n [-5, 2, -2, 3, -2],\n [-4, -3, -1, 4, 0],\n [1, -2, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -29925 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[1, -2, 2, 3, 1],\n [2, 2, -4, 3, 0],\n [5, -2, -1, 4, -1],\n [1, 3, 1, 3, -2],\n [4, 4, -2, 0, 2]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2582 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -2, -3, 4, 4],\n [-2, 3, 1, -2, 0],\n [-3, 1, -1, 2, -4],\n [4, -2, 2, -4, 3],\n [4, 0, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39825 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -4, 0, -1, -4],\n [-4, 3, -2, 0, -1],\n [0, -2, -1, 0, 1],\n [-1, 0, 0, 1, -3],\n [-4, -1, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8363 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 4) of the result:\nA =\n[[3, 2, -3, -4, 4],\n [1, 1, 3, -1, -2],\n [2, -2, -2, -4, -5],\n [-2, 1, 3, 3, 4],\n [-5, -1, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -565 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 5th power of the matrix:\n[[0, 4, 2, 2, -2],\n [4, 4, -1, 2, 0],\n [2, -1, -5, -2, 2],\n [2, 2, -2, -3, -3],\n [-2, 0, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13806 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, 1, 3, -4, -1],\n [5, 4, 3, -3, -5],\n [-4, 0, -1, -5, -5],\n [5, -2, -2, 0, 0],\n [4, 0, -5, 4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -57043 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (2, 1) of the result:\nA =\n[[5, 1, 1, 5, 1],\n [-4, -4, 0, 1, -3],\n [-2, -3, 1, 1, -2],\n [1, -1, -5, 4, -2],\n [1, -4, -4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7035 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 2, 5, 2, 2],\n [-5, -5, 4, -2, 0],\n [2, -4, -3, 0, 4],\n [-2, -4, 1, -2, 2],\n [2, 1, 4, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, 0, 2, -2, 0],\n [0, 3, 2, -1, -2],\n [2, 2, -5, 2, -1],\n [-2, -1, 2, -2, 0],\n [0, -2, -1, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 839 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[2, -1, 3, 3, -3],\n [4, 0, 0, -2, 5],\n [4, -3, -5, 1, -1],\n [4, 1, -5, 2, -3],\n [1, -3, -3, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3632 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[-4, 1, -2, 0, 2],\n [1, 1, 0, -1, -2],\n [-2, 0, -2, 2, 0],\n [0, -1, 2, 2, 0],\n [2, -2, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3792 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, -2, 2, -1, 0],\n [-2, 3, 2, 2, 0],\n [2, 2, 5, 0, -1],\n [-1, 2, 0, -1, 0],\n [0, 0, -1, 0, -3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4626 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, 2, 1, 0, -4],\n [1, 2, -5, 3, -2],\n [2, 4, 1, 4, 1],\n [-4, -5, -2, -4, 2],\n [4, 1, 2, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8062 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, 3, 0, 4, -5],\n [-5, 2, 0, 2, 2],\n [5, 2, 4, 1, 1],\n [4, -2, 3, -4, 5],\n [3, 4, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1082 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, -4, -5, 4, 5],\n [-1, 3, -1, 5, 4],\n [3, 4, 0, -3, -2],\n [-2, -5, -3, -3, -5],\n [3, 5, -5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11204 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, -4, -2, 0, 4],\n [-4, -3, -4, 4, 3],\n [-2, -4, 4, 3, 0],\n [0, 4, 3, 0, 4],\n [4, 3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 690990 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[-1, -1, 2, 4, -2],\n [3, 1, 1, -3, -2],\n [1, 5, 5, -1, -3],\n [-5, 1, 0, 4, 1],\n [-4, -2, -4, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -972 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 3) of the result:\nA =\n[[-5, -4, -4, -2, -3],\n [-5, -4, 5, 3, -5],\n [3, 1, -4, -4, -1],\n [-1, -2, 4, 4, -3],\n [-2, 4, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6222 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[-1, -3, 2, 2, 4],\n [-3, 0, 2, -4, 2],\n [2, 2, -1, -2, 0],\n [2, -4, -2, -4, -2],\n [4, 2, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 925 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 0, -3, -2, -5],\n [2, -5, -1, 0, -4],\n [1, 1, -5, -2, -2],\n [-1, -5, -5, 1, 3],\n [-5, -4, 0, 0, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -544680 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 2, -1, 2, 4],\n [2, -3, -2, 0, 4],\n [-1, -2, -4, 4, -3],\n [2, 0, 4, -4, -2],\n [4, 4, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 258539 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -1, 0, 0, 0],\n [-1, 3, 1, 2, 0],\n [0, 1, -5, 0, -3],\n [0, 2, 0, -3, 0],\n [0, 0, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6645 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, -4, 0, 1, -1],\n [-4, 0, -3, 3, 2],\n [0, -3, -2, -1, 4],\n [1, 3, -1, 2, 0],\n [-1, 2, 4, 0, -2]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9119 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 0, 1, 3, 1],\n [0, 1, 0, 2, 2],\n [1, 0, 1, -2, 2],\n [3, 2, -2, 4, -2],\n [1, 2, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8091 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -5, -4, 3, 2],\n [2, 4, -5, 0, 3],\n [2, -3, -2, -3, 0],\n [3, 2, 4, -2, -4],\n [2, 2, 5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20647 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[3, -5, 3, -4, -5],\n [2, 2, 5, -2, 2],\n [1, -4, -1, 4, -2],\n [-3, -5, -1, 4, 2],\n [3, 1, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10019 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, 0, -1, -2, 4],\n [0, -2, 0, -2, 2],\n [-1, 0, -5, -2, 0],\n [-2, -2, -2, 4, -4],\n [4, 2, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17029 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 3, -5, -1, -3],\n [-2, -2, 5, 1, 4],\n [5, 2, 5, 4, -1],\n [4, 1, -3, -3, -3],\n [-2, 0, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43873 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, -1, 4, -4, 5],\n [5, -1, 1, -4, 0],\n [1, -1, 3, -2, 4],\n [-5, 2, 2, 1, 2],\n [-4, -3, 3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15694 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[2, 1, 5, -1, -2],\n [4, 4, 4, 4, 0],\n [5, -5, -1, -2, -2],\n [1, 3, 2, 5, 2],\n [-1, 0, -4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9546 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-1, -4, -3, -2, 0],\n [-1, 4, -2, -4, 5],\n [-1, -1, 5, 1, -5],\n [-2, 5, -1, 2, 2],\n [-5, -1, 4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 338 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, 0, 1, 0, -2],\n [0, -5, -3, -1, 2],\n [1, -3, -1, 4, 0],\n [0, -1, 4, 2, -2],\n [-2, 2, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2565 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 3, -1, 2, -1],\n [3, -4, 1, 0, -2],\n [-1, 1, 1, -3, 2],\n [2, 0, -3, 1, -3],\n [-1, -2, 2, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 171542 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, 1, 4, 0, -1],\n [1, -3, 0, -2, 1],\n [4, 0, 3, 0, 0],\n [0, -2, 0, 4, -2],\n [-1, 1, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99992 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -3, -4, 5, 0],\n [-3, -4, -5, 2, -5],\n [-1, 5, 0, 5, -3],\n [1, -4, 1, -4, -1],\n [1, 5, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1063 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -5, -3, 3, 4],\n [-1, 2, -4, -3, 1],\n [4, -2, 3, 1, 5],\n [-5, -2, 4, 5, 0],\n [0, 4, 0, -1, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1637 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -4, 2, -4, 0],\n [-4, -4, 2, -2, -4],\n [2, 2, 1, -4, 0],\n [-4, -2, -4, 1, -2],\n [0, -4, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 554432 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 3, 0, -2, 2],\n [3, -5, 2, -3, 0],\n [0, 2, -4, -2, -2],\n [-2, -3, -2, 4, -2],\n [2, 0, -2, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19924 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -1, -4, -4, -2],\n [-1, -1, 0, 0, 1],\n [-4, 0, 4, 0, -4],\n [-4, 0, 0, -4, -3],\n [-2, 1, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -168564 | MATH |
[
{
"content": "Find the value at position (5, 1) of the 5th power of the matrix:\n[[4, -5, -2, 0, -2],\n [1, 1, 0, 3, -4],\n [4, 2, 2, 5, 4],\n [5, -2, 0, 5, 0],\n [-1, -5, -3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12388 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, -3, -1, 4, 2],\n [-3, -1, 0, -2, 0],\n [-1, 0, 3, 4, -4],\n [4, -2, 4, 0, 0],\n [2, 0, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4301 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^5 where A is:\n[[3, 2, 2, 0, -2],\n [2, -1, 1, -1, -1],\n [2, 1, 4, -2, 2],\n [0, -1, -2, -5, 2],\n [-2, -1, 2, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5038 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 2, 3, -4, 1],\n [-4, 0, -4, 4, 0],\n [-4, -5, 1, -3, -2],\n [0, -1, -2, 3, 0],\n [0, -4, 0, 1, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10422 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 3, 4, 5, -3],\n [4, 1, 1, -5, 2],\n [-2, -1, 0, -3, -1],\n [4, -1, -5, -3, -3],\n [-5, 1, -5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30087 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 1, -1, 1, 3],\n [4, 0, -5, 0, -5],\n [-2, 2, -1, -1, 4],\n [5, 2, 2, -5, -1],\n [-1, 2, -5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3888 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -4, -3, -2, -5],\n [1, 4, -3, -3, -3],\n [2, 3, 4, -4, 4],\n [4, -5, 3, 0, 3],\n [0, -4, -5, 2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1916 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 3) of the result:\nA =\n[[-5, 2, -3, 1, 0],\n [2, 3, 2, -4, 0],\n [-3, 2, 3, 0, -2],\n [1, -4, 0, 2, 0],\n [0, 0, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -432 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 2, 0, -5, 1],\n [-5, -3, 2, 3, -3],\n [-5, -5, 1, -1, -5],\n [0, 0, -2, 1, 1],\n [3, -5, -1, 4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1250 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -2, -2, -5, -5],\n [4, -4, -4, -5, 2],\n [0, 0, 4, 4, 3],\n [-1, -2, 5, 0, 2],\n [-5, 1, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87667 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, 1, -3, -4, -3],\n [-2, -2, 0, 1, -2],\n [4, 0, 3, 0, -3],\n [-5, 5, 4, 4, -1],\n [4, 4, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2078 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 4, -2, -2, -2],\n [4, -1, -1, 2, 4],\n [-2, -1, 5, -2, 2],\n [-2, 2, -2, 4, 1],\n [-2, 4, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 327556 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, -1, -2, 1, 0],\n [-1, -4, 2, 0, -3],\n [-2, 2, 2, 1, 0],\n [1, 0, 1, -4, -2],\n [0, -3, 0, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23029 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, 1, -3, -5, 2],\n [1, -4, 1, -3, 3],\n [2, -1, 1, -3, -5],\n [-5, 5, -4, 2, -5],\n [5, -1, 3, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37245 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 4, -4, 0, -1],\n [4, 4, -4, 2, 0],\n [-4, -4, 0, 4, 2],\n [0, 2, 4, 3, -3],\n [-1, 0, 2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3928 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 1, -1, 1, 4],\n [1, -1, 0, -3, 0],\n [-1, 0, 4, -2, -2],\n [1, -3, -2, 1, -4],\n [4, 0, -2, -4, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146475 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -5, -5, -5, -2],\n [-2, 2, -5, 4, -3],\n [5, -5, 3, 4, 3],\n [1, 2, -5, -1, -4],\n [-5, -3, 1, -5, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79369 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -4, -2, -3, -3],\n [4, -1, -3, 5, 1],\n [-1, -2, -3, -2, -4],\n [-5, -3, 5, -4, -5],\n [-5, -4, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43036 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, 5, 0, -5, 4],\n [-1, -5, 1, 4, 5],\n [2, 2, 1, -4, -1],\n [-2, -1, 4, 3, -2],\n [2, 2, -4, 0, -1]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3412 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, 4, 0, 0, -4],\n [4, 4, -4, 0, -2],\n [0, -4, -2, -4, -3],\n [0, 0, -4, 5, -2],\n [-4, -2, -3, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 382396 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 5, 2, 0, -3],\n [0, 1, 0, 4, 0],\n [-5, -3, 1, -2, -2],\n [1, 3, 5, -4, 3],\n [-3, 0, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12198 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, 0, 2, -4, 1],\n [0, -4, -4, -2, -2],\n [-3, 2, 1, -4, -3],\n [4, 3, -1, -4, -3],\n [2, -2, -4, -4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7994 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 0, 0, 0],\n [0, 3, -1, 2, 2],\n [0, -1, -4, -2, 2],\n [0, 2, -2, 4, 4],\n [0, 2, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10422 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 5, 1, -1, -4],\n [-1, 1, 1, -2, -5],\n [0, -3, 5, -1, -2],\n [-4, 1, -1, 1, 3],\n [-2, -1, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42641 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, -1, -1, 2, -2],\n [-2, 1, 5, -1, 0],\n [0, 0, 4, -1, -1],\n [3, 2, -2, 1, 2],\n [3, -1, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35852 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[0, 4, 5, -1, 3],\n [5, 5, -3, -4, 0],\n [1, -1, -5, -3, -3],\n [-2, 4, 0, -1, -5],\n [0, 3, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2353 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[2, 0, 1, 1, 4],\n [0, -3, 4, -1, 1],\n [1, 4, -2, 1, 0],\n [1, -1, 1, 2, -3],\n [4, 1, 0, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -4, 4, -4, 3],\n [1, 0, 1, 2, -5],\n [2, -3, -3, 0, -2],\n [-2, -2, 4, 3, 2],\n [-3, -5, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -40162 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -2, 5, 5, -3],\n [2, 2, 0, 3, 4],\n [-5, 2, 0, -5, -2],\n [-1, 1, 2, 3, 0],\n [4, 3, -2, 2, -3]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -902 | MATH |
[
{
"content": "What is the value at position (2, 2) of the matrix A^5 where A is:\n[[-2, 4, -2, 0, 3],\n [0, -5, -1, 3, -1],\n [0, -3, 2, 4, 5],\n [-2, -2, 5, -1, 4],\n [3, 2, 1, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5189 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, 4, 4, -4, -2],\n [2, -5, -1, 2, -4],\n [-4, 2, 4, 3, 1],\n [2, -1, -5, -2, -4],\n [-3, -3, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3402 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, -3, 1, 2],\n [5, 0, -2, 0, 5],\n [-5, 4, 2, -5, -1],\n [-4, 0, 3, -1, -2],\n [-4, -3, 0, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2223 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[-1, -1, 4, -3, 1],\n [0, -5, -2, 0, 5],\n [0, 5, -3, 0, 4],\n [0, 3, 3, -4, -2],\n [3, -2, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15416 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, -1, 0, 2, -2],\n [-1, 4, -4, -1, 5],\n [0, -4, 2, 4, 1],\n [2, -1, 4, 4, -2],\n [-2, 5, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 988637 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 5th power of the matrix:\n[[3, 3, -1, -2, 3],\n [3, -3, -1, -3, 4],\n [-4, -5, 4, -4, 2],\n [5, 2, -3, 1, 1],\n [-4, 3, -3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5306 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 4, -3, 0, -3],\n [4, 5, 3, 2, 2],\n [-3, 3, -5, -2, 0],\n [0, 2, -2, 0, -2],\n [-3, 2, 0, -2, -3]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1631 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, -1, 0, -2, -4],\n [-1, -2, 0, 0, -4],\n [0, 0, -2, -2, 0],\n [-2, 0, -2, 2, -4],\n [-4, -4, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -378847 | MATH |
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