messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 1, 0, 1, 2],\n [1, 1, 0, 0, -2],\n [0, 0, 2, 0, 0],\n [1, 0, 0, 4, -1],\n [2, -2, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10264 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 5, 4, 3, -4],\n [0, -2, -2, -1, -3],\n [-5, 2, -1, -3, 4],\n [1, 1, -5, 3, -4],\n [-1, -1, 2, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1406 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[1, 5, 0, 0, 5],\n [3, 0, -4, -4, -1],\n [-2, 5, -4, -3, 1],\n [2, 0, 5, -1, -5],\n [2, -3, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 902 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 3, -1, 2, 4],\n [4, 2, -5, -1, -3],\n [-5, -2, 2, -3, 4],\n [-4, 5, 3, 4, -1],\n [1, 5, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27947 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 1, -3, -2, 2],\n [1, 4, 0, -2, 4],\n [-3, 0, 3, -1, 2],\n [-2, -2, -1, 2, -2],\n [2, 4, 2, -2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194362 | MATH |
[
{
"content": "What is the value at position (4, 4) of the matrix A^4 where A is:\n[[4, 0, 0, 0, 1],\n [0, 0, -1, -1, 0],\n [0, -1, 4, -2, 0],\n [0, -1, -2, 1, 0],\n [1, 0, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^5 where A is:\n[[1, -2, -2, 2, 2],\n [-4, -4, -3, -3, -5],\n [-3, 0, 2, 4, 0],\n [-1, -2, -3, -2, 1],\n [-5, 1, -5, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2685 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[-5, 2, 2, 4, 4],\n [2, -5, 0, 2, -3],\n [2, 0, 0, 2, -1],\n [4, 2, 2, 3, 2],\n [4, -3, -1, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1395 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[0, 0, -4, 2, 0],\n [0, -3, 2, 0, 1],\n [-4, 2, -1, -2, -2],\n [2, 0, -2, -2, 0],\n [0, 1, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1896 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (2, 2) of the result:\nA =\n[[-3, -5, 2, 3, -2],\n [0, 3, 0, 3, -2],\n [2, 3, -2, -1, 2],\n [4, 0, 1, -3, 1],\n [2, 4, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -740 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, 0, -2, 2, 2],\n [0, -4, 1, 2, 2],\n [-2, 1, -4, -4, 3],\n [2, 2, -4, 2, 2],\n [2, 2, 3, 2, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 137064 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, 4, -2, 0],\n [0, -4, -1, 0, -2],\n [4, -1, 2, -3, -2],\n [-2, 0, -3, 3, 0],\n [0, -2, -2, 0, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3457 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 4) of the result:\nA =\n[[3, -2, 2, -2, 0],\n [-2, 2, -2, 2, 2],\n [2, -2, 0, -2, -3],\n [-2, 2, -2, -4, -4],\n [0, 2, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2808 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, -2, 4, -2, -2],\n [-2, 0, 3, 0, 0],\n [4, 3, -3, -2, -2],\n [-2, 0, -2, 4, 0],\n [-2, 0, -2, 0, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140637 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, -2, 5, 3, 2],\n [4, 4, -5, -4, 3],\n [2, -3, 2, -5, 4],\n [-2, -3, 0, 1, -2],\n [1, 3, 5, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254998 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, 2, -2, 4, -1],\n [2, 2, 0, 0, 0],\n [-2, 0, 2, 2, 0],\n [4, 0, 2, -2, -2],\n [-1, 0, 0, -2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -368 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 5th power of the matrix:\n[[-4, 0, 0, 2, -3],\n [0, 1, 0, 2, 2],\n [0, 0, 0, 0, -4],\n [2, 2, 0, -5, 0],\n [-3, 2, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1946 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (5, 1) of the result:\nA =\n[[4, 5, 1, 5, -1],\n [3, -3, -5, -2, 3],\n [-2, -4, 4, -1, -3],\n [3, -2, 0, -4, 0],\n [-3, 3, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16799 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 3, -2, -2, -1],\n [3, -1, 0, 0, -2],\n [-2, 0, -2, 0, -1],\n [-2, 0, 0, 5, 1],\n [-1, -2, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10726 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, -3, -5, -2, -4],\n [-4, -3, 2, 2, 1],\n [0, 3, -2, -5, 2],\n [1, 1, -3, -2, 4],\n [3, 0, -1, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56909 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, -1, -2, -2, -5],\n [1, 3, -3, -4, -3],\n [-5, 0, 5, 5, 1],\n [5, 5, -4, 2, 0],\n [-2, -1, 2, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 142288 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 0, -1, 0, 4],\n [0, 4, -2, 2, 0],\n [-1, -2, -3, -2, 4],\n [0, 2, -2, 1, 0],\n [4, 0, 4, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128669 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 0, -1, -2, 2],\n [-5, 3, -5, 2, -2],\n [3, 5, -1, -3, 3],\n [5, 3, -2, 5, -2],\n [2, -4, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10110 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[2, -2, -3, 0, 4],\n [-2, -1, -2, -2, -4],\n [-3, -2, -5, -2, 2],\n [0, -2, -2, -5, -2],\n [4, -4, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2002 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 3, -3, 4, -2],\n [0, 2, -1, -3, 0],\n [-2, 3, -3, -2, 1],\n [1, -2, 0, -3, 0],\n [-4, 2, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -823 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -5, 2, 1, 0],\n [0, 0, 3, -4, -5],\n [0, 4, 5, 2, -3],\n [4, -5, 3, -5, -3],\n [2, -3, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34433 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 5th power of the matrix:\n[[0, -5, -5, 2, 5],\n [-2, -5, 4, 1, -1],\n [-1, -5, 4, 5, 0],\n [3, 3, 2, -1, -5],\n [3, -5, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2847 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 1, 1, 3, 1],\n [5, -3, 5, -5, 2],\n [-3, 2, 2, -1, -5],\n [4, 1, 4, -1, 2],\n [3, 5, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41186 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-2, -4, -4, -4, -2],\n [-5, -2, -4, -1, -3],\n [2, -2, -5, -5, 4],\n [-3, 3, 1, -4, 3],\n [4, -4, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5521 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, 0, 3, 3],\n [1, -3, -2, 0, 5],\n [-1, -4, 0, -3, 2],\n [-4, -5, 3, -3, 5],\n [-5, 1, 4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3075 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 3, 1, 2, 3],\n [0, -1, 0, 5, -4],\n [-2, -3, 1, 3, -1],\n [0, 4, -4, -3, -3],\n [3, 1, 2, 5, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11252 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 2, 0, -4, -4],\n [2, 1, -3, 0, 2],\n [0, -3, -1, 0, 0],\n [-4, 0, 0, 4, 0],\n [-4, 2, 0, 0, -5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -450 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, -1, -3, 4, 0],\n [-1, 2, -2, -4, -1],\n [-3, -2, -1, 4, 4],\n [4, -4, 4, -2, 4],\n [0, -1, 4, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73410 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, 0, 0, -3],\n [0, -1, 0, 1, 2],\n [0, 0, 1, -2, -2],\n [0, 1, -2, 5, -2],\n [-3, 2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7481 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 0, -4, 0, -3],\n [0, 1, -3, 1, 3],\n [-4, -3, 4, -2, -2],\n [0, 1, -2, -2, -4],\n [-3, 3, -2, -4, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 306569 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 0, -4, -2, -4],\n [0, 0, 1, -2, 4],\n [-4, 1, 1, -1, 0],\n [-2, -2, -1, -2, -2],\n [-4, 4, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11592 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, 0, 1, -2, 4],\n [0, -1, 0, 3, -2],\n [1, 0, 0, -4, -2],\n [-2, 3, -4, 0, 3],\n [4, -2, -2, 3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8358 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, -1, 5, 1, -1],\n [-1, -4, -4, 0, -3],\n [5, -4, -3, 0, -2],\n [1, 0, 0, -2, -2],\n [-1, -3, -2, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -248889 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -4, 2, 1, -1],\n [-4, 0, 2, 4, -3],\n [2, 2, 4, -2, -4],\n [1, 4, -2, 2, 2],\n [-1, -3, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34894 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, -2, 0, -2, -1],\n [-2, -2, 2, -2, -1],\n [0, 2, 2, -2, 0],\n [-2, -2, -2, -4, 0],\n [-1, -1, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117352 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[5, -3, -2, -4, -2],\n [-3, 5, 0, -4, 0],\n [-2, 0, -4, 4, 1],\n [-4, -4, 4, 2, -2],\n [-2, 0, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1104 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[1, 3, 0, 2, 2],\n [3, -5, -4, 2, 2],\n [0, -4, -1, -4, 0],\n [2, 2, -4, 1, 2],\n [2, 2, 0, 2, 0]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2742 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -2, -2, -4, -4],\n [-2, 2, 1, 0, 4],\n [-2, 1, -4, -2, -4],\n [-4, 0, -2, 5, 4],\n [-4, 4, -4, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38803 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^5 where A is:\n[[-4, 0, 0, -5, 1],\n [2, -4, 2, 3, 0],\n [-1, 3, 5, 3, -5],\n [5, -3, 3, 5, -4],\n [-2, -2, -4, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14120 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, -2, 4, -1, -3],\n [-2, 4, 2, 2, -2],\n [4, 2, 2, 0, 4],\n [-1, 2, 0, 5, -3],\n [-3, -2, 4, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 561000 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 0, 0, -2, -2],\n [0, -1, 2, -1, -2],\n [0, 2, 3, -1, -4],\n [-2, -1, -1, 3, 0],\n [-2, -2, -4, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212487 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 0, 1, 0, 0],\n [0, -2, 2, -2, -1],\n [1, 2, 1, -2, -3],\n [0, -2, -2, 2, 0],\n [0, -1, -3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[-3, 4, -2, -1, 0],\n [4, -1, 0, 4, -3],\n [-2, 0, -4, -2, -2],\n [-1, 4, -2, 3, -2],\n [0, -3, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -833 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 3, -2, 4, 4],\n [0, -5, -2, 1, -5],\n [2, 4, 5, 0, -1],\n [4, 5, 3, -4, -1],\n [0, 1, -1, 3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 153921 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 4, 1, -2, 3],\n [5, -1, -2, 1, -2],\n [-3, 3, 5, 2, -5],\n [1, 3, 2, 2, 0],\n [5, -2, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13991 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 0, 2, 4, 1],\n [0, 2, 0, -2, 1],\n [2, 0, -4, 5, 2],\n [4, -2, 5, 4, 2],\n [1, 1, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35974 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, -3, 5, -1, 2],\n [2, -2, 5, 5, -5],\n [-5, -2, 0, 2, 0],\n [3, 3, -4, 4, -5],\n [-4, -1, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16650 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[5, 1, 0, 0, -4],\n [1, 5, -2, 0, -3],\n [0, -2, 0, 0, 0],\n [0, 0, 0, 2, 0],\n [-4, -3, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, 4, 0, -2, 0],\n [4, 4, 0, 2, -2],\n [0, 0, -3, -2, 3],\n [-2, 2, -2, 4, -2],\n [0, -2, 3, -2, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 128656 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 3, -3, -3, 0],\n [3, 2, 4, 2, -2],\n [-3, 4, 1, -4, 4],\n [-3, 2, -4, 0, -1],\n [0, -2, 4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5969 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 4, 0, 3, 2],\n [4, -4, 0, 0, 5],\n [0, 0, 5, 3, -4],\n [3, 0, 3, 0, 0],\n [2, 5, -4, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14622 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[3, 0, -2, -2, -2],\n [0, -1, 1, -2, -5],\n [-2, 1, 4, -3, -4],\n [-2, -2, -3, 5, -4],\n [-2, -5, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 584 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 2, 1, 2, 3],\n [2, 5, -1, 3, -2],\n [1, -1, -5, -1, -2],\n [2, 3, -1, -1, 1],\n [3, -2, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17779 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 0, 1, 2, 3],\n [0, 2, 2, 1, -2],\n [1, 2, -2, -4, 1],\n [2, 1, -4, 1, 0],\n [3, -2, 1, 0, -1]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 637 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -2, 0, 3, 0],\n [-2, -4, 0, 0, 2],\n [0, 0, -4, 2, -1],\n [3, 0, 2, -2, 2],\n [0, 2, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 116470 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[0, 0, -1, 3, 4],\n [2, 1, 1, 0, -1],\n [-2, -3, -3, 0, -2],\n [0, -3, -2, 3, -1],\n [1, 4, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, -3, 3, 5, 0],\n [-2, 1, 2, 0, -1],\n [0, -1, 2, -5, 5],\n [1, 4, 4, 5, -4],\n [3, -5, 5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8028 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -5, -2, -2, 3],\n [5, -1, -1, 0, -5],\n [-5, 3, -3, -2, -5],\n [3, 2, -4, 2, 1],\n [5, 0, -5, 1, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55342 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 3, -4, -2, 2],\n [3, 3, 0, -2, -2],\n [-4, 0, -3, -5, -4],\n [-2, -2, -5, -3, 0],\n [2, -2, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -450851 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 5th power of the matrix:\n[[5, -4, 1, -2, 2],\n [-4, -4, -1, 0, 4],\n [1, -1, 0, 0, -2],\n [-2, 0, 0, -1, -2],\n [2, 4, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2818 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 2, 2, 2, 2],\n [2, -2, -1, -1, 0],\n [2, -1, 3, 0, 0],\n [2, -1, 0, -3, -4],\n [2, 0, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23465 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -5, -5, -1, 5],\n [-1, 5, -5, 0, -5],\n [-1, 3, -1, 0, 2],\n [5, -5, -4, 3, -3],\n [0, -1, 5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52877 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -5, -2, 0, 1],\n [1, 1, -3, 0, 2],\n [-2, 2, -4, 4, 3],\n [3, 2, 4, 4, -5],\n [-4, 0, 4, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1165 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, -4, 0, -3, 4],\n [-4, 5, 0, 2, 5],\n [0, 0, -4, 4, -1],\n [-3, 2, 4, 0, 0],\n [4, 5, -1, 0, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240812 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, -2, 2, 4, 2],\n [-2, -3, -3, 0, 0],\n [2, -3, 0, 0, -1],\n [4, 0, 0, -5, 2],\n [2, 0, -1, 2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83381 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-2, 0, -2, 0, 2],\n [0, -1, 5, 2, -4],\n [-2, 5, 2, -2, 0],\n [0, 2, -2, -5, -2],\n [2, -4, 0, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, 2, 2, 4, 4],\n [2, 0, -2, 2, 0],\n [2, -2, -4, 0, 1],\n [4, 2, 0, -2, 1],\n [4, 0, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5041 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 5, 3, 3, 4],\n [-4, -2, 2, 1, -5],\n [-1, 1, -2, -5, 3],\n [-1, 5, -4, 2, 5],\n [-4, -3, 4, -5, 5]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1054 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-4, -1, 4, 0, 2],\n [-1, -2, 2, 2, -2],\n [4, 2, -5, -1, 4],\n [0, 2, -1, 4, -1],\n [2, -2, 4, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3116 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, -4, 2, 0, 0],\n [-4, 2, 5, -2, -4],\n [2, 5, 5, -2, 2],\n [0, -2, -2, 5, 2],\n [0, -4, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68479 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -1, -2, 0, 4],\n [-1, 2, -1, -2, 0],\n [-2, -1, -4, 1, -4],\n [0, -2, 1, -1, -2],\n [4, 0, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101515 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, -3, -3, -2, -1],\n [-5, -2, 5, 2, 4],\n [1, 3, -1, 4, -2],\n [2, 3, 1, 1, -1],\n [-2, 4, -5, 4, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 135163 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 4) of the result:\nA =\n[[1, -2, -1, -3, 3],\n [-2, -3, -2, 1, 0],\n [-1, -2, -1, 0, 1],\n [-3, 1, 0, 3, -1],\n [3, 0, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5902 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 0, -2, 2, 0],\n [0, 0, -4, 2, 2],\n [-2, -4, 5, 0, 1],\n [2, 2, 0, -2, -2],\n [0, 2, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120673 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 1, -2, -1, -1],\n [1, 3, 0, -4, -4],\n [-2, 0, 2, 0, -3],\n [-1, -4, 0, 0, -2],\n [-1, -4, -3, -2, 2]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 696 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -5, 1, -1, 4],\n [-5, -3, 1, 4, -5],\n [1, -1, -5, -5, -5],\n [5, 3, 5, -3, -1],\n [5, 4, 3, 0, 3]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2530 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 2, -2, 0, -2],\n [2, -3, -3, 2, 0],\n [-2, -3, -3, -2, 0],\n [0, 2, -2, 3, 2],\n [-2, 0, 0, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4109 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, 3, 2, -2, -2],\n [3, -5, -4, -4, 0],\n [-2, 5, 4, -3, -3],\n [-3, 0, 2, 5, 1],\n [-2, 5, -2, 5, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 175461 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[5, 5, 5, -4, -5],\n [3, -4, 2, 3, -2],\n [2, 3, 4, 4, -1],\n [1, 4, -2, -5, -3],\n [-1, -3, 5, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1299 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[0, 2, -3, 0, 0],\n [2, 4, -1, 3, 2],\n [-3, -1, 4, 3, 0],\n [0, 3, 3, 5, 4],\n [0, 2, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, 4, -4, -4, -3],\n [4, 1, -4, -5, 0],\n [3, -3, 0, -3, -5],\n [-1, 4, 5, -2, 1],\n [0, 4, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -119854 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[1, 2, -2, 0, 0],\n [2, -1, -2, -3, 2],\n [-2, -2, 0, 1, 2],\n [0, -3, 1, -4, 1],\n [0, 2, 2, 1, 2]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -506 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 2, 2, -4, -3],\n [2, 5, -4, 2, 2],\n [2, -4, 5, 1, 4],\n [-4, 2, 1, -5, -2],\n [-3, 2, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75037 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (5, 2) of the result:\nA =\n[[0, 2, 0, -2, -1],\n [2, 2, 0, -3, -2],\n [0, 0, 4, 0, 1],\n [-2, -3, 0, -3, 0],\n [-1, -2, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -722 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 2, 2, -2, 0],\n [2, 5, -2, 0, 1],\n [2, -2, -3, -3, 0],\n [-2, 0, -3, 4, 2],\n [0, 1, 0, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 127533 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, 1, 0, -4, 2],\n [1, 5, -1, -1, 1],\n [3, 5, 3, 3, 0],\n [4, 0, -3, -5, 1],\n [-2, -5, 2, 0, 0]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1064 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^5 where A is:\n[[-4, -5, -4, -2, -4],\n [-5, 1, 5, 5, 2],\n [0, -2, 0, -3, 2],\n [4, -4, -1, -5, 0],\n [-4, -2, 0, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1611 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, 2, 2, 1, 0],\n [2, 2, 2, 0, -2],\n [2, 2, 5, 0, 1],\n [1, 0, 0, 1, 0],\n [0, -2, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69781 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, -5, 1, 3, 2],\n [-1, -2, 1, -1, 1],\n [-5, -5, 4, -3, 5],\n [-4, -4, 1, 4, -4],\n [5, -2, -4, 0, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17577 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, -2, -1, -2, -3],\n [-1, 3, 2, 2, 2],\n [2, 1, 2, 5, 2],\n [2, 4, 1, -5, -2],\n [-2, -1, 4, 0, -2]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11001 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, 0, 2, 2, 1],\n [0, -4, 1, 5, -1],\n [0, 4, 2, 2, -3],\n [1, -5, -5, 1, 4],\n [3, 1, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4668 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 0, 0, 4, -2],\n [0, 2, -5, 4, -1],\n [0, -5, 3, 0, 0],\n [4, 4, 0, -4, 3],\n [-2, -1, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61190 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 4th power of the matrix:\n[[-4, 2, 0, -2, 2],\n [2, 2, -4, -2, 0],\n [0, -4, 3, 3, 1],\n [-2, -2, 3, 3, 2],\n [2, 0, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2232 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-3, 0, -4, 0, 0],\n [2, 1, 2, 3, 0],\n [-3, 4, -3, 5, -5],\n [5, -1, -2, 3, 3],\n [-1, 4, -2, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 278674 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 1, -4, -4, 2],\n [1, -5, -2, 2, 0],\n [-4, -2, 2, 2, 4],\n [-4, 2, 2, 2, 2],\n [2, 0, 4, 2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22594 | MATH |
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