messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[2, -2, 4, -1, 0],\n [-2, 2, -4, 1, -2],\n [4, -4, 3, 2, -4],\n [-1, 1, 2, 4, -2],\n [0, -2, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1838 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 5th power of the matrix:\n[[2, 1, -4, -1, 1],\n [1, 3, 1, 2, 2],\n [-4, 1, 2, 0, 0],\n [-1, 2, 0, 4, 4],\n [1, 2, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29159 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, -2, 0, 2, 5],\n [-2, -4, -2, -1, -1],\n [0, -2, -4, 4, 0],\n [2, -1, 4, 0, -2],\n [5, -1, 0, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 199626 | MATH |
[
{
"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[-2, -1, -3, 0, 2],\n [-1, -2, -2, 0, -4],\n [-3, -2, -4, -2, 0],\n [0, 0, -2, 4, 0],\n [2, -4, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -112 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, -3, -4, -4, 3],\n [5, -1, 1, -1, 1],\n [-2, 2, 5, 4, 5],\n [4, 1, 4, -1, 5],\n [0, -1, 1, -4, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45496 | MATH |
[
{
"content": "What is the value at position (5, 2) of the matrix A^5 where A is:\n[[4, -3, 0, 2, 2],\n [-3, 1, 2, 1, -1],\n [0, 2, -5, -2, 4],\n [2, 1, -2, -1, 0],\n [2, -1, 4, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8908 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 5, -5, -3, -3],\n [1, -5, 3, 5, 0],\n [-2, -3, -3, -4, -4],\n [4, -1, 3, -4, -4],\n [0, 4, -4, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43504 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, 0, -5, -1],\n [0, -1, 4, -1, 4],\n [0, 4, 2, -2, 2],\n [-5, -1, -2, -2, -1],\n [-1, 4, 2, -1, 0]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 490 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 0, 0, 3, 2],\n [0, 3, 2, 0, 2],\n [0, 2, 1, 0, 2],\n [3, 0, 0, -1, -1],\n [2, 2, 2, -1, 3]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 932 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 1, 2, 0, 2],\n [1, 0, 1, -2, 2],\n [2, 1, 2, 2, 2],\n [0, -2, 2, 3, 0],\n [2, 2, 2, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7127 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 2, 1, -1, 4],\n [1, 4, -2, 3, 5],\n [4, -4, 3, 3, -1],\n [5, -5, 1, 4, 4],\n [-2, 3, 0, -3, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17423 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, -1, -4, 4],\n [4, -4, 1, -4, 0],\n [-1, -2, 1, 2, -2],\n [-5, -5, -5, 5, -5],\n [-1, -2, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3971 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, 2, 0, 4, -5],\n [2, 4, -3, 2, -2],\n [2, 5, -5, -3, 0],\n [3, -4, 5, -5, 4],\n [-3, -2, 5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38102 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[4, 4, 0, 0, 1],\n [4, 4, -2, -2, 0],\n [0, -2, -3, 0, -4],\n [0, -2, 0, -4, 0],\n [1, 0, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -264 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -5, 2, -3, 0],\n [-2, 3, 1, 3, 4],\n [-3, -5, -1, -3, 0],\n [2, 5, -2, -1, -1],\n [-2, -2, -2, -2, -2]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 273 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -2, -2, 0, -3],\n [-2, -4, 0, 0, 3],\n [-2, 0, 4, -3, -5],\n [0, 0, -3, -1, -4],\n [-3, 3, -5, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32220 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 0, -4, -2, 0],\n [0, 3, -2, 0, -3],\n [-4, -2, 1, 2, -2],\n [-2, 0, 2, 4, 4],\n [0, -3, -2, 4, 3]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -442 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, -5, -2, -2, -4],\n [3, 3, -4, 3, 0],\n [2, 4, -2, -4, -4],\n [3, -5, 1, 5, -3],\n [-3, -4, 4, 0, 4]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7080 | MATH |
[
{
"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[-4, 4, -2, 2, 0],\n [4, 0, -2, 0, -4],\n [-2, -2, 2, 0, -2],\n [2, 0, 0, 4, 0],\n [0, -4, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1672 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 4, -4, -3, -2],\n [3, -3, 1, -3, 1],\n [1, 3, -4, 0, 3],\n [-4, -4, -1, 4, 4],\n [4, 2, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37471 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[-1, -1, 0, 2, 1],\n [-1, -3, 2, -1, -1],\n [0, 2, 5, 1, 0],\n [2, -1, 1, -4, 0],\n [1, -1, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 209 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 4, 0, 2, -2],\n [4, -4, 4, 0, -2],\n [0, 4, -3, -2, 4],\n [2, 0, -2, 5, 2],\n [-2, -2, 4, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3906 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 0, -4, 2, 2],\n [0, -5, -1, 2, -2],\n [-4, -1, 1, 2, 1],\n [2, 2, 2, -1, -5],\n [2, -2, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26867 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -5, 5, -4, -4],\n [-1, 4, 1, -5, 4],\n [-5, -5, 0, -4, -5],\n [0, -4, 0, 4, 2],\n [-4, 5, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 579983 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, 0, 2, -2, 0],\n [0, 0, 0, 2, -1],\n [2, 0, 1, 0, 4],\n [-2, 2, 0, 3, 4],\n [0, -1, 4, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9093 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 3, -4, -3, 4],\n [-4, -3, 0, -3, 4],\n [2, 5, 0, 1, -5],\n [-3, -3, -4, 1, 3],\n [-2, -1, -3, 5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44361 | 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, -5, 5, -4],\n [3, -4, -1, 2, -3],\n [0, -2, 5, 1, 4],\n [-3, 0, 4, 3, 5],\n [4, -5, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20649 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, 0, 0, -2],\n [0, -3, 0, 2, -3],\n [0, 0, 0, 2, 0],\n [0, 2, 2, -1, 4],\n [-2, -3, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4342 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, 2, -3, -1, 5],\n [2, 4, 0, -2, -2],\n [-3, 0, 0, 3, -2],\n [-1, -2, 3, -1, 0],\n [5, -2, -2, 0, -5]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2988 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, -1, -3, 5, 1],\n [3, -4, 2, 3, 5],\n [-3, -4, 1, -1, -1],\n [4, -1, -2, -1, -2],\n [0, -2, -4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5284 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 4, 0, 3, 3],\n [-3, -5, -5, -3, -1],\n [-3, 3, 3, -3, -3],\n [-1, -4, 0, 1, 3],\n [0, -3, -1, -2, -1]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -115 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, 2, 0, -5, 2],\n [2, -4, -2, -4, -2],\n [4, 1, 3, 2, 3],\n [2, -4, 1, -4, 5],\n [-4, -2, -5, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8820 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 4, 2, -4, -5],\n [-4, 1, -2, 4, -1],\n [1, -3, 4, -4, 1],\n [-1, -5, -5, 3, -1],\n [-5, 1, 3, 5, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1863 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, 0, -3, 2],\n [0, -4, -2, -4, 0],\n [0, -2, 3, 0, -2],\n [-3, -4, 0, 0, -2],\n [2, 0, -2, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9672 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 4, 4, 2, -1],\n [5, 5, 4, -5, 1],\n [-3, 4, 2, -3, -5],\n [-1, -4, 5, -2, -5],\n [3, 0, 2, 5, -2]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2335 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, -4, 3, -1, 0],\n [-3, -2, 0, 1, -5],\n [1, -5, -1, 0, -4],\n [4, 3, 4, 0, 1],\n [4, 2, 5, 4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23438 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 1) of the result:\nA =\n[[2, -2, 4, 2, 0],\n [5, 3, 5, -2, -4],\n [-4, -1, 4, 3, -3],\n [2, -2, 0, 4, 0],\n [-3, -1, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 268 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 3, 1, 0, 0],\n [3, -1, -2, -4, 1],\n [1, -2, -2, -1, 2],\n [0, -4, -1, 1, 4],\n [0, 1, 2, 4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9893 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[5, 2, 4, 0, -2],\n [2, -4, -2, 3, 0],\n [4, -2, 5, 1, 2],\n [0, 3, 1, 1, 0],\n [-2, 0, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31104 | MATH |
[
{
"content": "What is the value at position (1, 5) of the matrix A^4 where A is:\n[[-1, -2, -4, -2, 2],\n [-2, 2, 1, 2, -4],\n [-4, 1, -1, 0, -2],\n [-2, 2, 0, -5, -2],\n [2, -4, -2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 908 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -4, -4, 1, -5],\n [1, -5, 0, -3, 2],\n [0, 5, -4, 2, -1],\n [2, 2, 0, -4, 2],\n [5, 0, 0, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19064 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 5th power of the matrix:\n[[-4, 3, 5, 2, 1],\n [1, -1, -4, 5, 0],\n [4, -3, -2, 4, 5],\n [-4, -4, 2, 2, 4],\n [0, -1, 2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3214 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -1, -5, -5, -4],\n [2, 1, 4, 3, -1],\n [-4, 1, 2, 1, 1],\n [-1, -4, 0, -2, 4],\n [-4, 3, 1, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13113 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, 4, 4, -2, -3],\n [5, 2, -3, 1, 1],\n [1, 1, -4, 4, -3],\n [4, 3, -3, -4, 3],\n [4, 3, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[1, 0, 0, 0, 2],\n [0, -3, 0, 1, 2],\n [0, 0, -3, -2, 1],\n [0, 1, -2, 5, 0],\n [2, 2, 1, 0, 2]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[5, 0, 2, 0, -2],\n [0, -4, -2, -2, -1],\n [2, -2, 0, 4, -4],\n [0, -2, 4, -2, -2],\n [-2, -1, -4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -38 | 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, 3, 2, 1],\n [-3, -4, 1, -1, 0],\n [-2, -4, 3, -3, 1],\n [2, -4, 0, 5, 2],\n [1, 5, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74356 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, -2, 1, 2, 0],\n [-2, -5, -5, -2, 2],\n [1, -5, -5, 2, 0],\n [2, -2, 2, 0, 0],\n [0, 2, 0, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 285004 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, 0, -1, -2, 2],\n [0, 5, 4, 1, -5],\n [-1, 4, 5, 2, 0],\n [-2, 1, 2, 1, 1],\n [2, -5, 0, 1, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 147605 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, -1, 2, 0, 4],\n [-1, -2, 0, 1, 2],\n [2, 0, -5, 4, 4],\n [0, 1, 4, 1, 2],\n [4, 2, 4, 2, 3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13116 | MATH |
[
{
"content": "What is the value at position (2, 5) of the matrix A^5 where A is:\n[[-4, 1, 1, -2, 3],\n [2, -5, -4, -4, 5],\n [2, -5, -2, 4, -1],\n [3, 1, 2, 5, 3],\n [1, -1, -1, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4234 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -2, 3, 2, -4],\n [-2, 1, 0, -2, 0],\n [3, 0, 1, -3, 2],\n [2, -2, -3, 5, -2],\n [-4, 0, 2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, -5, 2, 0, 1],\n [-5, -3, 1, 2, 2],\n [2, 1, -1, -1, 0],\n [0, 2, -1, 3, -2],\n [1, 2, 0, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120567 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, 5, -2, -3, -4],\n [0, 2, 0, 3, -1],\n [-4, 2, 3, 4, -2],\n [0, 5, 4, 2, 3],\n [-1, 0, 5, -2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 349484 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 3) of the result:\nA =\n[[1, 3, 4, 5, 0],\n [0, 2, 5, -2, -3],\n [1, -1, -4, -4, 5],\n [0, 2, -5, 5, 0],\n [-4, -4, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18645 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 1, 2, 1, 0],\n [3, -3, 5, 0, -2],\n [-4, -5, -5, 5, 4],\n [-3, -2, -4, 5, 5],\n [5, -5, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54150 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[5, 0, 0, 5, 3],\n [-4, -2, -1, -5, 2],\n [2, 0, -1, 2, -3],\n [-3, -4, -1, -3, -3],\n [0, 2, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 478 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -5, -5, 4, 1],\n [1, -5, -5, -2, -1],\n [-1, -2, 2, 1, 3],\n [1, 4, -5, 1, -5],\n [1, 4, 2, 5, 3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -446 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^4 where A is:\n[[-3, -2, -2, 3, 1],\n [-3, 4, -1, 1, 2],\n [-5, -4, 1, 5, -4],\n [1, 3, 5, -4, 1],\n [-2, 5, -4, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3265 | MATH |
[
{
"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[-5, 0, 0, 1, 0],\n [0, -1, -2, 0, 0],\n [0, -2, 4, 0, 0],\n [1, 0, 0, 5, 2],\n [0, 0, 0, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 2) of the result:\nA =\n[[0, -1, 2, -3, -1],\n [-1, 3, -4, -3, -4],\n [2, -4, 4, 2, -1],\n [-3, -3, 2, -5, 2],\n [-1, -4, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -28305 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -2, -1, 4, -1],\n [-5, 0, 3, -4, 1],\n [0, -1, -2, -2, 0],\n [-2, -1, 0, -1, 1],\n [3, 4, 1, 1, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2211 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 2, -2, -5, -1],\n [2, -2, 2, 2, -3],\n [3, -3, -5, -4, 0],\n [4, -4, 0, -5, 5],\n [-5, -1, 4, 5, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 576104 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 2) of the result:\nA =\n[[2, -3, -3, -5, -3],\n [5, -5, 2, -5, -1],\n [3, 1, -2, 5, 3],\n [3, -4, 4, 4, 5],\n [0, -2, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24698 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 5, 4, 3, -1],\n [0, -5, 0, -4, 0],\n [3, 2, 3, 4, 2],\n [-3, 2, 0, 0, 0],\n [-3, 4, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7606 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[0, 3, 0, 0, 0],\n [3, 5, 0, 0, -4],\n [0, 0, 4, 2, 4],\n [0, 0, 2, 4, -2],\n [0, -4, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1616 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, 4, -3, 3, 0],\n [4, -4, -3, 0, -2],\n [-3, -3, 3, -1, 0],\n [3, 0, -1, 5, 2],\n [0, -2, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85962 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, -4, 2, -5, 1],\n [-4, -1, -2, -2, 0],\n [2, -2, 0, 0, -2],\n [-5, -2, 0, -2, 0],\n [1, 0, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31656 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 4, -4, 0, -5],\n [-5, 5, -3, -3, 5],\n [-1, -5, 4, 0, 1],\n [4, 5, -3, -2, 4],\n [5, 4, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37888 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, -4, 0, 0, 0],\n [-4, -5, 4, -2, 0],\n [0, 4, 3, 2, -1],\n [0, -2, 2, -2, -2],\n [0, 0, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 290176 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 0, -4, 4, 5],\n [1, 3, 0, -3, 1],\n [-1, -5, -3, -1, 1],\n [-3, 0, -1, -5, 4],\n [0, 2, -5, -4, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15340 | 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, 0, 4, 2],\n [4, -2, 2, -2, 4],\n [0, 2, 2, 0, -5],\n [4, -2, 0, -3, 4],\n [2, 4, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 971952 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, -3, 3, -1, 3],\n [4, 0, 3, 1, 1],\n [2, 1, 3, 5, 3],\n [0, 1, -4, 3, -5],\n [-5, -3, 0, -1, -4]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1950 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[3, 3, -1, -2, -2],\n [3, 4, -2, -2, -4],\n [-1, -2, 2, 2, 2],\n [-2, -2, 2, 4, 0],\n [-2, -4, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1462 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -3, 2, -2, 0],\n [-3, -5, -3, 1, 4],\n [2, -3, -5, 0, 2],\n [-2, 1, 0, -5, -4],\n [0, 4, 2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11514 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 4, 4, -2, 1],\n [4, -4, -2, -1, -4],\n [4, -2, 3, -3, 1],\n [-2, -1, -3, 0, 2],\n [1, -4, 1, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3817 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^5 where A is:\n[[4, -4, 5, 4, 0],\n [0, -4, -4, -4, 4],\n [-5, -1, 2, -4, -1],\n [2, 4, -1, -4, -3],\n [0, 5, 5, -1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8495 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -2, -1, -4, 3],\n [-4, 4, -4, 4, 3],\n [-3, 4, 1, -2, 0],\n [-2, 4, 1, -5, -3],\n [-3, -5, 0, 5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15783 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[2, 5, 1, 4, 2],\n [0, 3, -3, 4, 4],\n [3, -2, 1, 3, -4],\n [-4, 3, -3, 3, -1],\n [0, -4, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 0, 0, 1, 4],\n [0, 3, -4, -1, 0],\n [0, -4, -3, 0, 0],\n [1, -1, 0, -4, 2],\n [4, 0, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1710 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 0, 4, 2, 4],\n [4, -4, 3, -3, 2],\n [2, -3, -3, 0, -5],\n [-2, -5, -3, 3, -1],\n [-1, 5, -2, -3, -1]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11033 | MATH |
[
{
"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[5, -2, 2, -2, 5],\n [2, 0, 5, -1, -2],\n [-2, -2, 5, 3, -2],\n [3, 4, 0, 4, 1],\n [4, -3, 2, -3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -597 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 2, -4, 4, 2],\n [2, 3, -2, 0, -3],\n [-4, -2, 5, -3, -5],\n [4, 0, -3, -3, 2],\n [2, -3, -5, 2, -5]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5112 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 0, -5, 5, -4],\n [1, -5, 1, -2, 4],\n [0, 2, 3, 0, 5],\n [3, -2, 0, 2, 3],\n [-3, -4, 0, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5216 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, 2, 2, -2, 0],\n [2, -1, 0, 2, 0],\n [2, 0, -5, -1, 0],\n [-2, 2, -1, -4, -1],\n [0, 0, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34337 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, 0, 2, 2, 3],\n [0, -1, -1, -3, 4],\n [2, -1, -1, 2, -3],\n [2, -3, 2, 4, 2],\n [3, 4, -3, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19732 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[5, -2, 0, 5, -3],\n [-2, -5, -2, -2, -1],\n [0, -2, 3, -2, 2],\n [5, -2, -2, 2, -2],\n [-3, -1, 2, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24015 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 5, -4, -1, -2],\n [3, -1, 3, 5, 3],\n [-4, 3, -3, -2, -5],\n [-5, -5, 3, 5, 2],\n [-1, -1, 3, -3, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14202 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 3, 0, -4, -5],\n [-4, -5, 4, 4, 3],\n [4, 2, 1, -3, 2],\n [-4, -4, 5, 4, -3],\n [1, -5, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35315 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 4, -5, -2, -5],\n [-5, 4, -5, 1, 1],\n [-2, -4, -3, 2, 2],\n [5, 5, 0, 4, 3],\n [5, 3, -2, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6399 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, -3, 0, 2, 1],\n [-3, 0, 1, 2, -1],\n [0, 1, -2, 2, 0],\n [2, 2, 2, 1, 2],\n [1, -1, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11579 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 0, 2, -1, 0],\n [0, 4, -1, -2, 0],\n [2, -1, 4, 4, -4],\n [-1, -2, 4, -4, 4],\n [0, 0, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 494 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[0, 3, 2, -1, 2],\n [3, 3, 0, -2, 1],\n [2, 0, -3, -1, -3],\n [-1, -2, -1, -3, 0],\n [2, 1, -3, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75582 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 2, -1, -2, 0],\n [2, 0, -3, 0, 2],\n [-1, -3, 0, 4, -2],\n [-2, 0, 4, 5, 2],\n [0, 2, -2, 2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5494 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 0, -4, 2, 0],\n [0, -3, 0, 1, 2],\n [-4, 0, 4, 0, 0],\n [2, 1, 0, 3, -4],\n [0, 2, 0, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 973 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 2, -3, 5, 3],\n [-4, 0, -5, 1, -3],\n [1, -2, 3, -1, -3],\n [2, 0, -4, -3, 2],\n [4, 1, 4, 0, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10921 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, -3, -2, 0, 0],\n [-3, -2, 4, 2, 2],\n [-2, 4, 1, 0, -2],\n [0, 2, 0, 5, 2],\n [0, 2, -2, 2, 1]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7006 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[5, 3, 5, 4, 0],\n [2, 3, 4, -2, -5],\n [2, -4, 5, -5, 1],\n [4, 3, 5, 3, -3],\n [0, 1, 4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5270 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, 1, -2, -4, 2],\n [5, -1, 0, 5, 1],\n [4, -5, 2, -2, 3],\n [-5, 5, -4, 0, 5],\n [4, 5, -5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31990 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, 0, 2, 2, 0],\n [0, -5, 0, 2, 0],\n [2, 0, -1, 2, 0],\n [2, 2, 2, 4, 1],\n [0, 0, 0, 1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58328 | MATH |
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