messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, -3, -1, 3, -1],\n [-1, 4, 0, 5, -1],\n [5, -3, -4, 1, 3],\n [2, 2, -5, -5, 4],\n [2, -5, 0, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -99 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, 0, -1, 3, 1],\n [-1, -5, 3, 5, -3],\n [5, -1, 1, 0, 3],\n [-4, -2, -5, 2, 0],\n [4, -1, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2336 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-4, 2, 4, 3, 2],\n [2, 0, 0, -2, -1],\n [4, 0, 2, -2, 4],\n [3, -2, -2, -5, 2],\n [2, -1, 4, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 230 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[3, 0, 1, 0, 0],\n [0, -4, 1, -4, -4],\n [1, 1, 5, 0, -2],\n [0, -4, 0, -2, 2],\n [0, -4, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1314 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, 1, 0, -1, 1],\n [1, -3, 0, 5, -2],\n [0, 0, 0, 1, 3],\n [-1, 5, 1, 5, 2],\n [1, -2, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 187 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, -4, 1, 1, 2],\n [-4, 2, -2, 4, 3],\n [1, -2, -3, -2, 0],\n [1, 4, -2, 4, 0],\n [2, 3, 0, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15031 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, -1, -2, 0, 0],\n [-1, -1, 0, 0, -5],\n [-2, 0, -2, 0, 1],\n [0, 0, 0, -3, 0],\n [0, -5, 1, 0, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1747 | MATH |
[
{
"content": "Find the value at position (5, 3) of the 2th power of the matrix:\n[[-2, -1, 0, 1, 3],\n [-1, -4, 2, 0, 1],\n [0, 2, -5, -2, 0],\n [1, 0, -2, 4, 4],\n [3, 1, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 1, -4, 3, 4],\n [2, -1, -2, 0, -4],\n [-5, 4, 3, 0, 4],\n [3, 2, 3, 0, 4],\n [2, 3, 4, 1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1487 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[0, 0, 0, 1, 0],\n [0, -1, 0, -3, -2],\n [0, 0, 2, -1, -2],\n [1, -3, -1, -1, 1],\n [0, -2, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 187 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, -4, 0, 0, -2],\n [-4, 3, 0, -2, -1],\n [0, 0, -5, -2, 3],\n [0, -2, -2, 4, -1],\n [-2, -1, 3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -267 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^2 where A is:\n[[3, -2, 1, 2, -2],\n [-2, 5, 0, 3, -4],\n [1, 0, -2, -3, 4],\n [2, 3, -3, -2, 0],\n [-2, -4, 4, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 5, -5, -2, 4],\n [-4, 4, 5, 2, -2],\n [0, -2, 4, 2, 3],\n [-1, 4, -3, 1, -2],\n [-2, -5, 2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3207 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, -2, 4, -3, 1],\n [-3, 3, 4, -1, -1],\n [3, -3, 1, 1, 0],\n [2, 1, -1, -5, -1],\n [2, 0, -5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1775 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[5, 2, 0, 1, -2],\n [2, 4, -2, 2, -3],\n [0, -2, -1, 0, 0],\n [1, 2, 0, 0, -2],\n [-2, -3, 0, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3073 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, 0, 4, 0, 0],\n [0, 4, -1, 4, 4],\n [4, -1, 3, 4, -4],\n [0, 4, 4, -5, -1],\n [0, 4, -4, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 197 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 3) of the result:\nA =\n[[1, 0, -2, 3, -2],\n [4, 5, -3, 1, 3],\n [-1, -1, 4, 5, -3],\n [3, 2, -5, 2, -3],\n [2, 1, 0, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -411 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[5, -2, -3, -5, -4],\n [-3, -3, 4, -1, -4],\n [4, -5, -5, 5, -4],\n [2, -1, -2, 2, 4],\n [4, -5, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 635 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[2, 0, -1, -1, 0],\n [0, 0, 0, -3, 2],\n [-1, 0, 4, -1, -2],\n [-1, -3, -1, 5, -1],\n [0, 2, -2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, 0, -3, 0, 3],\n [0, -4, 2, 2, 2],\n [-3, 2, -3, 0, 0],\n [0, 2, 0, -2, -2],\n [3, 2, 0, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2226 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 4) of the result:\nA =\n[[1, 0, -2, 4, 3],\n [0, -4, -2, -1, -2],\n [-2, -2, 3, 0, 2],\n [4, -1, 0, -2, -3],\n [3, -2, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 2th power of the matrix:\n[[2, 0, -5, 3, -5],\n [2, 5, -4, 2, 0],\n [5, 2, -2, -2, -1],\n [0, 0, -5, 2, -5],\n [-3, 5, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 4) of the result:\nA =\n[[-1, 0, -3, -5, 0],\n [-3, -2, -5, 3, -2],\n [4, 4, -4, -5, -1],\n [4, 4, -1, -2, 2],\n [0, 4, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -244 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 2, 4, -2, 3],\n [2, -2, 4, 3, 4],\n [4, 4, -1, 0, 0],\n [-2, 3, 0, -1, -4],\n [3, 4, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43472 | 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, 1, 3],\n [3, 2, 5, -2, 3],\n [-3, 1, 3, 3, 3],\n [4, 5, 2, -2, 0],\n [-2, 1, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19991 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 2, 2, 2, 0],\n [2, 2, 2, 3, 0],\n [2, 2, 2, -2, 0],\n [2, 3, -2, -2, 0],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 147 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[0, 1, -5, 2, 0],\n [1, 2, 2, 0, 2],\n [-5, 2, -3, 4, 0],\n [2, 0, 4, 3, -1],\n [0, 2, 0, -1, 5]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 4, 1, 3, -1],\n [-4, -3, -5, -1, -4],\n [-2, 0, 2, 0, 3],\n [-4, 1, 3, -2, 0],\n [-2, -5, -1, -4, 1]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, -4, -3, -1, 0],\n [-4, -1, -2, 2, 4],\n [-3, -2, -5, -1, 0],\n [-1, 2, -1, -5, -1],\n [0, 4, 0, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1380 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[2, 0, 2, -1, -5],\n [-3, -3, 1, 0, 4],\n [-3, 5, 5, 0, -4],\n [-2, -1, -1, -5, 2],\n [0, 0, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 702 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, 0, 1, 1, 5],\n [-1, -5, -5, 5, -1],\n [1, 5, -1, 3, 4],\n [4, 5, 2, -5, 5],\n [4, -5, -5, 1, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 640 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, 0, 0, -1, 3],\n [0, -2, 1, 0, 0],\n [0, 1, -4, -1, 4],\n [-1, 0, -1, 0, 0],\n [3, 0, 4, 0, 4]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -27 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -2, -5, 0, -3],\n [-1, 1, 1, 4, -5],\n [3, -5, 5, 0, -5],\n [5, 1, -1, 1, 2],\n [4, -1, -2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 434 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^2 where A is:\n[[5, -4, 2, 0, -2],\n [-4, -1, 0, -2, 2],\n [2, 0, 2, -2, 1],\n [0, -2, -2, 3, 0],\n [-2, 2, 1, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "What is the value at position (4, 5) of the matrix A^3 where A is:\n[[5, -2, 2, -2, -2],\n [-2, 1, 1, -4, 0],\n [2, 1, -5, -3, 0],\n [-2, -4, -3, -5, 2],\n [-2, 0, 0, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 176 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, -5, -5, -4, -4],\n [0, -2, 2, -5, -5],\n [5, 0, -1, 5, 3],\n [-2, 2, -5, -4, 1],\n [-4, -1, 5, 4, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 526 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[2, 0, 1, -4, 2],\n [0, 5, 2, 1, 4],\n [1, 2, 4, 0, 0],\n [-4, 1, 0, 0, 4],\n [2, 4, 0, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 259 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[5, -2, 4, 3, -2],\n [1, 3, 4, 5, 2],\n [3, 2, 0, 4, 3],\n [-5, -4, 4, 2, 3],\n [5, 5, 3, 5, -4]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, 1, 2, 2, 2],\n [1, -2, -2, 0, 2],\n [2, -2, 5, 3, 2],\n [2, 0, 3, 4, -2],\n [2, 2, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11448 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[0, 2, -1, 4, 2],\n [2, -4, -1, 3, 0],\n [-1, -1, 5, -4, 0],\n [4, 3, -4, 5, 0],\n [2, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 130 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 3th power of the matrix:\n[[-3, 0, 2, 1, 2],\n [0, -1, 2, 4, -2],\n [2, 2, 4, 1, 2],\n [1, 4, 1, 3, -4],\n [2, -2, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -74 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 0, 1, -4, -5],\n [1, -3, 0, 5, -1],\n [-1, -3, -4, -5, 0],\n [1, -5, -1, -5, 0],\n [-5, 3, 0, 0, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19810 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-3, -2, -4, 0, -1],\n [0, 3, -5, 2, 0],\n [4, -2, -4, -1, 1],\n [3, -1, 4, -2, 0],\n [0, -1, 2, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -26 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -1, 2, 4, 0],\n [-1, 5, -3, -3, 0],\n [2, -3, 5, 4, 2],\n [4, -3, 4, -1, -3],\n [0, 0, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81842 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[3, 4, 0, 2, 0],\n [4, 1, -3, 4, -2],\n [0, -3, 0, -3, 0],\n [2, 4, -3, -3, 2],\n [0, -2, 0, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 4, -2, -4, 1],\n [3, -4, -2, 4, 1],\n [1, 4, -3, 2, 4],\n [0, -5, -3, -4, 1],\n [5, -4, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3254 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -5, -1, -5, 5],\n [4, -2, 1, 2, -3],\n [1, 1, 0, 3, -2],\n [-3, 3, 5, -5, -3],\n [4, -2, -1, -5, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1118 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 1, 3, 0, 4],\n [1, -2, 0, -2, -1],\n [3, 0, 5, 4, -2],\n [0, -2, 4, -4, 1],\n [4, -1, -2, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2111 | MATH |
[
{
"content": "Find the value at position (1, 4) of the 2th power of the matrix:\n[[0, 0, 0, -2, 2],\n [0, 0, 1, -3, 1],\n [0, 1, 0, -1, 1],\n [-2, -3, -1, 3, 0],\n [2, 1, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^2 where A is:\n[[5, -5, 2, -5, 0],\n [2, -5, 5, 3, 1],\n [3, 4, -4, 5, -1],\n [4, -3, -2, -3, -5],\n [-1, -2, 3, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | MATH |
[
{
"content": "What is the value at position (3, 3) of the matrix A^2 where A is:\n[[-1, 0, -2, 0, -1],\n [0, 0, 4, 2, 4],\n [-2, 4, -4, 4, -1],\n [0, 2, 4, 5, 0],\n [-1, 4, -1, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 5) of the result:\nA =\n[[-1, 5, 5, 3, 2],\n [1, -2, -4, 0, 4],\n [0, -1, -1, 3, 2],\n [-3, 1, 2, -2, 3],\n [-5, 5, -4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[1, -2, 4, -5, -4],\n [5, 3, -2, -2, -4],\n [-2, 0, 4, 0, 2],\n [5, 3, 4, -1, -2],\n [-3, 5, 5, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -102 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^3 where A is:\n[[-4, 2, 0, 5, 1],\n [2, 5, 4, 1, 1],\n [0, 4, 5, 0, 0],\n [5, 1, 0, -5, 0],\n [1, 1, 0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 2, -4, -4],\n [0, 0, 2, -4, 0],\n [2, 2, 0, -1, 0],\n [-4, -4, -1, 4, -4],\n [-4, 0, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15923 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[-5, -1, 0, 4, 4],\n [-2, -1, 0, 1, 2],\n [5, -3, -5, 3, -2],\n [4, 2, -3, 2, 0],\n [2, 0, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 332 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, 0, -1, 4, 4],\n [0, 4, 1, 2, -2],\n [-1, 1, -4, -2, 0],\n [4, 2, -2, -2, 0],\n [4, -2, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "What is the value at position (5, 1) of the matrix A^3 where A is:\n[[2, 2, 2, 2, -4],\n [2, 1, 3, -2, 1],\n [2, 3, -1, 1, 4],\n [2, -2, 1, -2, -1],\n [-4, 1, 4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -154 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -3, 5, 0, 2],\n [-1, -2, -3, -2, 0],\n [-1, -3, -4, 3, -4],\n [0, 1, 5, -2, 1],\n [-5, 5, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1938 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-3, 0, -1, 4, -1],\n [-5, -1, 3, 2, 2],\n [-5, 5, -4, -4, 3],\n [-1, -1, -4, 5, 4],\n [-1, -2, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 455 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-3, 5, -2, 0, -3],\n [2, 2, 1, -4, 1],\n [-2, 3, 0, -2, 5],\n [-3, -5, -4, -2, -3],\n [2, -4, -1, 3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -105 | MATH |
[
{
"content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[1, -2, -2, 0, -2],\n [-2, 2, -2, 0, 0],\n [-2, -2, 4, -2, 2],\n [0, 0, -2, 0, 2],\n [-2, 0, 2, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 244 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 0, 3, -5, 1],\n [4, -5, -4, -3, 0],\n [-3, -5, 4, 5, -2],\n [3, -2, 3, -4, -5],\n [-5, 1, -5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32437 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-1, 2, 1, 0, -5],\n [2, -4, 4, -5, 3],\n [1, 4, 4, -4, -2],\n [0, -5, -4, 3, -2],\n [-5, 3, -2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 674 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 2, -4, 5, 3],\n [3, -5, 4, -4, -2],\n [-2, -4, 1, -1, 1],\n [1, -2, 4, 0, -4],\n [-1, -5, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 260 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-1, -1, -5, -5, 2],\n [-1, -4, -1, 0, -3],\n [0, -2, 2, 1, 0],\n [-3, 0, -5, 1, -4],\n [-4, 3, -4, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 204 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[5, -2, -2, 0, -2],\n [-2, 0, -2, 4, -4],\n [-2, -2, 3, 5, 0],\n [0, 4, 5, 0, -2],\n [-2, -4, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 3, 3, 5, 5],\n [1, -3, -2, -3, 0],\n [0, 3, -4, 5, -1],\n [5, -1, 1, -3, 3],\n [-5, -1, -1, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43695 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 3, -2, -2, -1],\n [3, 4, 0, 1, 2],\n [-2, 0, -4, 3, 4],\n [-2, 1, 3, -1, -1],\n [-1, 2, 4, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 1, -3, 0, -2],\n [-4, 0, -3, 5, -4],\n [0, -1, 5, -3, -4],\n [3, -3, -2, -5, -1],\n [2, 5, -5, 4, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 592 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, 0, 4, -4, 0],\n [0, 2, 0, -2, 2],\n [4, 0, 3, -2, 2],\n [-4, -2, -2, -3, 0],\n [0, 2, 2, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39803 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-5, -4, -2, -1, 2],\n [-4, -1, 2, 2, -4],\n [-2, 2, 1, -2, 2],\n [-1, 2, -2, -5, 0],\n [2, -4, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 387 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-3, -2, 3, -3, 2],\n [0, -5, 5, -4, 4],\n [3, -2, 4, 2, 3],\n [3, 5, 0, 5, 5],\n [0, 4, 3, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3957 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 3, 3, -4, 4],\n [4, -3, -5, 1, -4],\n [1, 0, 2, -4, 1],\n [0, 5, 4, 1, 0],\n [4, 3, 3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 67 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, 0, 2, -3],\n [0, 1, -2, -4, 2],\n [0, -2, -4, 0, 0],\n [2, -4, 0, -2, -1],\n [-3, 2, 0, -1, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10109 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[5, 2, 1, 3, -1],\n [2, 2, 2, 0, -2],\n [1, 2, 0, -2, -2],\n [3, 0, -2, 3, -4],\n [-1, -2, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -1, -2, 2, 2],\n [-1, 1, 1, -2, 0],\n [-2, 1, -1, -2, 2],\n [2, -2, -2, -2, -2],\n [2, 0, 2, -2, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5468 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, -1, 2, 3, -3],\n [-3, -1, 1, -5, 3],\n [-4, 2, -4, -4, -1],\n [-3, -3, -5, 1, 1],\n [0, 0, -4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1845 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 3, 2, -5, -5],\n [-3, 1, 0, 0, 2],\n [5, 3, 3, 4, -5],\n [-3, 1, 2, -3, 3],\n [5, 4, 3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 489 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -3, 1, 2, -2],\n [-5, -5, -5, 2, 1],\n [1, 4, -2, 1, -4],\n [1, 4, -1, -2, 2],\n [0, -4, -2, 0, -5]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2227 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[-2, -4, 1, 2, 4],\n [-4, 5, 1, -4, 3],\n [1, 1, 0, -2, -2],\n [2, -4, -2, 1, -4],\n [4, 3, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2424 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 3, 0, 2, 0],\n [3, -1, -2, 0, 4],\n [0, -2, 1, 0, 2],\n [2, 0, 0, 5, -2],\n [0, 4, 2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2601 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, -1, 2, -5, 2],\n [-4, -4, -3, -2, 0],\n [2, 3, -2, -1, -4],\n [-4, 5, 5, 4, -4],\n [-4, 4, -5, 5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 593 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^2 where A is:\n[[-2, 4, 3, 4, 4],\n [1, -1, -5, -1, -2],\n [4, 1, 1, -4, 5],\n [-2, -5, -2, 0, -2],\n [2, -4, -3, 1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -25 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, 0, -1, 0, -4],\n [0, 1, 3, 2, -2],\n [-1, 3, 4, 2, 3],\n [0, 2, 2, 1, 0],\n [-4, -2, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 423 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -2, 5, -4, -5],\n [4, 0, -1, 3, -3],\n [-2, 0, -3, 2, 1],\n [-4, 1, 1, 4, 0],\n [4, -2, 1, 3, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1853 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[5, 2, 2, -2, 2],\n [2, 4, -2, -3, 0],\n [2, -2, 2, 2, 0],\n [-2, -3, 2, 5, 2],\n [2, 0, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4053 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, 1, 4, 5, 4],\n [-2, 0, 3, 0, -3],\n [1, 0, -4, 1, -5],\n [1, 2, 2, 5, -5],\n [-4, -3, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1444 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[3, -4, 2, -4, 0],\n [1, -5, -4, -2, -1],\n [-5, 5, -1, -2, -1],\n [-3, 3, 3, -4, 5],\n [-1, 1, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 111 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -4, 2, 2, -2],\n [0, 0, 3, 5, 4],\n [2, -5, 4, 3, -1],\n [-2, 4, 4, 3, 0],\n [3, 2, 5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 482 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[2, 4, 0, -3, -1],\n [-3, 1, -3, 1, -4],\n [-1, 0, 3, 4, 0],\n [4, 3, 5, 3, -2],\n [-1, 2, 5, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, 0, 1, 0],\n [0, 4, -1, 0, -2],\n [0, -1, -5, 2, 2],\n [1, 0, 2, 2, 0],\n [0, -2, 2, 0, -4]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 0, 2, -1, 4],\n [0, 3, 2, -4, 3],\n [2, 2, -4, 0, 2],\n [-1, -4, 0, -1, -2],\n [4, 3, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16280 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, -4, 2, -4, -3],\n [-4, -4, -2, -1, -1],\n [2, -2, 4, 0, 1],\n [-4, -1, 0, -3, -1],\n [-3, -1, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3383 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[-1, -4, 5, -3, 2],\n [-2, 5, 4, 5, 3],\n [-5, 0, 5, 0, 3],\n [-3, -1, -5, 3, 2],\n [5, 0, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 537 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[0, 0, 3, 0, 0],\n [0, 1, -2, 0, -2],\n [3, -2, 3, 1, -3],\n [0, 0, 1, 5, -2],\n [0, -2, -3, -2, -4]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[5, 5, 3, 3, -4],\n [1, -1, -5, -1, -2],\n [-3, -3, 4, -3, -4],\n [-4, 3, 0, -4, -2],\n [-2, -5, -1, 5, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -5, -1, -2, -5],\n [4, -4, -5, -3, -1],\n [4, -3, -3, 5, 2],\n [-3, -1, 3, 5, 0],\n [4, -4, 3, 4, -5]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, 1, 0, 0, 4],\n [2, 3, 5, -1, 3],\n [4, 3, -3, 4, 0],\n [-3, -4, -4, -1, 1],\n [-4, 5, 2, -1, 4]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 1, 2, -2, 4],\n [1, -5, 1, 0, 3],\n [2, 1, -4, 4, 0],\n [-2, 0, 4, 4, 3],\n [4, 3, 0, 3, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14254 | MATH |
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