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[[4, 1, -4, -1, 5],\n [4, 3, 0, -4, 2],\n [4, -3, 4, -4, 4],\n [1, -4, -1, 0, 5],\n [2, 5, -4, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[0, 2, -1, -3, -2],\n [2, -4, -2, 0, -2],\n [-1, -2, -2, -4, 0],\n [-3, 0, -4, -4, -5],\n [-2, -2, 0, -5, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 585 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 4) of the result:\nA =\n[[-4, -2, -5, 3, 1],\n [-5, 5, -4, -2, 2],\n [-4, -4, -3, 2, -4],\n [2, -2, 4, -5, 2],\n [5, 2, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[3, -4, -3, -5, -2],\n [2, -5, -4, -4, 2],\n [-5, 2, 5, 0, 2],\n [4, 1, 3, 3, 5],\n [-4, 0, 1, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 902 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^2 where A is:\n[[1, 0, 5, 3, -2],\n [-3, 0, -1, -3, -3],\n [2, 2, -4, 2, 4],\n [-5, 5, -3, 2, 1],\n [4, 0, 4, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -36 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-4, 0, 2, -3, 0],\n [0, -3, 0, 4, -4],\n [2, 0, 1, 3, 4],\n [-3, 4, 3, -2, -4],\n [0, -4, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-1, 2, 0, 2, -2],\n [2, -2, -2, -2, -2],\n [0, -2, 1, -2, 2],\n [2, -2, -2, 4, -1],\n [-2, -2, 2, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[-4, -3, -4, -4, -2],\n [-3, -2, -4, 2, 0],\n [-4, -4, -1, -4, 2],\n [-4, 2, -4, 3, 1],\n [-2, 0, 2, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, 2, 0, -1, -2],\n [2, -3, 3, 0, 1],\n [0, 3, -5, -1, 0],\n [-1, 0, -1, -3, 2],\n [-2, 1, 0, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -347 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-5, 0, 3, -4, 2],\n [3, 0, 2, 1, 1],\n [-4, -1, -5, -3, 1],\n [-2, 2, 5, -4, -3],\n [5, 0, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1105 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[0, -1, 0, 0, -3],\n [-1, 4, 3, 4, 4],\n [0, 3, -3, -4, 2],\n [0, 4, -4, 4, 1],\n [-3, 4, 2, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 257 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-3, 5, 2, 2, -2],\n [-5, 1, -4, 1, 0],\n [2, -4, 3, -2, 4],\n [4, 4, -4, 4, -5],\n [4, 3, 1, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -504 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[-3, 0, -4, 0, 0],\n [0, 0, 0, 3, 4],\n [-4, 0, 4, 0, -1],\n [0, 3, 0, 1, -4],\n [0, 4, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -3, -2, 1, -2],\n [-3, 2, 0, 0, 2],\n [-2, 0, 2, 0, 3],\n [1, 0, 0, -5, -2],\n [-2, 2, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2792 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 3, 1, 0, -4],\n [3, 0, 0, 1, 3],\n [1, 0, 2, 2, -3],\n [0, 1, 2, -1, 3],\n [-4, 3, -3, 3, -4]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -267 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, -5, 5, 1, -3],\n [-5, -2, -1, 4, 5],\n [-1, 4, -4, -1, 1],\n [-3, -4, -5, 5, -3],\n [5, -3, 0, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1429 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 4, -4, 0, -3],\n [-4, -5, -2, -1, 5],\n [5, -2, 1, -1, -5],\n [-5, 0, -5, -3, 4],\n [5, 0, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30126 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -4, 0, 1, 0],\n [-4, -3, 4, 5, -4],\n [0, 4, -3, 4, -3],\n [1, 5, 4, -1, 2],\n [0, -4, -3, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5937 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[-5, -4, 0, 0, -2],\n [-4, 4, 0, -3, 1],\n [0, 0, 5, 2, -2],\n [0, -3, 2, -1, -4],\n [-2, 1, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1168 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-5, 5, 0, -1, 4],\n [5, 3, -1, -3, 2],\n [0, -1, 1, 3, 0],\n [-1, -3, 3, 3, -1],\n [4, 2, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 615 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, 1, 2, 5, -1],\n [-4, 3, 4, -4, -1],\n [-4, -5, 5, 1, 3],\n [-3, -3, -5, 5, 0],\n [2, 5, -2, 1, -3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 249 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -4, 0, -1, 0],\n [-4, -1, -1, -1, 3],\n [-5, 5, 0, 1, -5],\n [-3, -1, -2, 0, 5],\n [1, -4, 4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2659 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 0, 2, -1, 2],\n [0, 3, 1, -1, -4],\n [2, 1, 0, -2, -1],\n [-1, -1, -2, -1, -1],\n [2, -4, -1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1554 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, -2, -2, 4, -2],\n [-2, -1, -4, 2, 2],\n [-2, -4, -1, 0, 0],\n [4, 2, 0, -4, 2],\n [-2, 2, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6111 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 3, 0, -2, -5],\n [2, 2, 2, 2, 2],\n [5, 2, -3, 0, 4],\n [-1, -4, -3, 1, 3],\n [3, -2, 1, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, 0, 4, 2, 1],\n [2, 0, 4, 3, -2],\n [1, 5, -4, 0, -5],\n [5, -2, -3, -1, 1],\n [1, 5, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -660 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 2, 1, 0, -2],\n [2, -4, -2, -1, 0],\n [1, -2, 0, 0, 1],\n [0, -1, 0, 4, -1],\n [-2, 0, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5258 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-1, 0, 0, 2, 0],\n [0, 3, 0, 4, 0],\n [0, 0, 5, -2, -4],\n [2, 4, -2, -4, -2],\n [0, 0, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-2, 0, 1, 4, -4],\n [0, 4, -4, 0, -3],\n [1, -4, 5, 0, 4],\n [4, 0, 0, -4, 0],\n [-4, -3, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6576 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-2, -5, 1, -3, 0],\n [1, 2, -4, -3, 1],\n [-5, 2, 0, 1, 0],\n [-2, -5, -5, -5, -5],\n [4, 4, -5, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3320 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -2, 2, 3, -2],\n [-3, 1, 4, -5, 3],\n [0, 2, -5, -4, 3],\n [1, 4, 2, 0, 3],\n [3, 3, -3, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1161 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -4, 0, -1, -2],\n [-1, -3, -3, -5, -2],\n [5, 1, 1, -3, -5],\n [3, -2, 1, -4, -1],\n [-1, 4, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 20867 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, -4, 1, 4, -4],\n [1, 5, -3, 5, -3],\n [-5, 3, -4, 1, -4],\n [-4, 4, -2, 0, 2],\n [0, -4, -1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-3, 0, 4, 0, 1],\n [0, 4, 0, 2, 0],\n [4, 0, 1, 0, 2],\n [0, 2, 0, -3, 0],\n [1, 0, 2, 0, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 139 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 2th power of the matrix:\n[[2, 0, 0, -3, -1],\n [0, -3, -2, -2, 0],\n [0, -2, 4, 2, 4],\n [-3, -2, 2, -5, -4],\n [-1, 0, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 2, -5, 0, 5],\n [3, 5, 0, 4, -5],\n [-2, 0, 4, -2, 3],\n [-3, -2, 0, -5, -2],\n [0, -3, 0, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -4, -1, 0, 1],\n [5, 3, 1, -1, -4],\n [4, 4, 1, 3, -2],\n [0, 2, 1, -2, -1],\n [2, 5, -4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6380 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, -2, 2, 0, -3],\n [0, 2, -5, -5, 2],\n [-3, 5, -5, -3, -3],\n [-3, -1, -2, 5, 2],\n [-3, 2, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, 2, 2, 0, -2],\n [2, -2, -2, 0, -2],\n [2, -2, 5, 2, -2],\n [0, 0, 2, 1, 0],\n [-2, -2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1517 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, 1, -1, -4, 2],\n [2, 4, -2, 3, 1],\n [-2, -3, -4, 4, 0],\n [3, -4, 2, -2, 1],\n [-5, 5, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2414 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -3, 2, 5, -3],\n [-2, 4, 0, -2, -1],\n [-3, -3, 0, -2, 3],\n [-2, 3, 0, 3, 3],\n [-4, 3, 0, 0, 4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -117 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 2, -2, 2, -2],\n [2, -1, 4, 0, 3],\n [-2, 4, 2, -1, 2],\n [2, 0, -1, 1, 0],\n [-2, 3, 2, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1978 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-5, -5, 0, 2, 2],\n [-5, 0, 3, -1, 5],\n [3, -1, -5, -3, -1],\n [0, -2, 1, 5, -1],\n [-2, -5, -4, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 423 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 2, 1, -2, 0],\n [2, 5, 4, -2, 3],\n [1, 4, 2, -2, 0],\n [-2, -2, -2, 1, 0],\n [0, 3, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29948 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-5, 4, 1, -4, -1],\n [0, 3, 4, -4, -3],\n [3, 0, -2, -1, 4],\n [4, 0, -5, 5, -1],\n [-3, 5, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[0, 0, 2, -4, 0],\n [0, 5, 2, -4, 2],\n [2, 2, -1, 0, 2],\n [-4, -4, 0, -4, 2],\n [0, 2, 2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 203 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[2, -1, -1, 3, 4],\n [-4, 2, 1, 4, 5],\n [4, -4, 4, -3, 4],\n [-5, 3, -2, 4, -2],\n [1, 5, -2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 0, 4, 1, -4],\n [-3, -3, -1, -5, -5],\n [-1, 2, 3, 1, -5],\n [-5, 0, -3, 4, 3],\n [5, 5, -2, -2, -2]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138 | 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, 0, -4],\n [-3, -2, -4, -2, 1],\n [1, 4, -5, 5, 5],\n [3, -4, -4, 1, -5],\n [-2, -1, 1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16469 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 2, 0, 4, -2],\n [2, 3, -2, -4, 0],\n [0, -2, 2, -2, 2],\n [4, -4, -2, 0, -2],\n [-2, 0, 2, -2, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25094 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, -1, -2, 0, 2],\n [-1, 4, -1, 0, 0],\n [-2, -1, 3, 0, 0],\n [0, 0, 0, -2, -1],\n [2, 0, 0, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 471 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[5, 2, -4, -3, 3],\n [-3, 5, -1, 0, -1],\n [1, 4, -4, 4, 1],\n [-2, 4, -1, -4, 1],\n [-4, -4, 4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2034 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -2, 2, -2, 0],\n [-2, -4, 4, 1, 0],\n [2, 4, -5, -2, 2],\n [-2, 1, -2, -2, 2],\n [0, 0, 2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, -4, -1, 2, 1],\n [-4, -2, 1, 2, 0],\n [-1, 1, -1, 5, 0],\n [2, 2, 5, 4, 0],\n [1, 0, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11147 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, -2, 2, -2, 2],\n [-2, 4, 0, -2, 0],\n [2, 0, 0, -1, 1],\n [-2, -2, -1, -1, 2],\n [2, 0, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 3) of the result:\nA =\n[[-1, 4, -1, -4, 1],\n [4, 0, 2, -2, -2],\n [-2, 5, -5, 3, -5],\n [5, -2, -1, 1, -4],\n [-4, -3, -4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -49 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -3, 5, 1, 1],\n [0, 4, 4, -2, 1],\n [4, 0, 1, -4, -3],\n [-2, 4, 4, -3, 0],\n [-2, -2, 1, 3, 1]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[-3, 0, 0, -2, 0],\n [0, -1, 2, 0, -1],\n [0, 2, -3, -3, -4],\n [-2, 0, -3, 5, 0],\n [0, -1, -4, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -312 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, -4, 0, -5, 3],\n [5, 1, -4, 4, 1],\n [-5, 0, -1, 0, -3],\n [-4, -2, -2, 3, 0],\n [0, 3, 2, 4, 5]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, 5, 4, 2, -5],\n [2, 2, 5, 3, -1],\n [-1, -4, -2, -4, -1],\n [1, 2, 0, -3, -3],\n [5, -5, 1, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2022 | MATH |
[
{
"content": "Find the value at position (3, 4) of the 4th power of the matrix:\n[[-5, -1, 2, 0, -2],\n [-1, 3, 1, 0, 4],\n [2, 1, 1, 4, 0],\n [0, 0, 4, 2, 2],\n [-2, 4, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 588 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -5, -3, -2, 2],\n [-1, 1, -5, 3, -4],\n [2, -1, -5, 5, 0],\n [5, 2, 2, -2, -2],\n [1, 2, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -469 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, -1, -1, -4, -2],\n [2, -3, 4, -2, 3],\n [2, 4, -3, 2, 5],\n [4, 3, 1, 3, -5],\n [-1, 0, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -198 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 5, 2, -1, 1],\n [-4, 2, 3, -2, -1],\n [-2, -2, 0, 4, -2],\n [1, 1, 5, -3, -3],\n [-1, -1, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1260 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 5, 5, 5, 3],\n [-1, 5, 3, 0, 3],\n [0, -2, -3, 3, -1],\n [3, 2, 5, -2, 2],\n [-4, 4, -1, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13812 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[2, 3, 0, 0, 1],\n [3, 0, 1, -2, 4],\n [0, 1, -1, -2, 0],\n [0, -2, -2, -5, 2],\n [1, 4, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3422 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -2, 0, 3, 4],\n [-2, -5, 2, 3, 0],\n [0, 2, 5, -1, 1],\n [3, 3, -1, 2, 2],\n [4, 0, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 359 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -1, 4, -2, 4],\n [-1, 5, 0, -2, 0],\n [4, 0, 1, -2, 0],\n [-2, -2, -2, 0, -2],\n [4, 0, 0, -2, 4]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -288 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-2, 3, -1, 2, 1],\n [0, 5, 2, -5, 3],\n [-5, 2, -5, -3, -5],\n [3, -1, 3, 3, -5],\n [2, 4, 4, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, -1, 0, -1, -3],\n [-1, 4, -5, -2, 2],\n [0, -5, 0, -4, -4],\n [-1, -2, -4, -5, -2],\n [-3, 2, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42657 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, 1, 0, -4, -4],\n [0, 0, 3, 2, -5],\n [4, -3, -5, -1, -3],\n [-3, 3, 1, -3, -3],\n [0, 3, 4, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -361 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[3, -1, 2, -4, 5],\n [-3, 4, -2, 5, 2],\n [5, 3, -3, -5, 5],\n [1, 2, 4, -1, -1],\n [4, -5, 4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[0, -4, 0, -2, -3],\n [-4, 0, -3, 2, 4],\n [0, -3, 5, 2, -2],\n [-2, 2, 2, -4, -2],\n [-3, 4, -2, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 510 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^4 where A is:\n[[-5, 0, -4, 2, -2],\n [0, -5, -1, 0, 2],\n [-4, -1, -3, 5, 4],\n [2, 0, 5, -5, 2],\n [-2, 2, 4, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5416 | MATH |
[
{
"content": "Find the value at position (5, 1) of the 3th power of the matrix:\n[[5, 1, -5, 3, 3],\n [5, 0, -5, 5, 0],\n [0, 1, 1, 4, 0],\n [2, 1, -3, -3, 1],\n [-4, -1, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -283 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[-5, 3, -2, -2, 0],\n [3, -1, 2, -2, 1],\n [-2, 2, -5, 0, 0],\n [-2, -2, 0, -4, -4],\n [0, 1, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -196 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, 2, 0, -2, -3],\n [2, 0, 0, 2, 0],\n [0, 0, 0, 0, -2],\n [-2, 2, 0, 5, -2],\n [-3, 0, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2877 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 2th power of the matrix:\n[[-2, 2, 1, 2, 2],\n [2, 5, -4, 2, 0],\n [1, -4, 0, 0, -1],\n [2, 2, 0, -4, 1],\n [2, 0, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 0, -1, -2, 2],\n [0, 4, 4, 5, 2],\n [-4, -3, 5, 4, 1],\n [5, -3, -3, -4, -4],\n [4, -3, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1369 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 0, 4, 1, -4],\n [4, -3, -4, 5, 5],\n [5, 4, 4, -5, 5],\n [-4, 3, 1, -5, 0],\n [-2, 4, 3, 4, -3]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 187 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -2, 2, -2, 0],\n [-2, 3, -4, -1, 4],\n [2, -4, 2, 0, 1],\n [-2, -1, 0, -5, 2],\n [0, 4, 1, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3059 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 4, -3, 0, 3],\n [4, 3, -2, -2, 1],\n [-3, -2, -2, -2, -4],\n [0, -2, -2, 0, -1],\n [3, 1, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1183 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, -3, -3, 5],\n [-4, 3, -5, -5, 0],\n [2, -3, 5, -3, 5],\n [2, 4, 3, 0, -2],\n [1, -3, -3, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, 2, -5, 4, -1],\n [3, 4, 0, 0, 4],\n [3, 1, 3, 2, 3],\n [2, 3, 0, 3, -1],\n [-3, -4, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1468 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-5, 0, 5, 3, 5],\n [-3, -1, 1, 4, 4],\n [0, -4, -4, 2, 4],\n [-2, 4, 4, 2, -4],\n [-1, 0, -3, 0, 3]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 2, -2, -3, 0],\n [2, 4, -4, 0, 3],\n [-2, -4, -1, 2, 4],\n [-3, 0, 2, -2, 2],\n [0, 3, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 335 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -1, -5, -2, -2],\n [-2, -2, 4, -1, 5],\n [-4, 1, -4, 3, -3],\n [-4, 1, 2, 1, -2],\n [-5, -4, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22407 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[5, 4, -1, 2, 0],\n [4, -2, -4, 0, -2],\n [-1, -4, -4, 2, -2],\n [2, 0, 2, 5, -2],\n [0, -2, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 265 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -4, 0, 0, -1],\n [-4, 4, -4, 3, 1],\n [0, 5, 5, -1, -3],\n [5, -1, -1, 2, -5],\n [2, -1, 5, 3, 1]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[5, 1, 0, 3, 0],\n [1, -3, -2, -2, -4],\n [0, -2, -3, -2, 1],\n [3, -2, -2, 0, -1],\n [0, -4, 1, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 257 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 4) of the result:\nA =\n[[5, -1, 4, 2, -1],\n [1, -3, -1, -5, -4],\n [-3, -1, 2, 2, 3],\n [-5, 2, 2, -3, 2],\n [5, 2, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 3th power of the matrix:\n[[2, 3, -4, 3, -2],\n [4, -3, 1, -2, -5],\n [-4, 1, 0, -3, -4],\n [-1, 0, 3, 0, 3],\n [4, 4, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 0, -4, 0, 2],\n [0, 1, 0, 0, -2],\n [-4, 0, 4, -1, 4],\n [0, 0, -1, 5, 2],\n [2, -2, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1896 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-3, -2, 0, 2, -1],\n [-2, 2, 0, 3, -2],\n [0, 0, 0, -2, 1],\n [2, 3, -2, 0, 0],\n [-1, -2, 1, 0, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 204 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[5, 3, 2, 4, -2],\n [3, -2, 3, 0, 0],\n [2, 3, 5, 1, 2],\n [4, 0, 1, -4, -1],\n [-2, 0, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2753 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[2, -4, 1, 0, 2],\n [3, 4, 2, 5, -5],\n [3, -5, 5, -5, -3],\n [2, -2, -3, 4, -4],\n [-2, 1, 3, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 635 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[1, -5, -2, -1, -2],\n [-5, 4, -5, 1, 5],\n [0, 5, -4, -2, 0],\n [0, -1, -2, -5, -4],\n [3, 1, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2581 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 2, -4, 4, 0],\n [2, 3, -2, 0, -1],\n [-4, -2, -1, 0, 0],\n [4, 0, 0, 5, -2],\n [0, -1, 0, -2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19975 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 1, 0, 4, 0],\n [-5, 4, -5, -3, -4],\n [4, 3, 1, -3, 2],\n [5, -5, -4, -3, 0],\n [2, -4, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27270 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[1, 2, -1, 0, -2],\n [2, -2, 1, 1, 2],\n [-1, 1, -4, 2, 2],\n [0, 1, 2, -4, 4],\n [-2, 2, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 904 | MATH |
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