messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-5, -1, 0, -4, 2],\n [-1, 5, 2, -2, -1],\n [0, 2, -1, -2, -4],\n [-4, -2, -2, 5, 0],\n [2, -1, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 367 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[1, 0, 0, 1, -3],\n [0, 2, 0, 1, 3],\n [0, 0, -3, -2, -4],\n [1, 1, -2, -3, 3],\n [-3, 3, -4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 339 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 2, -1, -2, -2],\n [2, -2, 0, 3, -1],\n [-1, 0, 4, 2, 0],\n [-2, 3, 2, -2, -2],\n [-2, -1, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3181 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, -2, 2, -4, -5],\n [0, 0, -5, 0, 3],\n [2, -3, 3, 5, 2],\n [1, -4, 1, 3, 4],\n [4, 4, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 0, 2, -3, 1],\n [0, -3, 4, 2, 0],\n [2, 4, 5, 0, 0],\n [-3, 2, 0, -2, 1],\n [1, 0, 0, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 798 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[1, 0, -2, 0, -3],\n [0, 2, -3, 0, -2],\n [-2, -3, 4, 2, 4],\n [0, 0, 2, 2, 1],\n [-3, -2, 4, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 384 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 2, 4, 0, -2],\n [2, -1, 4, -5, 0],\n [4, 4, -2, 0, 1],\n [0, -5, 0, -4, 4],\n [-2, 0, 1, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 290 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[5, 0, 0, 5, 0],\n [0, -1, -2, 0, -2],\n [0, -2, -3, -4, 1],\n [5, 0, -4, 4, -4],\n [0, -2, 1, -4, -3]], determine the value at position (5, 3).\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^2 where A is:\n[[5, 0, 4, -2, 2],\n [0, 2, 4, 1, -2],\n [4, 4, 4, -2, 0],\n [-2, 1, -2, -3, -1],\n [2, -2, 0, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 420 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[5, -3, -1, -2, 2],\n [2, -2, 1, -4, -4],\n [-4, 2, 4, -5, -5],\n [-2, -2, -3, -5, -4],\n [-3, -5, -1, 3, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 548 | 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, 5, 4, 0],\n [1, 4, -1, -2, 1],\n [-3, -5, -5, 4, -3],\n [3, -4, -3, 0, 1],\n [2, 0, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17240 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-5, 0, 4, 0, -5],\n [5, -5, 3, -2, -1],\n [2, 5, 0, -3, 5],\n [1, 5, 3, -4, 5],\n [-5, 2, 4, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[2, -1, 0, -1, 1],\n [-1, -5, -2, -1, 1],\n [0, -2, 4, 0, 0],\n [-1, -1, 0, -1, 4],\n [1, 1, 0, 4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 3th power of the matrix:\n[[-1, 5, 4, 3, 3],\n [3, 3, 5, -2, 1],\n [1, 0, 0, 4, -4],\n [-4, 0, 1, -2, -4],\n [3, -1, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 233 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 0, 1, 0, 1],\n [1, -2, 0, -4, -1],\n [5, -1, -1, 2, -5],\n [-2, -5, -2, 4, -4],\n [-2, -4, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3720 | 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, -5, 2, -1, 0],\n [0, 2, 5, -4, -2],\n [-4, -1, -4, -1, -2],\n [2, 0, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26814 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, 2, 0, 2, 0],\n [2, 4, 5, 4, -2],\n [0, 5, 5, -1, -2],\n [2, 4, -1, -5, -2],\n [0, -2, -2, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1953 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, -2, 2, 1, -3],\n [-2, 5, 0, 4, 0],\n [2, 0, 5, 0, -3],\n [1, 4, 0, -2, -1],\n [-3, 0, -3, -1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33792 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -1, -4, 3, 0],\n [-1, 2, -1, 0, 2],\n [-4, -1, 4, 0, -4],\n [3, 0, 0, -2, -2],\n [0, 2, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 794 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[3, 0, 1, -2, -3],\n [-3, 2, 0, -3, 2],\n [4, 4, 0, 3, -4],\n [-5, 4, 5, -3, 0],\n [-2, -2, 3, -5, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 364 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, 4, 1, 4, 5],\n [2, -2, 1, -3, -4],\n [4, -1, -1, -4, 3],\n [-1, 5, 0, 2, -5],\n [-2, -1, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 426 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, -4, 4, -5, -2],\n [-4, 3, 1, 5, 0],\n [-4, -3, 1, 2, -5],\n [-2, -2, -5, -1, -1],\n [-3, -5, 1, 1, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 829 | MATH |
[
{
"content": "Find the value at position (3, 5) of the 4th power of the matrix:\n[[0, 2, 2, 1, -5],\n [3, 4, -1, 3, 3],\n [-3, 4, -5, -3, -3],\n [1, 0, 0, -2, -5],\n [-1, -1, 5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1176 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 4) of the result:\nA =\n[[0, 0, 2, 4, -2],\n [0, 1, 0, 2, 4],\n [2, 0, -4, 1, 0],\n [4, 2, 1, -4, 0],\n [-2, 4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^3 where A is:\n[[4, 0, -1, 2, -2],\n [0, -1, -2, 2, 4],\n [-1, -2, 2, -2, 0],\n [2, 2, -2, 5, 0],\n [-2, 4, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[0, 5, 5, -4, 5],\n [2, 3, -4, -3, -2],\n [2, 0, 3, -1, -3],\n [-1, -5, -3, -2, 3],\n [5, 0, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 188 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[2, 2, -2, -2, 5],\n [0, -2, 5, -4, 4],\n [3, 1, -2, -1, 4],\n [1, 1, 3, -5, -3],\n [3, 0, 1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-3, -5, -2, -3, 0],\n [-2, 3, 0, 0, -2],\n [2, -4, 5, 0, 1],\n [-3, 5, -4, 3, 2],\n [3, -3, 2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, 0, -2, 2, 0],\n [0, 4, -1, 2, 5],\n [-2, -1, 5, -2, 2],\n [2, 2, -2, -5, 2],\n [0, 5, 2, 2, 0]]\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^3 where A is:\n[[1, 5, -3, 0, 3],\n [0, 5, -1, 2, 0],\n [0, -1, -5, 0, -4],\n [4, 3, 2, -3, 1],\n [-1, -4, 1, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 396 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-2, 0, 2, 0, -1],\n [0, -3, -4, -2, 3],\n [2, -4, 0, 2, -3],\n [0, -2, 2, -4, -4],\n [-1, 3, -3, -4, -1]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[5, 2, 2, 0, 4],\n [2, 1, 0, 0, -4],\n [2, 0, 5, 2, -2],\n [0, 0, 2, 5, 2],\n [4, -4, -2, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2973 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 1, -2, 0, 2],\n [-2, -2, -5, -3, 5],\n [-3, 2, 1, -3, 5],\n [2, 2, -1, -5, -3],\n [5, 1, -4, -5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2653 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 4, -4, 2, 0],\n [2, 3, -1, -3, 0],\n [0, 3, 2, -2, -2],\n [-2, 0, -3, 1, -4],\n [1, 2, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 967 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, -1, 5, 1, -4],\n [-2, 3, -3, 0, 4],\n [1, -5, 3, 5, 3],\n [2, 1, 3, -2, 5],\n [-3, 1, 5, -3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -4, 0, 4, 2],\n [-4, 1, -2, -5, -4],\n [0, -2, -5, -2, 0],\n [4, -5, -2, 1, 0],\n [2, -4, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51870 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, 3, 4, 5, 3],\n [-1, -5, 1, -4, 4],\n [-2, -5, 5, -1, -2],\n [-4, 3, -4, -2, -4],\n [3, -5, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -195 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[2, -1, -1, 1, -1],\n [1, 3, 0, 2, 3],\n [-3, -4, -3, -2, 3],\n [-3, 5, -5, 3, -5],\n [5, -3, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 0, 0, 3, 2],\n [0, 4, 4, 1, -3],\n [0, 4, -3, -4, 1],\n [3, 1, -4, -4, 0],\n [2, -3, 1, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29107 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 0, 4, -5, 4],\n [0, 2, 0, 0, 1],\n [4, 0, 2, -3, 3],\n [-5, 0, -3, 3, -1],\n [4, 1, 3, -1, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1354 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 0, -1, 4, 5],\n [1, 1, -5, 4, -2],\n [-1, 4, -1, -3, -5],\n [0, -5, 3, -5, -2],\n [5, 2, 1, -5, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4434 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -4, 2, 4, -1],\n [-4, -5, -1, 4, 0],\n [2, -1, -5, -2, 3],\n [4, 4, -2, 0, 2],\n [-1, 0, 3, 2, -5]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 332 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (4, 3) of the result:\nA =\n[[-4, -4, 2, -2, -4],\n [5, 5, 2, -2, 3],\n [2, -3, 2, 4, 5],\n [-2, -1, 5, 5, 2],\n [2, 4, -5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^2 where A is:\n[[-2, 0, 0, 2, 2],\n [0, -4, -2, -2, -2],\n [0, -2, 4, 3, 0],\n [2, -2, 3, 0, 2],\n [2, -2, 0, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^2 where A is:\n[[0, 4, 0, -3, 4],\n [4, 4, -1, -4, 0],\n [0, -1, -2, -2, 0],\n [-3, -4, -2, -3, -2],\n [4, 0, 0, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | 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, 4, 0, -2],\n [1, -4, -1, 0, 0],\n [4, -1, 1, -2, 0],\n [0, 0, -2, -3, -2],\n [-2, 0, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11885 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[0, 0, 0, 4, 4],\n [0, -2, 2, -2, 5],\n [0, 2, -5, 0, 0],\n [4, -2, 0, -4, 2],\n [4, 5, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -316 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -4, -3, -3, -1],\n [0, 1, -3, 0, 3],\n [2, -5, 4, 1, -4],\n [4, 4, -5, -3, 2],\n [1, 2, -5, -4, 5]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -86 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 3th power of the matrix:\n[[4, 0, 4, 3, -3],\n [0, 2, 3, -1, 0],\n [4, 3, 3, 0, 0],\n [3, -1, 0, 3, -2],\n [-3, 0, 0, -2, 0]]\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^3 where A is:\n[[-4, -2, 0, 0, 2],\n [-2, 1, -1, -2, 0],\n [0, -1, 3, -1, 1],\n [0, -2, -1, 0, 2],\n [2, 0, 1, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -162 | MATH |
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