messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 4) of the result:\nA =\n[[-4, 0, 2, -2],\n [0, -2, 1, 1],\n [2, 1, 1, 2],\n [-2, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (1, 4) of the result:\nA =\n[[1, 0, -2, 2],\n [0, 3, 2, 0],\n [-2, 2, -1, -2],\n [2, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-4, 1, -3, 0],\n [-4, -1, 3, -2],\n [4, -2, -1, 1],\n [3, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -176 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 3, 0, 1],\n [3, -3, 0, -3],\n [0, 0, 2, 2],\n [1, -3, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 908 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, -4, -4, 4],\n [3, -3, 4, -1],\n [4, 0, 2, 4],\n [0, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -150 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -2, 0, 0],\n [-2, -1, -2, -4],\n [0, -2, -2, 0],\n [0, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4498 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 2, -4, -1],\n [2, -1, 0, 0],\n [-4, 0, -2, 3],\n [-1, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12573 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, -2, 1, 3],\n [-3, -2, -3, 3],\n [4, -3, -3, 3],\n [1, -2, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[3, 0, 0, -2],\n [0, 3, 4, -2],\n [0, 4, 2, 0],\n [-2, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (3, 4) of the result:\nA =\n[[0, -2, -2, -2],\n [-2, 3, -4, 2],\n [-2, -4, 4, 0],\n [-2, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -4, 3, -3],\n [3, 0, 0, -3],\n [-2, 2, -2, -2],\n [-4, 1, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 592 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, -2, 0, -2],\n [-2, -2, 1, 2],\n [0, 1, 1, 0],\n [-2, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 289 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 2, 2, -4],\n [-2, 2, -4, 2],\n [2, -2, -2, 0],\n [1, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 216 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 2, -3, -4],\n [-1, 3, 4, -4],\n [3, -2, 3, 2],\n [-1, -1, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, 2, 3, 1],\n [2, 3, 0, 4],\n [-2, 0, -2, 4],\n [1, 4, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1696 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, -3, 2, 3],\n [2, -2, 2, -4],\n [-3, 1, 3, 3],\n [3, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 3, 4, 0],\n [-1, -3, 3, 2],\n [-1, 3, -1, 4],\n [0, 4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1870 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 3, -2, 3],\n [3, -2, -2, -1],\n [-2, -2, 1, 2],\n [3, -1, 2, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1280 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[1, 2, -2, 3],\n [2, 3, 4, 1],\n [2, -3, 4, 2],\n [3, 3, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 3, 1, 2],\n [3, 4, 1, -2],\n [1, 1, 3, -2],\n [2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3564 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[-3, -2, 3, -2],\n [-4, 2, 3, 1],\n [-4, -1, -2, 1],\n [-3, -4, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 2th power of the matrix:\n[[1, 0, 1, 0],\n [0, 0, 4, 0],\n [1, 4, 2, 2],\n [0, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -2, 0, 0],\n [-2, 1, 3, 0],\n [0, 3, -3, 0],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 4, 4, 1],\n [4, -2, -1, -2],\n [4, -1, 4, 0],\n [1, -2, 0, -1]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1337 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 0, -4, -3],\n [0, 2, -1, 2],\n [-4, -1, 4, -2],\n [-3, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7247 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[4, -3, 0, 0],\n [-3, -1, 2, -4],\n [0, 2, 1, 2],\n [0, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, 2, 0],\n [0, 3, 0, 2],\n [2, 0, 4, -2],\n [0, 2, -2, 3]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-1, -1, 4, -1],\n [-4, -2, 1, 1],\n [-3, 4, -4, -1],\n [4, 3, 1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[4, -4, 2, 2],\n [-4, 2, 4, -1],\n [2, 4, 4, -3],\n [2, -1, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-3, 3, -3, -4],\n [1, -1, 1, 3],\n [-3, -4, 0, 4],\n [-2, -4, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[1, -4, 0, -4],\n [2, -4, 1, -3],\n [-1, -1, 3, 3],\n [3, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -52 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[-4, 0, 2, 4],\n [1, 4, 2, -1],\n [-2, 3, -3, 2],\n [0, -3, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -26 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -1, 0, 2],\n [-1, 3, 0, 2],\n [0, 0, -4, 2],\n [2, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4138 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-3, -2, 3, 3],\n [-1, 2, -2, 3],\n [-2, 0, -3, 3],\n [3, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 2th power of the matrix:\n[[2, 0, 0, -3],\n [0, 2, 3, -2],\n [0, 3, 2, 4],\n [-3, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, 1, 3, 0],\n [3, 0, -2, 3],\n [2, 2, -1, 2],\n [4, -2, 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": "For the matrix power A^2 where A =\n[[3, 3, -4, 3],\n [-2, 2, 2, -2],\n [1, 2, -4, -3],\n [3, 1, 0, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[0, 1, 0, -1],\n [1, 3, 0, -2],\n [0, 0, -4, 3],\n [-1, -2, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 3, 2, -3],\n [3, 1, 1, 0],\n [2, 1, 0, -1],\n [-3, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 775 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 4, -1, -1],\n [-2, -3, -2, 1],\n [-2, 3, 1, 0],\n [-2, 1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3344 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 2, 2, -2],\n [2, 4, -3, -1],\n [2, -3, -3, 0],\n [-2, -1, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, 0, 0, -1],\n [0, -3, 0, 2],\n [0, 0, 2, 2],\n [-1, 2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 285 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[1, -2, 0, 0],\n [-2, 3, -3, 3],\n [0, -3, 4, 0],\n [0, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^2 where A is:\n[[-4, -3, 0, 4],\n [2, -2, 0, 4],\n [1, 2, 1, -2],\n [3, 3, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[-2, -1, 2, 3],\n [-4, -1, 1, 0],\n [1, 4, 0, 0],\n [-4, 3, 3, -3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 0, -1, -2],\n [0, 0, 0, -2],\n [-1, 0, -2, -1],\n [-2, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, 0, 0],\n [2, 4, 2, 2],\n [0, 2, -2, 0],\n [0, 2, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5290 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 3th power of the matrix:\n[[2, 1, 3, -3],\n [1, 1, -1, -1],\n [-4, 3, 0, -3],\n [3, 4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | 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, -1, 0],\n [-2, 1, 0, 0],\n [-1, 0, 4, 1],\n [0, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 103 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 2th power of the matrix:\n[[-2, 2, -3, 3],\n [-1, -1, 3, 0],\n [4, 0, -4, 0],\n [1, -1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, 0, 0, 0],\n [0, 2, 0, -4],\n [0, 0, 0, 1],\n [0, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 2, 4, -2],\n [4, -1, 1, -4],\n [1, 1, -1, -1],\n [-4, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1152 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 2th power of the matrix:\n[[-2, 2, -1, -2],\n [2, -1, 2, 0],\n [-1, 2, 1, 0],\n [-2, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -1, 1, 0],\n [-1, 3, 0, 0],\n [1, 0, 0, 4],\n [0, 0, 4, -1]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, -2, -2, 0],\n [-2, 0, -2, 2],\n [-2, -2, 3, 0],\n [0, 2, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2073 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[4, -2, 2, 0],\n [-2, -1, 2, -2],\n [2, 2, 2, 0],\n [0, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -114 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^3 where A is:\n[[-3, -2, -2, 0],\n [-2, 4, -1, 2],\n [-2, -1, -2, -2],\n [0, 2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "What is the value at position (4, 4) of the matrix A^3 where A is:\n[[-2, -4, -2, -2],\n [-4, 1, -1, 2],\n [-2, -1, -4, -4],\n [-2, 2, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -52 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-2, -4, 2, -3],\n [-4, 4, 2, -3],\n [-1, -3, 2, 0],\n [4, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -146 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-4, -3, -1, -1],\n [-4, -1, -3, 2],\n [-4, -4, -3, -2],\n [4, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 437 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, 2, -2, -4],\n [0, -2, 0, 0],\n [-4, -4, 0, -2],\n [0, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2625 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 0, 3, -3],\n [3, -4, -2, -2],\n [0, -4, 3, 3],\n [-3, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1186 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 4, 0, 3],\n [0, 1, -4, -2],\n [3, -2, -4, -4],\n [4, 2, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 2, 2, -1],\n [3, 1, -1, 0],\n [1, -1, -3, -1],\n [3, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 158 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -2, 1, -1],\n [-2, 3, 0, 2],\n [1, 0, 0, 1],\n [-1, 2, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 625 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -1, 4, 4],\n [3, -4, -4, 4],\n [-4, -1, -2, 4],\n [3, 4, -3, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2074 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, 0, 0, -4],\n [0, 1, -2, 2],\n [0, -2, 0, -3],\n [-4, 2, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1048 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[3, 1, 0, 1],\n [1, -1, -2, 0],\n [0, -2, -4, 0],\n [1, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -2, -1, 0],\n [-2, -2, -2, -1],\n [-1, -2, -3, -4],\n [0, -1, -4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19074 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 0, 2, 0],\n [1, 0, 3, 4],\n [0, 4, 0, -3],\n [3, -1, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1170 | MATH |
[
{
"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, 2, -4, 1],\n [-2, 4, -4, -1],\n [3, 3, -4, -2],\n [1, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[4, 1, -2, 3],\n [1, -4, -2, 2],\n [-2, -2, 2, 0],\n [3, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 3th power of the matrix:\n[[-4, 2, -3, 1],\n [2, -3, 0, 4],\n [-3, 0, 2, -2],\n [1, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 170 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 2, 3, -1],\n [2, -3, 1, -2],\n [3, 1, -1, 2],\n [-1, -2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 147 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, 0, 2, -2],\n [0, 1, 0, 2],\n [2, 0, -3, 1],\n [-2, 2, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, -4, 0, -1],\n [-3, -2, -3, 0],\n [-1, 3, -1, 1],\n [1, -3, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 435 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 2) of the result:\nA =\n[[4, 2, -2, -4],\n [2, 2, 2, 1],\n [-2, 2, -1, 2],\n [-4, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, -3, -1, -3],\n [-3, 3, -3, 1],\n [-4, -3, 4, 4],\n [4, -2, 0, 0]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-3, 2, -2, 0],\n [2, 4, 0, 0],\n [-2, 0, 3, 2],\n [0, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -3, 0, 0],\n [-3, 4, 1, -2],\n [0, 1, 1, 0],\n [0, -2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 728 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 2, 2, 0],\n [2, 0, 2, -1],\n [2, 2, -3, -3],\n [0, -1, -3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -144 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 1, 2, 0],\n [1, 4, 1, 0],\n [2, 1, -2, 2],\n [0, 0, 2, -2]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 3, 1, -1],\n [-1, 3, -4, 0],\n [-2, 3, -4, 0],\n [-2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 895 | MATH |
[
{
"content": "For the matrix power A^2 where A =\n[[0, 4, 3, 2],\n [-2, 2, 2, 3],\n [-2, 4, 3, 4],\n [0, -2, -1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the value at position (1, 4) of the 3th power of the matrix:\n[[0, 1, -3, -1],\n [0, 1, -2, 0],\n [4, -2, -1, 0],\n [1, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -2, 4, -2],\n [-2, 2, 0, 0],\n [4, 0, 1, -2],\n [-2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 745 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -1, 0, 2],\n [-1, -3, 0, 0],\n [0, 0, -2, 2],\n [2, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 217 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -1, 2, 4],\n [-1, 2, -2, -4],\n [2, -2, -3, 2],\n [4, -4, 2, 4]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 845 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, 0, -3, -2],\n [0, 2, 4, -2],\n [-3, 4, -3, -2],\n [-2, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 3th power of the matrix:\n[[4, 2, 0, 0],\n [2, 4, 1, -4],\n [0, 1, 2, 2],\n [0, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, -1, 1, 0],\n [2, -4, -4, -4],\n [3, -3, 2, 4],\n [-2, -4, 1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (2, 2) of the result:\nA =\n[[2, -2, -2, 3],\n [-2, -4, -1, 1],\n [-3, 2, 3, 2],\n [0, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Calculate the matrix power A^2 and find the value at position (1, 2) of the result:\nA =\n[[0, -2, 4, -3],\n [0, 4, 0, 2],\n [2, 3, -3, -3],\n [3, 4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-2, 4, -3, -1],\n [0, -2, 2, -4],\n [-4, 0, 1, 2],\n [0, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[0, -2, -3, 3],\n [3, 3, -3, 2],\n [4, 2, 0, 1],\n [4, 4, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-4, 3, 2, -1],\n [3, -2, 2, -2],\n [0, 2, 2, -4],\n [0, 1, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, -3, -3, 4],\n [-3, -1, -3, 3],\n [2, 3, -3, 1],\n [3, -2, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, 0, 4],\n [0, -4, 3, 0],\n [0, 3, 3, -1],\n [4, 0, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-4, -2, -2, 0],\n [-2, -3, 0, 0],\n [-2, 0, -2, -4],\n [0, 0, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 217 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[4, 1, -2, -2],\n [1, -4, -2, 0],\n [-2, -2, -4, 0],\n [-2, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
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