messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[21, -14, 40, -9, -11],\n [-12, 9, -17, -24, 4],\n [20, -15, 28, 28, -5],\n [-69, 58, -52, 9, -37],\n [27, -20, 39, 21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-6, -7, 0, -5, -6],\n [23, 21, 21, 11, 9],\n [4, 3, 6, 1, 0],\n [24, 18, 36, 6, 0],\n [-15, -5, -45, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[27, 12, -10, 16, -7],\n [26, 36, 9, 18, 36],\n [-53, -5, 27, 4, 14],\n [-41, -11, 19, -30, 18],\n [4, 3, 5, -17, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-22, 23, -7, -27, -12],\n [4, 15, 25, 45, 44],\n [-42, 26, -27, -76, -63],\n [-49, -40, 45, -24, 1],\n [-18, -47, 48, 15, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1, 0, 0, -5, 7],\n [1, 15, -15, -11, 19],\n [3, -10, 10, -11, 13],\n [-6, 50, -50, 10, -2],\n [-3, 0, 0, 15, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[42, 36, 24, 16, 24],\n [51, 18, 24, -20, 12],\n [-43, 30, -3, 67, -21],\n [-12, 0, 6, -54, 30],\n [36, 54, 28, 46, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-16, -16, -4, -4, 20],\n [4, 4, 1, 1, -5],\n [-24, -24, -6, -6, 30],\n [-24, -24, -6, -6, 30],\n [-4, -4, -1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-36, 48, -3, -15, 0],\n [-33, 34, 6, -18, -26],\n [-21, 14, 24, -12, -70],\n [57, -14, 0, 60, 38],\n [24, 9, 19, 38, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-9, -7, -1, 25, 28],\n [-29, -19, 11, 1, -24],\n [55, 31, -41, -28, 13],\n [7, 9, 15, 11, 18],\n [1, 3, 9, 15, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, 1, 57, -42, 4],\n [15, -6, -2, -14, 0],\n [-60, 52, 32, 26, 2],\n [-3, -31, 13, 10, -2],\n [15, -23, -39, 45, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-28, -34, 23, 28, -23],\n [0, -2, 3, 28, -3],\n [23, 26, -16, 4, 16],\n [23, 28, -19, -24, 19],\n [-9, -12, 9, 24, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, -30, 19, -12, -1],\n [22, -1, -27, 30, 19],\n [-39, -23, 14, 66, 56],\n [8, 1, 6, -30, -22],\n [48, 11, -23, -42, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-1, -14, -5, 50, 31],\n [1, -1, 0, -5, -1],\n [-2, 20, 6, -44, -34],\n [2, 7, 3, -37, -20],\n [-1, -2, -1, 14, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[71, -50, -2, 35, 13],\n [-89, 55, 8, -31, -10],\n [34, -35, 2, 29, 5],\n [-30, 5, 10, 11, 5],\n [9, -28, 2, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, 9, 0, 18, -15],\n [-30, -18, 0, -36, 30],\n [25, 15, 0, 30, -25],\n [0, 0, 0, 0, 0],\n [-20, -12, 0, -24, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[3, -4, 29, -3, 31],\n [-12, -26, 10, -9, 2],\n [6, 0, 34, -2, 38],\n [3, -2, 23, -2, 25],\n [12, 20, 8, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[8, -22, -22, -2, -28],\n [12, 30, -42, -30, -24],\n [8, 20, -28, -20, -16],\n [-16, -26, 54, 34, 36],\n [7, 14, -24, -16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-9, -18, 15, -3, 12],\n [0, 0, 0, 0, 0],\n [15, 30, -25, 5, -20],\n [-3, -6, 5, -1, 4],\n [-18, -36, 30, -6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[6, -31, 17, 47, 55],\n [51, -5, 60, 1, 12],\n [15, 3, 17, -1, -11],\n [-9, -27, -1, 43, 43],\n [-51, 11, -60, -27, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -10, 0, 3, 0],\n [-10, -8, 12, 4, 2],\n [9, 2, -18, -3, -3],\n [17, -2, -42, -5, -7],\n [-24, 12, 72, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, 25, -20, -15, -15],\n [-18, -15, 12, 9, 9],\n [36, 30, -24, -18, -18],\n [30, 25, -20, -15, -15],\n [-36, -30, 24, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[38, 12, 44, -20, -14],\n [-26, -48, -32, 44, 20],\n [3, -30, 2, 22, 7],\n [-2, 48, 0, -36, -12],\n [-12, -48, -16, 40, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[48, -15, 36, 2, -22],\n [60, -30, 36, -2, -32],\n [-12, 20, 4, 6, 12],\n [-30, 10, -22, -1, 14],\n [24, 5, 28, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[25, -25, 52, -19, 19],\n [14, -6, -10, -3, -28],\n [-17, -41, -1, -18, 32],\n [5, -31, -9, -7, 6],\n [-27, 5, -34, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-38, 0, 59, 4, 21],\n [-56, 0, 28, 40, 62],\n [50, 0, -15, -40, -60],\n [-42, 0, 0, 36, 55],\n [34, 0, -13, -20, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[2, -12, -8, -4, 6],\n [-13, 42, 24, 22, -39],\n [8, -12, -4, -12, 24],\n [-12, 18, 6, 18, -36],\n [-7, 33, 21, 13, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-6, 28, -27, 14, -7],\n [-16, 38, 17, 24, 29],\n [8, -31, 5, 7, -18],\n [8, 18, -15, -48, 13],\n [19, -42, 48, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-28, 0, 40, 10, 2],\n [-14, -5, -24, -19, 14],\n [32, 17, 10, -6, -27],\n [4, 3, 1, -3, -4],\n [-20, -6, 0, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[20, -36, 40, -14, 14],\n [-20, 45, -43, 20, -29],\n [12, -29, 19, -24, 7],\n [44, -36, -16, 32, -62],\n [18, -18, -28, 14, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[5, -14, -14, -7, -12],\n [-14, 40, 44, 20, 29],\n [18, 22, -15, -46, 25],\n [-15, -40, 5, 45, -45],\n [6, 40, 16, -24, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-30, 8, -16, -11, 0],\n [-24, -20, -20, -4, 0],\n [6, 27, 11, -3, 0],\n [18, -51, -3, 15, 0],\n [42, 2, 26, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, 3, -6, -3, -4],\n [-6, -11, -48, 11, -37],\n [8, -12, 24, 12, 16],\n [6, 15, 54, -15, 42],\n [6, -29, -12, 29, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-24, -17, -2, 20, -7],\n [25, -34, 12, -2, -45],\n [10, -8, 8, 2, -8],\n [6, -21, 14, 14, -15],\n [-8, -25, -2, 8, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[41, -8, 27, 26, 0],\n [1, -55, -44, -27, -23],\n [56, -50, 6, -6, -46],\n [32, -1, 25, 25, 23],\n [22, -37, -11, -27, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-22, 30, -26, 20, -38],\n [-10, 12, -8, 2, -2],\n [9, -12, 10, -7, 13],\n [-18, 21, -13, 1, 2],\n [2, -6, 10, -16, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, -37, -14, 70, -1],\n [29, -6, 15, -46, 3],\n [25, -12, -4, -27, 10],\n [-19, 32, 36, -31, -18],\n [-23, 10, -27, 16, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[4, 0, 20, -12, -16],\n [-6, 0, -30, 18, 24],\n [5, 0, 25, -15, -20],\n [-4, 0, -20, 12, 16],\n [-5, 0, -25, 15, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[30, -45, -9, -24, -12],\n [-25, 42, 15, 17, 16],\n [-25, 30, -5, 25, 0],\n [-25, 36, 5, 21, 8],\n [15, -24, -7, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, 6, -33, -6, -12],\n [-2, -2, -12, 2, -8],\n [-2, -5, -36, 14, -65],\n [-1, 13, 18, -15, 30],\n [0, -18, -12, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[31, -6, 32, 14, -41],\n [-12, -16, -16, -22, 2],\n [17, -18, 4, -20, -37],\n [1, -38, 6, -17, -26],\n [-32, 20, -17, 16, 57]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-20, 8, 4, -32, 20],\n [26, -13, 0, 36, -21],\n [27, -29, 31, 4, 8],\n [25, -10, -5, 40, -25],\n [20, -21, 22, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[22, 38, 6, 4, -8],\n [17, 3, 21, 14, -18],\n [10, 12, 6, 4, -6],\n [20, 24, 12, 8, -12],\n [17, 32, 3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-47, -18, 24, -7, -21],\n [7, 8, -1, -13, -1],\n [53, 10, -30, -11, 3],\n [15, -24, -17, -33, -41],\n [3, -2, -2, -15, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, -16, -12, -16, 8],\n [-10, -20, -15, -20, 10],\n [-10, -20, -15, -20, 10],\n [-6, -12, -9, -12, 6],\n [4, 8, 6, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[15, 4, -13, 2, -3],\n [3, 37, 11, 23, -48],\n [-7, -1, 9, -3, 0],\n [11, 4, -15, 8, -3],\n [18, 1, -33, 16, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-7, -15, -16, -4, 29],\n [-30, -22, 12, -6, 26],\n [-3, -8, 7, -3, -6],\n [-9, -26, 7, -9, 0],\n [3, -8, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, 20, 16, 20, -16],\n [8, -20, -16, -20, 16],\n [6, -15, -12, -15, 12],\n [-6, 15, 12, 15, -12],\n [10, -25, -20, -25, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[31, -13, 0, 14, -10],\n [-9, -3, 0, -6, 30],\n [12, -10, 0, 4, 16],\n [44, -18, 0, 20, -16],\n [34, -12, 0, 16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, 13, 15, 4, 8],\n [-20, -36, -34, 18, -34],\n [8, 10, 18, 28, -4],\n [0, -3, 3, 24, -12],\n [-14, -24, -25, 3, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, -12, -6, 31, -34],\n [-1, 14, 18, -27, 36],\n [-44, 4, -24, -32, 20],\n [-3, -12, -18, 21, -30],\n [14, 2, 12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, 19, 21, -15, -17],\n [39, 15, 11, 7, 3],\n [0, -67, -19, 7, 7],\n [42, -49, -11, 9, -19],\n [-3, -30, 7, -20, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, 18, 24, -6, 24],\n [-18, -18, -24, 6, -24],\n [18, 18, 24, -6, 24],\n [-15, -15, -20, 5, -20],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-13, -8, -7, 4, -5],\n [17, -22, 2, -30, -11],\n [46, 28, 34, 2, -4],\n [0, 19, 15, 0, -13],\n [-5, 22, 10, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-18, -24, 6, 6, 6],\n [15, 20, -5, -5, -5],\n [18, 24, -6, -6, -6],\n [18, 24, -6, -6, -6],\n [12, 16, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, -20, 33, -29, -18],\n [16, 46, -58, 50, 39],\n [1, -22, -10, -13, 65],\n [1, -26, 19, -8, -27],\n [-41, -86, 64, -68, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-29, 23, 5, 11, -16],\n [15, -20, -5, -35, 20],\n [-3, 25, 19, 13, 8],\n [6, -12, -12, 24, -18],\n [7, -1, 7, -27, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[42, 0, 33, 25, 22],\n [-30, -22, -22, -32, 0],\n [33, -15, 27, 10, 28],\n [-15, 3, -12, -7, -10],\n [24, 26, 17, 31, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, 11, -2, 2, -24],\n [21, -15, 15, -3, -6],\n [-9, -7, 13, -3, 23],\n [-14, -40, -2, -4, 23],\n [-24, -4, -8, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[11, 7, -16, 11, -15],\n [-14, -22, 28, -14, 30],\n [7, 11, -14, 7, -15],\n [-8, -16, 18, -8, 20],\n [25, 5, -30, 25, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, -60, 0, 30, 10],\n [38, -18, -19, 28, -16],\n [8, 12, -4, -2, -6],\n [-50, 0, 25, -25, 25],\n [36, -36, -18, 36, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, -24, 6, 4, -46],\n [51, -9, -9, -11, 17],\n [-72, 54, -45, -12, 9],\n [-15, -6, 36, -2, 39],\n [21, 36, -36, 32, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-6, -4, -2, -10, 10],\n [-12, -6, 42, 66, -48],\n [17, 10, -25, -29, 17],\n [37, 23, -26, -10, -5],\n [7, 3, -36, -60, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[25, -34, 34, -32, -49],\n [7, -24, 8, -35, -24],\n [4, -6, -29, -6, 33],\n [25, 8, 5, 11, 26],\n [45, -6, -10, -7, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-9, 0, 5, 14, 5],\n [-20, -4, 12, 16, 0],\n [13, 8, -9, 10, 15],\n [-28, -2, 16, 36, 10],\n [16, 5, -10, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-13, 19, 27, 7, 0],\n [-11, 23, -3, 9, -30],\n [-35, -11, 37, -9, 46],\n [-10, -27, -26, -20, 5],\n [-48, 11, 16, 14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-32, 28, -28, -8, 42],\n [12, -33, 22, 33, -6],\n [-10, 68, -35, -48, 7],\n [-7, -43, 12, 5, -3],\n [10, -32, 21, 36, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, -12, 19, -41, 18],\n [-12, 14, -18, 17, -6],\n [51, -38, 41, -15, 4],\n [12, -35, 15, -23, 27],\n [3, 13, -26, 44, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[3, 0, 9, 18, 9],\n [0, 0, 0, 0, 0],\n [6, 0, 18, 36, 18],\n [-1, 0, -3, -6, -3],\n [4, 0, 12, 24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[44, 20, 5, -33, 32],\n [9, -12, -19, -17, 11],\n [-27, -6, -25, 2, -10],\n [-22, -34, 14, 11, -31],\n [-20, 4, 10, 18, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-13, -21, -40, -1, 8],\n [29, -37, 52, -47, -42],\n [-19, 31, -12, 33, 18],\n [19, 0, -30, -45, 5],\n [-42, -13, -30, 30, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, 12, -12, -8, -16],\n [4, -6, 6, 4, 8],\n [8, -12, 12, 8, 16],\n [8, -12, 12, 8, 16],\n [-4, 6, -6, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, 24, 30, -24, -12],\n [-8, -8, -10, 8, 4],\n [-8, -8, -10, 8, 4],\n [-8, -8, -10, 8, 4],\n [4, 4, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[32, -32, -13, -69, 3],\n [6, -5, -3, -12, 1],\n [-39, 9, 34, 57, -14],\n [-43, -12, 42, 36, -42],\n [43, -5, -35, -54, 29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-25, 15, 30, -30, 30],\n [5, -3, -6, 6, -6],\n [10, -6, -12, 12, -12],\n [-15, 9, 18, -18, 18],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-11, 8, 27, 24, -10],\n [3, 38, -6, -1, 35],\n [-13, -23, 36, 27, -41],\n [3, -30, 39, 18, -48],\n [-9, 22, 8, 13, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-8, 0, 12, 2, -8],\n [20, 0, -30, -5, 20],\n [-4, 0, 6, 1, -4],\n [-24, 0, 36, 6, -24],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, -6, 4, -8, -4],\n [-20, 7, 8, -21, -17],\n [-26, -23, 30, 11, 39],\n [48, 7, -34, -5, -29],\n [4, 26, -16, 30, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-34, -9, -1, 32, -4],\n [-12, 8, 22, 18, 12],\n [2, 7, 13, 2, 8],\n [24, 14, 16, -18, 12],\n [-6, 4, 11, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-24, -28, 11, 15, 13],\n [12, 12, -15, -3, -9],\n [17, 20, -7, -11, -9],\n [10, 12, -3, -7, -5],\n [-9, -4, 35, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-24, 16, -4, 12, -37],\n [-33, -26, -15, -11, -19],\n [16, 67, 66, 32, 10],\n [63, -11, -10, -19, 17],\n [-13, -43, -12, -31, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, 16, -4, -8, -18],\n [-30, 4, 5, 19, -3],\n [-22, -4, 12, 18, 8],\n [-18, -10, 5, 10, 12],\n [2, 40, 24, 24, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[9, 0, -18, 15, -12],\n [-15, 0, 30, -25, 20],\n [-9, 0, 18, -15, 12],\n [-3, 0, 6, -5, 4],\n [12, 0, -24, 20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 0, 6, 0, 6],\n [12, 0, -24, 0, -24],\n [18, 0, -36, 0, -36],\n [6, 0, -12, 0, -12],\n [-9, 0, 18, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[16, 9, -4, -12, -28],\n [-72, -7, 12, 50, 10],\n [50, -32, 16, -68, 18],\n [20, 21, -20, 12, 8],\n [34, 7, -4, -29, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-7, -22, -8, -23, 30],\n [18, 30, 6, 27, -48],\n [35, 32, -10, 36, -64],\n [-3, 8, 2, 20, -6],\n [-21, -28, 2, -34, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[67, 13, 69, 58, -44],\n [17, 22, 1, -1, -22],\n [-27, -17, -11, -12, 28],\n [38, 23, 14, 17, -40],\n [14, 13, -6, -7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-36, -11, -7, -39, 23],\n [-6, 9, -12, 0, 6],\n [24, -26, 38, 6, -22],\n [24, 4, 8, 24, -16],\n [-18, -33, 24, -36, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, 30, -15, -25, 5],\n [-18, -36, 18, 30, -6],\n [18, 36, -18, -30, 6],\n [15, 30, -15, -25, 5],\n [-9, -18, 9, 15, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-12, 8, -14, 26, -16],\n [22, -35, -8, -29, 30],\n [24, -11, 3, -17, 2],\n [-62, 34, 3, 37, -4],\n [0, 11, 3, 8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, 6, -1, -5, 6],\n [-9, -3, 0, 4, -3],\n [0, -3, 3, -5, -3],\n [-12, 3, -7, 17, 3],\n [-9, -3, 0, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-35, -42, -27, -34, 15],\n [-18, 30, -24, -30, -6],\n [-27, -33, -66, -66, -4],\n [-20, -36, -18, -22, 15],\n [34, 20, 32, 45, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, 65, 22, 14, -41],\n [-15, -25, 25, 5, -5],\n [10, 42, -14, -6, -6],\n [18, 3, -57, -15, 33],\n [-11, -1, -4, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[18, -15, 3, 3, 18],\n [21, 6, -7, 6, 19],\n [-15, -33, 6, -3, -9],\n [25, 16, 37, -10, 13],\n [-5, 6, -47, 16, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 11, 24, -11, 26],\n [6, -16, 15, -6, -9],\n [24, 9, -20, 0, 0],\n [-39, 9, 15, -1, 1],\n [-14, -11, 21, 0, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[13, -13, 10, 29, 12],\n [-22, -25, 5, -10, -3],\n [48, 14, -20, 28, 7],\n [-58, 20, 38, -34, -6],\n [23, 20, -7, 11, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-54, 36, 14, 4, -40],\n [-31, 20, 27, 17, -27],\n [30, -28, 0, 3, 7],\n [34, -28, -10, -4, 16],\n [-32, 22, 18, 10, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[6, -6, -24, 18, 24],\n [-3, 21, 30, -15, -30],\n [14, 25, -17, 29, 17],\n [-10, -5, 25, -25, -25],\n [-6, -12, 6, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[4, -12, 24, 8, 20],\n [-6, 18, -36, -12, -30],\n [2, -6, 12, 4, 10],\n [16, -12, 8, 8, 40],\n [3, -9, 18, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[40, 18, 51, -2, -28],\n [20, 12, 14, -16, -2],\n [-19, -49, 22, 32, -71],\n [15, 7, -6, -22, 4],\n [28, -8, 24, -48, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [8, -12, 4, -24, -24],\n [4, -6, 2, -12, -12],\n [2, -3, 1, -6, -6],\n [12, -18, 6, -36, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
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