messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[-18, -30, -6, -30, -24],\n [14, 26, -6, 32, 16],\n [-10, -14, -14, -8, -16],\n [-4, -4, -12, 2, -8],\n [-12, -20, -4, -20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-19, 2, -1, -21, -3],\n [27, 2, 5, 11, 7],\n [8, 12, 16, -46, 0],\n [7, -8, 0, 32, -10],\n [-22, 8, 0, -44, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[14, -8, 14, -48, 39],\n [5, -19, -11, -53, 1],\n [-22, 26, 6, 84, -4],\n [19, 24, 39, 8, 23],\n [28, 2, 16, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-38, 9, 6, 17, 5],\n [-16, -35, -30, 9, -7],\n [26, 4, 15, -7, 4],\n [-57, -61, -47, 28, -1],\n [-7, -22, -15, -3, 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[[-8, -6, -8, 2, -8],\n [7, 11, 9, 0, 7],\n [26, -15, 14, -17, 26],\n [-36, -4, -28, 16, -36],\n [-28, 2, -20, 14, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[20, 6, 30, 40, -58],\n [4, -1, -15, 8, -11],\n [-13, -15, -18, -34, 39],\n [-7, -26, -27, -21, 29],\n [10, -24, -6, -33, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-5, -6, -12, -28, -8],\n [3, -18, -9, -39, -18],\n [-13, 6, -20, -52, -8],\n [9, -36, -9, -39, -26],\n [15, -45, 1, 7, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 0, 0, 24, -24],\n [36, 0, 0, -36, 36],\n [24, 0, 0, -24, 24],\n [24, 0, 0, -24, 24],\n [-6, 0, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-4, -24, -2, -8, -18],\n [-44, 42, -7, -13, 18],\n [22, -9, -20, -33, 27],\n [-28, -42, 7, 1, -54],\n [-26, 57, 3, 10, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[5, 6, 3, 4, 3],\n [0, 0, 0, 0, 0],\n [20, 24, 12, 16, 12],\n [-30, -36, -18, -24, -18],\n [-15, -18, -9, -12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-32, -36, 4, -20, -24],\n [0, -3, -13, 1, -18],\n [-40, -42, 18, -26, -12],\n [10, 9, -11, 7, -6],\n [-10, -15, -15, -5, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[3, 0, 3, 4, -5],\n [2, -2, 0, 6, -10],\n [-8, -7, -15, 1, -10],\n [-11, -13, -24, 7, -25],\n [3, 6, 9, -6, 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[[23, -7, 0, 1, 3],\n [-3, 3, 0, 3, 9],\n [13, -11, 0, -10, -30],\n [10, -8, 0, -7, -21],\n [9, 3, 0, 9, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, -15, 6, -36, 24],\n [-22, 7, -1, 12, -25],\n [4, 4, -4, 28, 8],\n [-12, -22, 10, -32, 18],\n [-4, -15, 9, -50, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[3, -18, 9, 27, -36],\n [-24, -27, -18, 9, 18],\n [-24, -31, -37, 19, 28],\n [26, 25, 33, -7, -36],\n [-21, -21, -49, 12, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[27, 19, 55, 47, -13],\n [-11, -26, -54, -58, -13],\n [-1, -5, -22, 14, 14],\n [-10, 17, 43, 64, 26],\n [10, -20, -24, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-1, -30, 11, -20, 6],\n [55, -2, 20, -25, -14],\n [-27, -15, -9, 15, 16],\n [-5, 13, 4, 20, -15],\n [26, 11, 1, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[14, 5, 2, 12, 18],\n [8, 0, -6, -6, 6],\n [14, 13, 22, 48, 30],\n [-6, -9, -18, -36, -18],\n [-6, -9, -18, -36, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-5, -18, 12, -4, 29],\n [10, 13, -24, -17, -8],\n [-46, -1, 33, -34, 29],\n [-29, 24, 0, -42, -3],\n [-38, 56, -6, -42, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, -24, 16, -4, -20],\n [-36, 36, -24, 6, 30],\n [-18, 18, -12, 3, 15],\n [-36, 36, -24, 6, 30],\n [-12, 12, -8, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-18, -15, -21, -23, 21],\n [-8, 5, -70, -46, 0],\n [0, -5, 11, 5, 1],\n [-18, -20, -10, -18, 22],\n [-11, -40, 35, 3, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[14, 35, 12, 8, 6],\n [7, 1, -47, 3, 28],\n [-15, -25, -36, 9, 24],\n [-51, -38, -30, 35, 10],\n [-51, -38, -30, 35, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-8, 12, -12, 0, -12],\n [-2, -45, 9, -6, 9],\n [-10, -1, -11, -2, -11],\n [12, 6, 12, 3, 12],\n [-16, 0, -18, -3, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[16, 16, 20, -28, -8],\n [-24, 16, 10, 2, 42],\n [-12, -24, -27, 33, -3],\n [-4, -20, -21, 23, -10],\n [12, 24, 27, -33, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-17, 18, 16, -31, 1],\n [26, 1, -16, 41, -3],\n [-19, 48, 20, -48, 4],\n [8, -23, 14, 15, 5],\n [-32, -56, 46, 46, -48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[1, 4, 4, 1, 5],\n [-6, -24, -24, -6, -30],\n [-6, -24, -24, -6, -30],\n [3, 12, 12, 3, 15],\n [-4, -16, -16, -4, -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[[-39, 20, -17, 33, 7],\n [2, -48, -24, 60, 16],\n [-26, -10, -2, 18, 9],\n [-37, 28, 1, 12, -3],\n [23, -8, 9, -42, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 44, 22, -35, 47],\n [9, -52, 4, -29, -20],\n [14, -33, 0, 4, -25],\n [-50, 79, 2, 40, -48],\n [-15, 9, -26, 47, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-7, -10, -1, -9, 7],\n [25, 10, 25, 0, 20],\n [7, 9, 6, -11, 6],\n [-10, 20, -20, -15, -23],\n [8, -10, 14, 6, 16]]\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, -3, 2, 4, -3],\n [36, -18, 12, 24, -18],\n [36, -18, 12, 24, -18],\n [0, 0, 0, 0, 0],\n [-24, 12, -8, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, -15, 18, -15, 9],\n [10, -25, 30, -25, 15],\n [10, -25, 30, -25, 15],\n [10, -25, 30, -25, 15],\n [-2, 5, -6, 5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, 18, 10, -21, 2],\n [14, 6, 34, -22, 0],\n [6, 42, 22, 44, -16],\n [4, 60, 48, 71, -42],\n [-7, -42, -50, -80, 43]]\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, 27, 1, -3, -47],\n [-1, 23, 12, -28, 0],\n [-26, -18, 4, 0, 5],\n [-62, -12, 12, -30, -8],\n [-45, 30, 25, -39, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[19, 17, 21, -6, 16],\n [6, -6, 18, 12, 24],\n [-18, -18, -18, 8, -12],\n [-4, 4, -12, -8, -16],\n [-21, -24, -18, 13, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1, 12, -12, -17, -6],\n [-28, -24, 34, 40, 20],\n [15, -16, -5, 21, -17],\n [-9, 16, 7, -23, 21],\n [4, -20, 11, 28, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[13, -41, -6, 7, -13],\n [25, -15, -10, -30, 15],\n [12, 23, 10, -31, 27],\n [-30, 9, -42, 27, -27],\n [-43, 34, -68, 22, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[4, -16, 0, -24, 16],\n [-4, 16, 0, 24, -16],\n [4, -16, 0, -24, 16],\n [-2, 8, 0, 12, -8],\n [-4, 16, 0, 24, -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[[15, 15, -3, -9, -9],\n [20, 20, -4, -12, -12],\n [-5, -5, 1, 3, 3],\n [25, 25, -5, -15, -15],\n [-5, -5, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-30, 30, 18, 18, 36],\n [-5, 5, 3, 3, 6],\n [0, 0, 0, 0, 0],\n [15, -15, -9, -9, -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[[0, -2, -3, 2, 2],\n [6, -33, 53, -25, -47],\n [10, -36, 38, -20, -45],\n [36, -7, 18, -23, -8],\n [-4, 25, -46, 21, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[16, 62, 0, -13, -7],\n [-12, 2, 5, 30, 14],\n [-1, -17, 30, 38, 4],\n [8, -25, -35, -44, 32],\n [-21, 12, 35, 44, -62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1, -1, -6, -6, 4],\n [1, 1, 6, 6, -4],\n [0, 0, 0, 0, 0],\n [2, 2, 12, 12, -8],\n [-1, -1, -6, -6, 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, -8, 0, -16, -4],\n [-6, -2, 0, -4, -1],\n [6, 2, 0, 4, 1],\n [6, 2, 0, 4, 1],\n [-6, -2, 0, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-25, 30, -15, 15, -5],\n [0, 0, 0, 0, 0],\n [-30, 36, -18, 18, -6],\n [-30, 36, -18, 18, -6],\n [15, -18, 9, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[3, 6, -6, 3, -3],\n [1, 2, -2, 1, -1],\n [1, 2, -2, 1, -1],\n [4, 8, -8, 4, -4],\n [-4, -8, 8, -4, 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[[-6, -27, -15, -12, -9],\n [6, 32, 14, 12, 6],\n [-8, 9, -29, -16, -39],\n [8, -14, 30, 16, 42],\n [-8, 4, -28, -16, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[13, 7, 0, -2, 7],\n [26, 9, 25, -34, 34],\n [-10, -14, -13, 8, -9],\n [30, 20, -13, 12, 5],\n [7, 10, 0, 4, 0]]?\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, -26, 8, -38],\n [-23, -36, -25, -3, -11],\n [17, 0, -18, -16, -50],\n [-7, -38, 19, -39, 17],\n [-4, 15, 13, 21, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-12, 5, 7, 19, 12],\n [-10, 5, 5, 20, 5],\n [-8, 10, -2, 46, -32],\n [10, -5, -5, -20, -5],\n [2, -6, 4, -29, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[28, 24, -18, -34, 34],\n [30, 24, -45, -9, 9],\n [16, 17, -15, -16, 10],\n [-38, -46, 39, 37, -13],\n [2, 5, 21, -27, 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[[30, -30, 0, 24, 18],\n [0, 0, 0, 0, 0],\n [-20, 20, 0, -16, -12],\n [10, -10, 0, 8, 6],\n [20, -20, 0, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[30, 22, -24, 17, -31],\n [-68, 25, 85, -14, 47],\n [10, 10, -4, 7, -13],\n [-2, 42, 6, 11, -3],\n [-38, 18, 46, -7, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-16, -16, -8, -12, 24],\n [-16, -16, -8, -12, 24],\n [-12, -12, -6, -9, 18],\n [12, 12, 6, 9, -18],\n [-16, -16, -8, -12, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-15, 11, 34, -36, -18],\n [-29, -14, 10, 35, 45],\n [22, -8, -37, 16, -1],\n [-44, -7, 34, 7, 17],\n [-60, -27, 18, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[20, 16, 20, 4, 0],\n [10, 8, 10, 2, 0],\n [-20, -16, -20, -4, 0],\n [-30, -24, -30, -6, 0],\n [-30, -24, -30, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[11, -1, 14, -9, -19],\n [-3, -3, -6, 1, 7],\n [-17, -5, -26, 11, 33],\n [20, -10, 20, -20, -30],\n [8, -4, 8, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-11, 17, -13, 1, -29],\n [12, -4, -4, -12, 8],\n [-25, -5, 25, 35, 5],\n [-5, -1, 5, 7, 1],\n [-4, 12, -12, -4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[38, 4, -50, 22, -28],\n [-5, -41, -15, -6, -51],\n [13, 12, -5, -5, 20],\n [0, 39, 15, 15, 39],\n [12, 23, -15, 31, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-20, -6, -28, 8, 16],\n [-20, -6, -28, 8, 16],\n [-16, -16, -28, -16, -4],\n [-4, 10, 0, 24, 20],\n [4, -8, 1, -20, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-10, -10, 14, 7, 0],\n [40, 12, -26, -36, -14],\n [-12, 28, -6, 2, 20],\n [12, -26, 0, 2, -19],\n [28, 26, -26, -30, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 15, 21, -3, -3],\n [-32, 4, -16, -2, -36],\n [-20, -8, -52, -5, -36],\n [6, -16, -25, 2, 6],\n [-32, 11, -9, -4, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[13, -28, 18, 40, -12],\n [-10, 20, -14, -34, 8],\n [-5, 11, 3, 19, 15],\n [18, -30, 6, 6, -30],\n [-14, 29, -3, 11, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-5, 1, -5, 0, 2],\n [-10, 2, -10, 0, 4],\n [-25, 5, -25, 0, 10],\n [-15, 3, -15, 0, 6],\n [15, -3, 15, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 18, 15, 0, 18],\n [24, -24, -20, 0, -24],\n [-6, 6, 5, 0, 6],\n [-6, 6, 5, 0, 6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-10, -8, -6, -4, -6],\n [-17, -20, -3, -20, -15],\n [2, 8, -6, 14, 6],\n [-21, -20, -9, -15, -15],\n [34, 24, 24, 7, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-5, -4, -5, 6, -5],\n [-30, -24, -30, 36, -30],\n [25, 20, 25, -30, 25],\n [-25, -20, -25, 30, -25],\n [5, 4, 5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[14, 9, 20, 9, 29],\n [14, 15, 10, 1, 11],\n [-6, -3, -10, -5, -15],\n [-22, -27, -10, 3, -7],\n [-2, 0, -5, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[3, 0, 5, -5, 6],\n [18, 0, 30, -30, 36],\n [-9, 0, -15, 15, -18],\n [0, 0, 0, 0, 0],\n [-18, 0, -30, 30, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[22, 2, -4, -6, -40],\n [3, -3, -3, -18, 15],\n [24, 0, -6, -18, -30],\n [14, -2, -5, -21, -5],\n [-10, -2, 1, -3, 25]]\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, -24, -22, 42],\n [-54, -34, -4, 34, -5],\n [-6, 28, -18, -14, 65],\n [-18, -5, 41, 7, -21],\n [-36, -49, -23, 38, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-30, 24, -12, -30, -12],\n [-5, 4, -2, -5, -2],\n [10, -8, 4, 10, 4],\n [-30, 24, -12, -30, -12],\n [-25, 20, -10, -25, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-2, 4, 12, -12, 2],\n [0, 0, 0, 0, 0],\n [-5, 10, 30, -30, 5],\n [-2, 4, 12, -12, 2],\n [4, -8, -24, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-7, 19, 14, 1, -2],\n [-26, -3, -29, 37, 3],\n [14, 2, 38, -36, -10],\n [36, -32, -34, -10, 14],\n [-31, 17, -26, 45, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, -24, -16, -8, 20],\n [-20, 30, 20, 10, -25],\n [-12, 18, 12, 6, -15],\n [-12, 18, 12, 6, -15],\n [-20, 30, 20, 10, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-15, 25, -10, -20, 25],\n [9, -7, -1, 13, -10],\n [-27, 5, 17, -41, 20],\n [15, -33, 17, 19, -30],\n [27, -21, -3, 39, -30]]\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, 20, -20, 0, -4],\n [14, 41, -25, -8, 19],\n [10, -25, 25, 0, 5],\n [34, 29, -5, -12, 35],\n [-18, -31, 15, 8, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -35, -23, 8, 5],\n [-6, -14, -11, 5, 8],\n [-23, 4, -11, 35, 56],\n [-38, -63, -51, 12, 35],\n [-3, 8, 2, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[5, 27, -17, 22, -2],\n [13, 20, -28, -1, 26],\n [9, 3, -17, -14, 26],\n [29, 14, -18, -15, 38],\n [18, 12, -10, -4, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-16, -18, -16, 32, -32],\n [-25, -31, -25, 0, 35],\n [-22, -12, -22, 8, -14],\n [-22, -19, -22, 30, -34],\n [-6, 0, -6, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, 4, 8, -12, 0],\n [-19, 22, -6, -1, 25],\n [-5, -13, -6, 13, -10],\n [-14, 1, -8, 10, 5],\n [7, -26, -2, 13, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, 6, 6, 0, 6],\n [0, -5, -5, 0, -5],\n [0, 2, 2, 0, 2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-10, 0, 12, 6, 10],\n [-25, 0, 30, 15, 25],\n [-30, 0, 36, 18, 30],\n [0, 0, 0, 0, 0],\n [-15, 0, 18, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-4, -1, -4, -5, 3],\n [12, 3, 12, 15, -9],\n [-12, -3, -12, -15, 9],\n [20, 5, 20, 25, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[34, 16, -27, 35, -41],\n [50, -3, -19, 4, 6],\n [26, -1, 4, 33, -28],\n [28, 6, -6, 34, -31],\n [24, 4, -20, -4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-13, -5, 27, 24, -14],\n [-6, 18, 0, 8, 6],\n [32, -5, -54, -54, 22],\n [-7, -2, 12, 10, -5],\n [-9, -12, 18, 10, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-39, 27, 34, 42, 32],\n [18, 4, -8, -8, -14],\n [16, -27, 9, -11, -8],\n [-27, 44, -3, 66, 46],\n [37, 0, -46, -16, -19]]\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, -28, -18, -22, -30],\n [-60, -52, -26, 56, -16],\n [-28, -4, -34, 8, -32],\n [-38, -48, -7, 30, -5],\n [-47, -52, -15, 35, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, -24, -36, 11, 8],\n [12, -26, -22, -10, 3],\n [46, 5, -28, -22, 41],\n [-28, -34, 12, -48, -20],\n [24, -35, -18, -53, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-44, -60, -10, 11, 16],\n [-20, -29, -33, -15, 2],\n [8, 13, 49, 28, 0],\n [8, 15, -24, 3, 35],\n [24, 32, -32, -26, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[36, -62, 18, -54, -19],\n [1, -24, -66, -31, 53],\n [-23, 20, 22, 41, -33],\n [29, 8, 26, -17, -4],\n [-10, 2, 26, 16, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-3, -4, -22, -6, 1],\n [-6, 0, -24, -6, 0],\n [3, -8, -8, -3, 2],\n [15, -16, 20, 3, 4],\n [-9, 20, 14, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[7, 26, 79, -6, -84],\n [29, -46, 0, 19, 11],\n [-9, 56, -1, -46, -30],\n [-20, 32, -47, 9, 24],\n [-50, 78, -6, -50, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[16, 0, 24, -12, -24],\n [28, -12, 12, 12, 12],\n [7, -3, 3, 3, 3],\n [18, -2, 22, -8, -18],\n [-14, 6, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-12, -8, -8, 8, 0],\n [18, 12, 12, -12, 0],\n [3, 2, 2, -2, 0],\n [0, 0, 0, 0, 0],\n [-18, -12, -12, 12, 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[[-15, -13, -11, -13, 13],\n [-20, -20, -22, -16, 40],\n [-15, -15, 21, 33, -45],\n [-5, -3, 10, 7, -27],\n [-20, -21, 4, 19, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[16, 20, -24, 16, -12],\n [24, 30, -36, 24, -18],\n [4, 5, -6, 4, -3],\n [4, 5, -6, 4, -3],\n [-12, -15, 18, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, -5, -20, 10],\n [0, 0, -6, -24, 12],\n [0, 0, -5, -20, 10],\n [0, 0, -1, -4, 2],\n [0, 0, -6, -24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[14, -12, 20, -2, 2],\n [-23, 6, -42, 5, -1],\n [-22, -39, -15, 6, 4],\n [30, -39, 1, 0, 8],\n [30, -15, 17, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-27, 19, 27, -38, 5],\n [10, 25, -20, 26, 63],\n [7, -40, -12, 29, -38],\n [29, -20, -26, 29, -6],\n [4, -2, -17, 17, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-30, -18, 0, -36, 12],\n [-30, -18, 0, -36, 12],\n [5, 3, 0, 6, -2],\n [15, 9, 0, 18, -6],\n [-5, -3, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
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