In linear algebra, the rank of a matrix is defined as the greatest number of linearly independent rows or columns that it encompasses. This significant principle frequently serves as a determinant for the solutions of a linear equation system. To find the rank, one might employ methods such as row reduction or utilize the rank-nullity theorem.
| Topic | Problem | Solution |
|---|---|---|
| None | Find the rank of the matrix \[ A = \begin{bmatrix… | First, we perform Gaussian elimination on matrix A to put it in row-reduced echelon form (RREF). |