Matrix Transformations: Elementary Row Operations

This lecture covers the concept of elementary row operations on matrices, defining when two matrices are row-equivalent, and the process of transforming a matrix into row-echelon form. It also explores the Gauss method and the uniqueness of reduced row-echelon form. Additionally, it discusses the properties of matrices in row-echelon form, the relationship between row-equivalent matrices, and the rank of a matrix. The lecture concludes with the application of elementary row operations to find the rank of a matrix and the formation of linearly independent vectors from pivot columns.