Every Matrix is Row Equivalent to a Row Reduced Echelon Matrix

Last updated Nov 1, 2022

Let $F$ be a Field and let $m, n \in \mathbb{N}$. Then for every $A \in F^{m \times n}$ there exists $R \in F^{m \times n}$ so that

1. $A \sim_{R} R$,
2. $R$ is a Row Reduced Echelon Matrix.

By applying Gaussian Elimination, we can find a an $R \in F^{m \times n}$ such that the statement holds. $\blacksquare$

• Row Equivalent Matrices
• Matrix