Row Equivalent Matrix for Homogeneous System has same Solutions/Corollary

Theorem
Let $\mathbf A$ be a matrix in the matrix space $\mathbf M_{m,n}\left({\R}\right)$ such that:


 * $\mathbf A \mathbf x = \mathbf 0$

represents a homogeneous system of linear equations.

Then:
 * $\left\{{\mathbf x: \mathbf A \mathbf x = \mathbf 0}\right\} = \left\{{\mathbf x: \operatorname{rref}\left({\mathbf A}\right) \mathbf x = \mathbf 0}\right\}$

where $\operatorname{rref}\left({\mathbf A}\right)$ is the reduced row echelon form of $\mathbf A$.

Proof
Follows from Row Equivalent Matrix for Homogeneous System has same Solutions and from Matrix Row Equivalent to Reduced Echelon Matrix.