Suppose $A$ is an $m\times n$ matrix with extended echelon form $N$. Suppose the reduced row-echelon form of $A$ has $r$ nonzero rows. Then $C$ is the submatrix of $N$ formed from the first $r$ rows and the first $n$ columns and $L$ is the submatrix of $N$ formed from the last $m$ columns and the last $m-r$ rows. Then

1. The null space of $A$ is the null space of $C$, $\nsp{A}=\nsp{C}$.
2. The row space of $A$ is the row space of $C$, $\rsp{A}=\rsp{C}$.
3. The column space of $A$ is the null space of $L$, $\csp{A}=\nsp{L}$.
4. The left null space of $A$ is the row space of $L$, $\lns{A}=\rsp{L}$.