\begin{definition}[Definition:Echelon Matrix/Echelon Form]
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix whose order is $m \times n$.
$\mathbf A$ is in '''echelon form''' {{iff}}:
:$(1): \quad$ The leading coefficient in each non-zero row is $1$
:$(2): \quad$ The leading $1$ in any non-zero row occurs to the right of the leading $1$ in any previous row
:$(3): \quad$ The non-zero rows appear before any zero rows.
\end{definition}