\begin{definition}[Definition:Echelon Matrix/Echelon Form/Non-Unity Variant/Definition 2]
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix whose order is $m \times n$.
$\mathbf A$ is in '''non-unity echelon form''' {{iff}} it contains no adjacent rows of the form:
:$\begin {pmatrix}
0 & 0 & \cdots & 0 & x_1 & x_2 & \cdots \\
0 & 0 & \cdots & 0 & y_1 & y_2 & \cdots \\
\end {pmatrix}$
where:
:$(1): \quad y_1 \ne 0$
:$(2): \quad x_1$ can be any value at all, including $0$.
\end{definition}