Definition:Echelon Matrix/Echelon Form/Non-Unity Variant

Definition
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix whose dimensions are $m \times n$.

The matrix $\mathbf A$ is in echelon form if:
 * $(1): \quad$ 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.