Definition:Echelon Matrix/Echelon Form/Non-Unity Variant/Definition 2

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

$\mathbf A$ is in echelon form 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 $0$.

Also see

 * Equivalence of Definitions of Non-Unity Variant of Echelon Form