Echelon Matrix/Examples/Arbitrary Example 3

Example of Echelon Matrix

 * $\begin {bmatrix}

0 & 1 & 0 & 2 \\ 1 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 \\ \end {bmatrix} $ is not an echelon matrix, because the leading $1$ in row $2$ is to the left of the leading $1$ in row $1$.