Non-Unity Variant of Echelon Matrix/Examples/Arbitrary Matrix 2

Examples of Non-Unity Echelon Matrices

 * $\begin {bmatrix}

1 & 0 & 1 & 2 & 3 \\ 2 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ \end {bmatrix} $ is not an echelon matrix, because the leading coefficient of row $2$ is in the same column as that of the row above it.