Echelon Matrix/Examples/Arbitrary Example 1

Example of Echelon Matrix

 * $\begin {bmatrix}

1 & 0 & -1 & 2 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 1 \\ \end {bmatrix} $ is an echelon matrix, but not a reduced echelon matrix, because the leading $1$ in row $3$ is not the only $1$ in its column.