Echelon Matrix/Examples/Arbitrary Example 6

Example of Echelon Matrix

 * $\begin {bmatrix}

1 & 6 & -1 & 4 & 2 \\ 0 & 0 & 1 & 2 & -3 \\ 0 & 0 & 0 & 1 & 5 \\ \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.