Echelon Matrix/Examples/Arbitrary Example 5

Example of Echelon Matrix

 * $\begin {bmatrix}

1 & 5 & 4 & 2 \\ 0 & 6 & 0 & 9 \\ 0 & 0 & 1 & 7 \\ 0 & 0 & 0 & 0 \\ \end {bmatrix}$ is not an echelon matrix, because the leading coefficient of row $2$ is not $1$.

It is, however, a non-unity variant of an echelon matrix.