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

Examples of Non-Unity Echelon Matrices

$\quad \begin {bmatrix} 1 & 0 & 1 & 2 & 3 \\ 2 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 \\ \end {bmatrix}$

is not an echelon matrix, because the leading coefficient of row $2$ is in the same column as that of the row above it.

Sources

• 1998: Richard Kaye and Robert Wilson: Linear Algebra ... (previous) ... (next): Part $\text I$: Matrices and vector spaces: $1$ Matrices: $1.5$ Row and column operations: Exercise $1.3 \ \text {(b)}$