Non-Unity Variant of Echelon Matrix/Examples

Examples of Non-Unity Echelon Matrices

Arbitrary Matrix 1

$\begin {bmatrix}

0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ \end {bmatrix} $ is an echelon matrix.

Arbitrary Matrix $2$

$\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.

Arbitrary Matrix $3$

$\begin {bmatrix}

1 & 1 & 1 & 1 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 4 \\ \end {bmatrix} $ is a non-unity echelon matrix.

Arbitrary Matrix $4$

$\begin {bmatrix}

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

Arbitrary Matrix $5$

$\begin {bmatrix}

1 & 1 & 1 & 1 & 1 \\ 0 & 2 & 2 & 2 & 2 \\ 0 & 0 & 0 & 3 & 3 \\ \end {bmatrix} $ is a non-unity echelon matrix.

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 $1.3$