Non-Unity Variant of Echelon Matrix/Examples

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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.


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