Lower Triangular Matrix switch rows

Question

$$\begin{bmatrix} 4 & 2 & 8 \\ -2 & 5 & 0\\ 3 & 0 & 0\end{bmatrix}$$

Is this matrix considered lower triangular because you can switch R1 and R3 to have that pattern? Or does this matrix not have a basic square pattern? Thanks.

Answer 1

It is not a lower triangular matrix though it can be converted to a lower triangular matrix by performing a row swap as you said.

A matrix, $A$ is a lower triangular if whenever $i<j$, $A_{ij}=0$.

For your matrix $A_{13} \ne 0$ even though $1 < 3$.

By following a definition strictly, we can then design algorithm or state theorems based on the structure assumed without ambiguity.