Com
# Definition
Elementary matrices are denoted as $E$ are exactly 1 [[Elementary Row Operations (ERO)|operation]] done on an [[Identity Matrix|identity matrix]]. Reversing the operation will return the identity matrix.
# Examples
> [!example] Examples of elementary matrices
> $
\text{ Row Swap } (R_1 \leftrightarrow R_2) \quad
E_1 =
\begin{bmatrix}
0 & 1 & 0 \\
1 & 0 & 0 \\
0 & 0 & 1
\end{bmatrix}
> $
>
> $
\text{Row Scaling } (R_2 \to 5 R_2) \quad
E_2 =
\begin{bmatrix}
1 & 0 & 0 \\
0 & 5 & 0 \\
0 & 0 & 1
\end{bmatrix}
> $
> $
\text{Row Addition } (R_2 \to R_2 + 3 R_1) \quad
E_3 =
\begin{bmatrix}
1 & 0 & 0 \\
3 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
> $
# Resources
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