Answer
See below
Work Step by Step
Let's reduce $A$ to the row-echelon form
$\begin{bmatrix}
1 & -3\\
-2 & 8
\end{bmatrix}\approx \begin{bmatrix}
1 & -3\\
0 & 2
\end{bmatrix}\approx\begin{bmatrix}
1 & -3\\
0 & 1
\end{bmatrix}\approx \begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$
where $1. A_{12}(2)\\
2.M_2 (\frac{1}{2}) \\
3. A_{21}(3)$
Thus, $T(x)=Ax=A_{12}(-2)M_2(2)A_{21}(-3)x$
The transformation of $R^2$ with the matrix of transformation $A$ is a product of a linear stretch in the y-direction followed by a linear stretch in the y direction and followed by a shear parallel to the x-axis.
