Answer
See below
Work Step by Step
Let's reduce $A$ to the row-echelon form
$\begin{bmatrix}
1 & 2\\
3 & 4
\end{bmatrix}\approx \begin{bmatrix}
1 & 2\\
0 & -2
\end{bmatrix}\approx\begin{bmatrix}
1 & 0\\
0 & -2
\end{bmatrix}\approx \begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix}$
where $1. A_{12}(-3)\\
2. A_{21}(1)\\
3. M_2 (\frac{1}{2})$
Thus, $T(x)=Ax=A_{12}(3)A_{21}(-1)M_2(-2)x$
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 shear parallel to the x-axis and followed by a shear parallel to the y-axis.
