Answer
See explanation
Work Step by Step
$T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ is a horizontal shear transformation that leaves
$\mathbf{e}_{1}$ unchanged and maps $\mathbf{e}_{2}$ into $\mathbf{e}_{2}+3 \mathbf{e}_{1}$
Given Question
\[
\begin{array}{c}
T\left(e_{1}\right)=e \\
T\left(e_{2}\right)=e_{2}+3 e_{1}=\left[\begin{array}{c}
3 \\
1
\end{array}\right] \\
A=\left[\begin{array}{cc}
1 & 3 \\
0 & 1
\end{array}\right]
\end{array}
\]
Standard matrix
