$T: R^{2} \rightarrow R^{2}$ is defined by
$$
T\left(\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}\right]\right)=\left[\begin{array}{c}
x_{1}+7 x_{2} \\
3 x_{1}-4 x_{2}
\end{array}\right]
$$
and $B=\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\}$ and $B^{\prime}=\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\},$ where
$$
\mathbf{u}_{1}=\left[\begin{array}{l}
2 \\
2
\end{array}\right], \quad \mathbf{u}_{2}=\left[\begin{array}{r}
4 \\
-1
\end{array}\right] ; \quad \mathbf{v}_{1}=\left[\begin{array}{l}
18 \\
8
\end{array}\right], \quad \mathbf{v}_{2}=\left[\begin{array}{r}
10 \\
5
\end{array}\right]
$$