Chapter 3.5, Problem 7E

Given
${\text{v}}_{\text{1}}=\left(\begin{array}{l}1\\ 2\end{array}\right)$ , ${\text{v}}_2=\left(\begin{array}{l}2\\ 3\end{array}\right)$ , $S=\left(\begin{array}{cc}3& 5\\ 1& -2\end{array}\right)$
find vectors ${\text{w}}_{\text{1}}$ and ${\text{w}}_2$ so that S will be the transition matrix from $\{{\text{w}}_{\text{1}},{\text{w}}_2\}$ to $\{{\text{v}}_{\text{1}},{\text{v}}_2\}$ .