Chapter 2, Problem 8SE

Find a matrix A such that the transformation x ↦ Ax maps $\left[\begin{array}{l}1\\ 3\end{array}\right]$ and $\left[\begin{array}{l}2\\ 7\end{array}\right]$ into $\left[\begin{array}{l}1\\ 1\end{array}\right]$ and $\left[\begin{array}{l}3\\ 1\end{array}\right]$, respectively. [Hint: Write a matrix equation involving A, and solve for A.]