Chapter 1.8, Problem 17E

Let T : ℝ² ⟶ ℝ² be a linear transformation that maps $\text{u}=\left[\begin{array}{c}5\\ 2\end{array}\right]$ into $\left[\begin{array}{c}2\\ 1\end{array}\right]$ and maps $\text{v}=\left[\begin{array}{c}1\\ 3\end{array}\right]$ into $\left[\begin{array}{c}-1\\ 3\end{array}\right]$. Use the fact that T is linear to find the images under T of 3u, 2v, and 3u + 2v.