Let T : ?2 ? ?2 be a linear transformation that maps and

QUESTION:

Let \(T: \mathbb{R}^2 \rightarrow \mathbb{R}^2\) be a linear transformation that maps \(\mathbf{u}=\left[\begin{array}{l}5 \\ 2\end{array}\right]\) into \(\left[\begin{array}{l}2 \\ 1\end{array}\right]\) and maps \(\mathbf{v}=\left[\begin{array}{l}1 \\ 3\end{array}\right]\) into \(\left[\begin{array}{r}-1 \\ 3\end{array}\right]\). Use the fact that T is linear to find the images under T of \(3 \mathbf{u}, 2 \mathbf{v}\), and \(3 \mathbf{u}+2 \mathbf{v}\).