Chapter 2.2, Problem 26E

a. Find the scaling matrix A that transforms $\left[\begin{array}{l}2\\ -1\end{array}\right]$ into $\left[\begin{array}{l}8\\ -4\end{array}\right]$ .
b. Find the orthogonal projection matrix B that transforms $\left[\begin{array}{l}2\\ 3\end{array}\right]$ into $\left[\begin{array}{l}2\\ 0\end{array}\right]$ .
c. Find the rotation matrix C that transforms $\left[\begin{array}{l}0\\ 5\end{array}\right]$ into $\left[\begin{array}{l}3\\ 4\end{array}\right]$ .
d. Find the shear matrix D that transforms $\left[\begin{array}{l}1\\ 3\end{array}\right]$ into $\left[\begin{array}{l}7\\ 3\end{array}\right]$ .
e. Find the reflection matrix E that transforms $\left[\begin{array}{l}7\\ 1\end{array}\right]$ into $\left[\begin{array}{l}-5\\ 5\end{array}\right]$ .