Chapter 11.FOM, Problem 4P

(a) Let $T=\left[\begin{array}{cc}3& 0\\ 0& 1\end{array}\right]$. What effect does $T$ have on the gray square in Table 1?

(b) Let $S=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$. What effect does $S$ have on the gray square in Table 1?

(c) Apply $S$ to the vertices of the square, and then apply $T$ to the result. What is the effect of the combined transformation?

(d) Find the product matrix $W=TS$.

(e) Apply the transformation $W$ to the square. Compare to you final result in part (c). What do you notice?