Chapter 4.1, Problem 1E

Show that each of the following are linear operators on ${ℝ}^2$ . Describe geometrically what each linear transformation accomplishes.
(a) $L(x)={(-x_1,x_2)}^T$
(b) $L(x)=(-x)$
(c) $L(x)={(x_2,x_1)}^T$
(d) $L(x)=\frac{1}{2}x$
(e) $L(x)=x_2{e}_2$