Chapter 4.3, Problem 1E

For each of the following linear operators L on ${ℝ}^2$ , determine the matrix A representing L with respect to $\{e_1,e_2\}$ (see Exercise 1 of Section 1.2) and the matrix B representing L with respect to $\{u_1={(1,1)}^T,u_2={(-1,1)}^T\}$ :
(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) $L(x)=x_2{e}_2$