(Solved): oblem 2 ( 3 pts) Let L:R2R2 be the linear operator that reflects across the line x2=x1. ...

oblem 2 ( 3 pts) Let $L:{\mathbb{R}}^2?{\mathbb{R}}^2$ be the linear operator that reflects across the line $x_2=?x_1$. (a) Find $L\left(\left[\begin{array}{l}1\\ 0\end{array}\right]\right)$ (b) Find $L\left(\left[\begin{array}{l}0\\ 1\end{array}\right]\right)$ (c) Find $L\left(\left[\begin{array}{c}2\\ ?2\end{array}\right]\right)$ (d) Plot the three vectors from (a)-(c) and their images under $L$. (e) Find a matrix $A$ such that $L(\stackrel{?}{x})=A\stackrel{?}{x}$. (f) Find a general formula for $L$ (not involving $A$ ), i.e. $L\left(\left[\begin{array}{l}{x}_1\\ x_2\end{array}\right]\right)=$