Chapter 6.1, Problem 73E

Show that $T$ from Exercise $71$ is represented by the matrix

$A=\left[\begin{array}{cc}\frac{1}{2}& \frac{1}{2}\\ \frac{1}{2}& \frac{1}{2}\end{array}\right]$.

Proof Let $T$ be the function that maps $R^2$ into $R^2$ such that $T\left(u\right)={\text{proj}}_{v}u,$ where $v=\left(1,1\right)$

(a) Find $T\left(x,y\right)$	(b) Find $T\left(5,0\right)$
(c) Prove that $T$ is a linear transformation from $R^2$ into $R^2$.