Chapter 6.1, Problem 71E

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 $R^2$.