Chapter 6.3, Problem 21E

Finding the Standard Matrix and the Image In Exercise $11-22$, (a) find the standard matrix $A$ for the linear transformations $T$, (b) use $A$ to find the image of the vector $v$, and (c) sketch the graph of $v$ and its image.

$T$ is the projection onto the vector $w=\left(3,1\right)$ in $R^2:T\left(v\right)=2{\text{proj}}_{\text{w}}v$, $v=\left(1,4\right)$.