Chapter 6.3, Problem 17E

To determine

(a)

To find:

The standard matrix $A$ for the given linear transformation $T$.

$T$ is the clockwise rotation ($\theta$ is negative) of $60°$ in $R^2$, $v=\left(1,2\right)$.

To determine

(b)

To find:

The image of vector $v=\left(1,2\right)$ using standard matrix $A$.

To determine

(c)

To plot:

The graph of vector $v=\left(1,2\right)$ and its image $\left(\frac{1}{2}+\sqrt{3},1-\frac{\sqrt{3}}{2}\right)$.