Chapter 6.CR, Problem 63CR

To determine

(a)

To find:

The standard matrix A for the given condition,

$\begin{array}{l}T:R^3\to R^3\\ T\left(\text{v}\right)={\text{proj}}_u\text{v}\end{array}$

Here, $\text{u}=\left(0,1,2\right)$.

To determine

(b)

To prove:

The S is of the form $S\left(\text{v}\right)={\text{proj}}_{w_1}\text{v}+{\text{proj}}_{w_2}\text{v}$ for the given condition.

To determine

(c)

To prove:

The kernel of T is equal to the range of S for the given condition.