Chapter 6.2, Problem 39E

Finding the Nullity and Describing the Kernel and Range In Exercises $33-40$, let $T:R^3\to R^3$be a linear transformation. Find the nullity of $T$ and give a geometric description of the kernel and range of $T$.

$T$ is the projection onto the vector $v=\left(1,2,2\right)$:

$T\left(x,y,z\right)=\frac{x+2y+2z}{9}\left(1,2,2\right)$