Chapter 6.2, Problem 28E

Finding the Kernel, Nullity, Range, and Rank In Exercises 19-32, define the linear transformation T by $T\left(x\right)=Ax$. Find (a) $ker\left(T\right)$, (b) $nullity\left(T\right)$, (c) $range\left(T\right)$and (d) $rank\left(T\right)$.

$A=\left[\begin{array}{ccc}-\frac{1}{3}& \frac{2}{3}& -\frac{1}{3}\\ \frac{2}{3}& \frac{1}{3}& \frac{2}{3}\\ -\frac{1}{3}& \frac{2}{3}& -\frac{1}{3}\end{array}\right]$