Chapter 6.2, Problem 25E

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

$A=\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& 0\\ 1& 0& 1\end{array}\right]$