Chapter 6.4, Problem 13P

For Problems $10-14$, find $\text{Ker}\left(T\right)$ and $\text{Rng}\left(T\right)$, and hence, determine whether the given transformation is one-to-one, onto, both, or neither. If $T^{-1}$ exists, find it.

$T\left(x\right)=Ax$, where $A=\left[\begin{array}{ccc}1& 2& -1\\ 2& 5& 1\end{array}\right]$.