Chapter 6.3, Problem 2P

Consider $T:{ℝ}^3\to {ℝ}^2$ defined by $T(x)=Ax\text{,}$ where $A=\left[\begin{array}{ccc}1& -1& 2\\ 1& -2& -3\end{array}\right]$. For each below $x$, find $T\left(x\right)$ and thereby determine whether $x$ is in Ker $(T).$

(a) $x=(7,5,-1)$

(b) $x=(-21,-15,2)$

(c) $x=(5,25,-5)$