Chapter 6.1, Problem 40E

Writing For the linear transformation from Exercise $34,$ find (a) $T\left(2,4\right)$, (b) the preimage of $\left(-1,2,2\right)$ (c) Then explain why the vector $\left(1,1,1\right)$ has no preimage under this transformation.

Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations $T:R^n\to R^m$ by $T\left(v\right)=Av$. Find the dimensions of $R^n$ and $R^m$.

$A=\left[\begin{array}{rr}\hfill 1& \hfill 2\\ \hfill -2& \hfill 4\\ \hfill -2& \hfill 2\end{array}\right]$