Chapter 6.1, Problem 35E

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 $R^m$.

$A=\left[\begin{array}{rrrr}\hfill 1& \hfill 0& \hfill 0& \hfill 0\\ \hfill 0& \hfill -1& \hfill 0& \hfill 0\\ \hfill 0& \hfill 0& \hfill 1& \hfill 0\\ \hfill 0& \hfill 0& \hfill 0& \hfill 2\end{array}\right]$