Answer
$\left[ {\begin{array}{*{20}{c}}
1&2\\
1&{ - 2}
\end{array}} \right]$
Work Step by Step
Take the standard basis for $R^2$, which is ${(1,0),(0,1)}=\{{e_1,e_2}\}$.
Then, $T(1,0)=(1+2(0),1-2(0))=(1,1)\\
T(0,1)=(0+2(1),0-2(1))=(2,-2)
$
Therefore, the matrix corresponding to linear transformation $T$ is given by:
$A=[T(e_1)$ $T(e_2)]$
$=\left[ {\begin{array}{*{20}{c}}
1&2\\
1&{ - 2}
\end{array}} \right]$
