Answer
$\left[ {\begin{array}{*{20}{c}} 4&1\\ 0&0\\{2}&{-3} \end{array}} \right]$
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)=(4(1)+0,0,2(1)-3(0))=(4,0,2)\\
T(0,1)=(4(0)+1,0,2(0)-3(1))=(1,0,-3) $
Therefore, the matrix corresponding to the linear transformation $T$ is given by:
$A=[T(e_1)$ $T(e_2) ]$ $=\left[ {\begin{array}{*{20}{c}} 4&1\\ 0&0\\{2}&{-3} \end{array}} \right]$
