Answer
$\left[ {\begin{array}{*{20}{c}} 3&0&{-2}\\ 0&2&{ - 1} \end{array}} \right]$
Work Step by Step
Take the standard basis for $R^3$, which is
${(1,0,0),(0,1,0),(0,0,1)}=\{{e_1,e_2,e_3}\}$
Then,
$T(1,0,0)=(3(1)-2(0),2(0)-0)=(3,0)\\
T(0,1,0)=(3(0)-2(0),2(1)-0)=(0,2)\\
T(0,0,1)=(3(0)-2(1),2(0)-1)=(-2,-1) $
Therefore, the matrix corresponding to the linear transformation $T$ is given by:
$A=[T(e_1)$ $T(e_2)$ $T(e_3)]$ $=\left[ {\begin{array}{*{20}{c}} 3&0&{-2}\\ 0&2&{ - 1} \end{array}} \right]$
