Answer
$\left[ {\begin{array}{*{20}{c}} 0&0&0&0\\ 0&0&0&0\\0&0&0&0\\0&0&0&0 \end{array}} \right]$
Work Step by Step
Take the standard basis for $R^4$, which is
${(1,0,0,0),(0,1,0,0),(0,0,,0),(0,0,0,1)}=\{{e_1,e_2,e_3,e_4}\}$.
Then,
$T(e_1)=(0,0,0,0)\\
T(e_2)=(0,0,0,0)\\
T(e_3)=(0,0,0,0)\\
T(e_4)=(0,0,0,0)
$
Therefore, the matrix corresponding to the linear transformation $T$ is given by:
$A=[T(e_1)$ $T(e_2)$ $T(e_3)$ $T(e_4)]$ $=\left[ {\begin{array}{*{20}{c}} 0&0&0&0\\ 0&0&0&0\\0&0&0&0\\0&0&0&0 \end{array}} \right]$
