Let $$A=\left[\begin{array}{ccc} -3 &3 &6\cr 3 &0 &-3 \end{array}\right].$$ Find dimensions of the kernel and image of $T(\vec{x}) = A \vec{x}$.
${\rm dim } ({\rm Ker } (A)) =$ ,
${\rm dim } ({\rm Im } (A)) =$ .