Answer
$(-1,-2)$
Work Step by Step
In this case the transformation is linear if $T(v_1+v_2)=T(v_1)+T(v_2)$ and $T(av_1)=aT(v_1)$ for any $v_1,v_2$ in the domain and any $a$ scalar.
Hence, here
$T(0,-1)=-\frac{2}{3}T(1,1)+\frac{1}{3}T(2,-1)=-\frac{2}{3}(2,3)+\frac{1}{3}(1,0)=(-\frac{4}{3},-2)+(\frac{1}{3},0)=(-1,-2)$
