Answer
(a) $G(1,0)= (2,0)$.
(b) $G(1,1)= (1,3)$
(c) $G(2,1)= (3,3)$
Work Step by Step
Since $G$ is linear map, then we have
(a) $G(1,0)=\frac{1}{2}G(2,0)=\frac{1}{2}(4,0)=(2,0)$.
(b) $G(1,1)=G(1,0)+G(0,1)=\frac{1}{2}G(2,0)+\frac{1}{3}G(0,3)\\= (2,0)+\frac{1}{3}G(-3,9)=(2,0)+(-1,3)=(1,3)$
(c) $G(2,1)=G(2,0)+G(0,1)= G(2,0)+\frac{1}{3}G(0,3)\\= (4,0)+\frac{1}{3}G(-3,9)=(4,0)+(-1,3)=(3,3)$
