Answer
a) $(x,0)$
b) Projection of $(x,y)$ onto the x-axis.
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.
a) Hence here $T(x,y)=xT(1,0)+yT(0,1)=x(1,0)+y(0,0)=(x,0)+(0,0)=(x,0)$
b) This is the projection of $(x,y)$ onto the x-axis.
