Answer
a) $(5,1)$
b) $(1/3,-5/3,z)$
Work Step by Step
We know that $T(v_1,v_2,v_3)=(2v_1+v_2,v_1-v_2)$
Thus $T(2,1,4)=(2(2)+1,2-1)=(5,1)$
Let $(x,y,z)$ be the pre-image of $(-1,2)$. Then $T(x,y,z)=(2x+y,x-y)=(-1,2)$.
Thus $2x+y=-1,x-y=2$. From this we get $x=1/3,y=-5/3, z=z.$
