Answer
a) $(-1,3,2)$
b) Pre-image is: $(1,-1,2)$
Work Step by Step
a)
We know that $T(v_1,v_2,v_3)=(v_1+v_2,v_2+v_3,v_3)$
Thus $T(-2,1,2)=(-2+1,1+2,2)=(-1,3,2)$
b)
Let $(x,y,z)$ be the pre-image of $(0,1,2)$.
Then $T(x,y,z)=(x+y,y+z,z)=(0,1,2)$.
Thus $z=2$, $y+z=1\\y+2=1\\y=-1$, $x+y=0\\x+(-1)=0\\x=1$.
From this we get $x=1,y=-1,z=2.$
So the pre-image is $(1,-1,2)$
