Answer
$$T(2,3,0)= (1,5,4)$$
The pre-image of $(-11,-1,10)$ is $(5,-6,z)$
Work Step by Step
We know that $T(v_1,v_2,v_3)=(v_2-v_1,v_1+v_2,2v_1)$
Thus $T(2,3,0)=(3-2,2+3,2 \times 2)=(1,5,4)$
Let $(x,y,z)$ be the pre-image of $(-11,-1,10)$. Then
$T(x,y,z)=(y-x,x+y,2x)=(-11,-1,10).$
Thus,
$ y-x=-11,x+y=-1,2x=10$
From this we get $x=5,y=-6$.
$z$ is not determined.
So, the pre-image of $(-11,-1,10)$ is $(5,-6,z)$.
