Chapter 6 - Linear Transformations - 6.1 Introduction to Linear Transformations - 6.1 Exercises - Page 300: 2

$(1,2)$

We know that $T(v_1,v_2)=(2v_2-v_1,v_1,v_2)$ Thus $T(0,6)=(2\cdot6-0,0,6)=(12,0,6)$ Let $(x,y)$ be the pre-image of $(3,1,2)$. Then $T(x,y)=(2y-x,x,y)=(3,1,2).$ Thus $2y-x=3,x=1,y=2$ From this we get $x=1,y=2$. So the pre-image of $(12,0,6)$ is $(1,2)$