How Do You Calculate the Preimage of a Vector Under a Linear Transformation?

[Aristotle]

Consider the linear transformation T: R3 --> R3 /w T(v1,v2,v3)=(0, v1+v2, v2+v3)

What is the preimage of w=(0,2,5) ?I tried setting up the system of equations and got v1+v2= 2 and v2+v3=5 but after that I got kinda lost in how to find the individual solutions?

 

[RUber]

I think all you can really solve for sure is the interval between v1 and v3, I would put them in terms of v2.
You should end up with a description of the space that translates into (0,2,5).