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

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SUMMARY

The discussion focuses on calculating the preimage of the vector w=(0,2,5) under the linear transformation T: R3 --> R3 defined by T(v1,v2,v3)=(0, v1+v2, v2+v3). Participants established the equations v1+v2=2 and v2+v3=5, leading to the conclusion that individual solutions for v1 and v3 can be expressed in terms of v2. The final result describes a space of solutions that maps to the vector (0,2,5).

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Aristotle
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Moved from a technical math section, so missing homework template
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?
 
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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).
 

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