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## Homework Statement

From Hoffman and Kunze:

Is there a linear transformation T from [tex]R^3[/tex] to [tex]R^2[/tex] such that T(1,-1,1)=(1,0) and T(1,1,1)=(0,1)?

## Homework Equations

[tex] T(c\alpha+\beta)=cT(\alpha)+T(\beta) [/tex]

## The Attempt at a Solution

I don't really understand how to prove that there is a linear transformation with these coordinates. I think I begin by defining another arbitrary, linearly independent, transformation such as T(1,0,0)=(1,1). Then I don't really know where to go from here.