1. The problem statement, all variables and given/known data 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)? 2. Relevant equations [tex] T(c\alpha+\beta)=cT(\alpha)+T(\beta) [/tex] 3. 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.