1. The problem statement, all variables and given/known data Let R2 => R2 be a linear transformation for which we know that: L(1,1) = (1,-2) L(-1,1) = (2,3) What is: L(-1,5) and L(a1,a2)? 2. Relevant equations I dont know where to start. I tried writing (-1,5) as a linear combo of (1,1) and (-1,1), but that got me nowhere. Am i suppose to find a basis? How do i do that? 3. The attempt at a solution (-1,5) = a(1,1) + b(-1,1) Transforming it into a 2 x 3 matrix and row reducing it, i get a = 2, b = 3. If i am on the right track, what do i do next?