1. The problem statement, all variables and given/known data Let V=<sinx,cosx> and T: V --> V be a transformation defined by T(f)=df/dx +f. Prove T is linear. 3. The attempt at a solution T(f+g) = cosx-sinx+sinx+cosx T(f)+T(g) = (sinx+cosx)'+sinx+cosx = T(sinx)+T(cosx) T(αf)=αcosx +αsinx αT(f)= α(cosx+sinx) Since we proved both addition and scalar, we can conclude that T is linear.