Let V=<sinx,cosx> and T: V --> V be a transformation defined by T(f)=df/dx +f. Prove T is linear.
The Attempt at a Solution
T(f+g) = cosx-sinx+sinx+cosx
T(f)+T(g) = (sinx+cosx)'+sinx+cosx
Since we proved both addition and scalar, we can conclude that T is linear.