Linear Mapping/ Differential Proof

mj1357

1. The problem statement, all variables and given/known data

If f: R to Rm is linear, prove that f'(a) exists for all a in R, with dfa= f.

2. Relevant equations

dfa = f'(a)h

3. The attempt at a solution

Not really sure how to prove it. It makes sense to me that dfa = f because if f is linear then it should be equal to a linear mapping.