algebra22333

Question

Let

V be the real vector space of functions from (0; 1) to R. Let W be the

set of innitely-di
erentiable functions in

V . Let W+ be the set of positive-

valued functions in

W. We will denote by f0 the derivative of the function

f

.

(a) Prove that

W is a subspace of V .

(b) Let

f and g be vectors inW+. Prove that f and g are linearly independent

if and only if

fg0