so i have no idea how to approach this second part of the problem. for the first part, i've figured out that the vectors in the set s are indeed linearly independent. but as far as the second part is concerned, i have no idea what the question even is.

any help is appreciated.

thanks !!

Let V be the vector space of infinitely differentiable functions on R.

1. prove that the set S={e^x, x, x^2} is linearly independent

2. Find the matrix of the inner product <f,g> = integrate from -1 to 1 of f(x)g(x)dx on Span(S) with respect to the ordered basis {e^x, x, x^2}.

heres an image