Thread: Gram Schmidt Orthogonalization with functions

Hi. I have a quick question. Seems so simple, but for some reason I can't figure out how to start:

Consider the vector space of continuous functions on the interval [0,1]. We define the scalar product of two such functions f, g by the rule:

<f, g> = integral from 0 -> 1 of f(t)g(t) dt.

Let V be the subspace of functions generated by the two functions f(t) = t and g(t) = t^2. Find an orthonormal basis for V.

The part I'm stuck on is.. what do I start with? (what's v_1?) The answer key says rad 3 * t, but I'm not sure how the book got that.

Thank you!

Let t be v1. Then normalize v1 and solve v2

gottt it. darn i feel dumb. thank you