Hey guys, I've been thinking about this problem for some time now, but I'm not really sure how to proceed to do it. I think the inner product stuff is throwing me off.

Let V be the vector space of all polynomials of degree 2 or less on the unit interval and define

$\displaystyle \langle f,g \rangle = \int^1_0 fg\,dt $

Find a basis for the orthogonal complement of {t-1,t^2}