Hi, I have this problem and don't know how to go about it:

(P2 being the set of all polynomials of degree less than or equal to 2)

Let p(x), q(x) Є P2. You may assume that:

<p(x), q(x)> = $\displaystyle \int p(x)q(x)dx$ (with limits from -1 to 1) defines an inner product on P2.

(A) Find a basis for the subspace of P2:

V= {a+b+ax+bx^2|a,b Є R}

(B) Using the inner product defined above and the basis vectors found in (A), use the Gram-Schmidt procedure to find an orthonormal basis for V.

Thank you.