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

(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.