1. ## Inner product/subspace help!

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)> = $\int p(x)q(x)dx$ (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.

2. What is it that you are having trouble with?

3. Finding a basis for the subspace of P2, to get started, given that I have a rule: V= {a+b+ax+bx^2|a,b Є R}. No idea?

4. Let's rearrange some of the terms in that set.

$\{a(x+1)+b(x^2+1)\ |\ a,b\in \mathbb{R}\}$

Can you see how to pick the basis now?

5. I'm sorry,

What do we do the procedure on? What inner product?
What's the basis got to do with it?

6. I'm just looking at part A of your problem. It just asks you to find a basis for your set. So far, it has nothing to do with inner product space or Gram-Schmidt.

7. For (A), is the basis {(0,1,1),(1,0,1)}

As in: x+1 = (0,1,1)
x^2 + 1 = (1,0,1)

8. Looks good. Now are you able to do Gram-Schmidt?