Define an inner product on P2 by <p,q> = ʃ (-1 to 1) p(x)q(x) dx. Let U (element of) P2 be the subspace spanned by {x,x^2}
(a) Find an orthonormal basis for U
(b) Find the polynomial in U that is as close as possible to f(x)=1 (for the norm corresponding to the above inner product).
Can someone help me solve this question? Thank you in advance.
I am a year 12 student who made the mistake of undertaking a university subject. I am absolutely clueless in applying the Gramm-Schmidt process.
I have managed to solve section a but I'm facing difficulties with section b.