(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define an inner product on P_{2}by <f,g> = integral from 0 to 1 of f(x)g(x)dx. find an orthonormal basis of P_{2}with respect to this inner product.

2. Relevant equations

So this is a practice problem and it gives me the answer I just don't understand where it came from. It says, "We first find a basis of P_{2}then use Gram-Schmidt to create an orthonormal basis. Fix a basisB= {f_{1}(x) = 1, f_{2}(x) = x - 1/2, f_{3}(x) = (x-1/2)^{2}}." then it goes on to use Gram-Schmidt which I understand. I just don't get where the basis came from, if anyone can explain. Thanks!

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# Homework Help: Inner product as integral, orthonormal basis

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