Let the vector space P^{2} have the inner product langle p,qrangle=int_{-1}^{1} p(x)q(x)dx. Find the following for p = 1 and q = x^{2}. (a) ⟨p,q⟩ (b) ∥p∥ (c) ∥q∥ (d) d(p,q)

CoormaBak9 2021-03-12 Answered
Let the vector space P2
have the inner product p,q=11p(x)q(x)dx.
Find the following for p=1 and q=x2.
(a)p,q(b)p(c)q(d)d(p,q)
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Expert Answer

l1koV
Answered 2021-03-13 Author has 100 answers

Given that the vector space P have the inner product
p,q=11p(x)q(x)dx.
Also given that p=1 and g=x2
We calculate the value of as follows:
p,q=11p(x)q(x)dx
=11x2dx
Therefore, the value of p,q=23

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