1. In the space C[0, 1] of continuous functions on the interval 0

Given the space C0,1 of continuous function on the interval 0≤x≤1, with the inner product defined as…

Answered: (a) Show (by calculation) that {u1(x),…

(a) Show (by calculation) that {u1(x), u2(x)} is an orthonormal set. (b) Find the projection p(x) of f(x) onto Span(u1(x), U2(x)).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A: This question is about application of functional analysis

Question

1. In the space C[0, 1] of continuous functions on the interval 0 <x < 1,
with the inner product (f(x), g(x)) = | f(x)g(x) dx
0.
given the functions
u1 (x) = 1
u2(xr) = V3 (2.r – 1) , S(x) = 2?
(a) Show (by calculation) that {u1(x), u2(x)} is an orthonormal set.
(b) Find the projection p(x) of f(x) onto Span(u1(x), u2(x)).

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