Use the inner product < f,g >= = f(a)g(x)da in the vector space C"[0, 1] to find the orthogonal projection of ƒ(z) = 2z² + 4 onto the subspace V spanned by g(x) = 2 — — and h(z) = 1.projv (f) =

Given: The functions are fx=2x2+4, gx=x-12 and hx=1. The inner product is given by f,g=∫01fxgxdx in…

Answered: Use the inner product < f, g >= =…

Use the inner product < f, g >= = f(x)g(x)da in the vector space Cº [0, 1] to find the orthogonal projection of f(x) = 2x² + 4 onto the subspace V spanned by g(x) = 2- projy (f) and h(x) = 1.

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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Question

Use the inner product < f,g >= = f(a)g(x)da in the vector space C"[0, 1] to find the orthogonal projection of ƒ(z) = 2z² + 4 onto the subspace V spanned by g(x) = 2 — — and h(z) = 1.
projv (f) =

Expert Solution

Step 1

Given: The functions are $f (x) = 2 x^{2} + 4$ , $g (x) = x - \frac{1}{2}$ and $h (x) = 1$ .

The inner product is given by $<f, g> = \int_{0}^{1} f (x) g (x) d x$ in the vector space $C^{0} [0, 1]$ .

To find: The value of ${Proj}_{V} (f) =$ .

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