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
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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) =
Transcribed Image Text: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 fx=2x2+4gx=x-12 and hx=1.

The inner product is given by f,g=01fxgxdx in the vector space C00,1.

To find: The value of ProjVf=.

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