Let Consider the inner product f(2)=-9, g(x)=-72-1 and h(z)=9z² 9z-4. (p.q) p(-1)(-1)+p(0)g(0) + p(1)q(1) in the vector space P of polynomials of degree at most 2. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of P spanned by the polynomials f(z), g(z) and h(z). -9 9x^2-6

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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Let
Consider the inner product.
f(z) -9, g(x)=-72-1 and h(z) 92²-9z-4.
(p.q) p(-1)g(-1)+p(0)q(0) + p(1)q(1)
in the vector space P, of polynomials of degree at most 2. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of
P₂ spanned by the polynomials f(x), g(x) and h(z).
{-9
-7x
9x^2-6
Transcribed Image Text:Let Consider the inner product. f(z) -9, g(x)=-72-1 and h(z) 92²-9z-4. (p.q) p(-1)g(-1)+p(0)q(0) + p(1)q(1) in the vector space P, of polynomials of degree at most 2. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of P₂ spanned by the polynomials f(x), g(x) and h(z). {-9 -7x 9x^2-6
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