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Given the inner product space of polynomials with real coefficients, degree ≤n_(P₁(R),+,,°), where, Pn = {p(x)=anx +...+a₁x +ão | a¡¤R, İ= {0, 1,...,n}}, 。 : PnxPn →R+ : (p(x), q(x)) → p(x) q(x) = f(x)q(x) dx and the subset S={p₁(x)=1, p₂2(x)=x, P³(x)=2x²+x+1} of Pn. Find an orthonormal basis of the vector subspace W=span(p₁(x),p2(x),p³(x)).

Given the inner product space of polynomials with real coefficients, degree ≤n_(P₁(R),+,,°), where, Pn = {p(x)=anx +...+a₁x +ão | a¡¤R, İ= {0, 1,...,n}}, 。 : PnxPn →R+ : (p(x), q(x)) → p(x) q(x) = f(x)q(x) dx and the subset S={p₁(x)=1, p₂2(x)=x, P³(x)=2x²+x+1} of Pn. Find an orthonormal basis of the vector subspace W=span(p₁(x),p2(x),p³(x)).

Advanced Engineering Mathematics
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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5B Given the inner product space of polynomials with real coefficients, degree <n (P₁(R),+‚·‚°), where, P₁ = {p(x)=anx" +...+a₁x +ão | a¡€ R, i={0, 1,...,n}}, • : PnxPn →R+ : (p(x), q(x)) → p(x)•q(x) = f p(x) q(x) dx and the subset S={p₁(x)=1, p₂(x)=x, p³(x)=2x²+x+1} of Pn. Find an orthonormal basis of the vector subspace W=span(p₁(x),p2(x),p3(x)).
Transcribed Image Text:5B Given the inner product space of polynomials with real coefficients, degree <n (P₁(R),+‚·‚°), where, P₁ = {p(x)=anx" +...+a₁x +ão | a¡€ R, i={0, 1,...,n}}, • : PnxPn →R+ : (p(x), q(x)) → p(x)•q(x) = f p(x) q(x) dx and the subset S={p₁(x)=1, p₂(x)=x, p³(x)=2x²+x+1} of Pn. Find an orthonormal basis of the vector subspace W=span(p₁(x),p2(x),p3(x)).
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