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Given the inner product space of polynomials with real coefficients, degree

Given the inner product space of polynomials with real coefficients, degree

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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5C Given the inner product space of polynomials with real coefficients, degree <n (P₁(R),+,., °), where, P₁ = {p(x)=anx¹ +...+a₁x +ão | a¡¤R, iɛ {0,1,...,n}}, 0: : Pn-Pn →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 the projection of the vector r(x) = 2x5-x onto W and then write it as a sum of polynomials r(x) = s(x) + m(x), s(x)=W, m(x)= W¹.
Transcribed Image Text:5C Given the inner product space of polynomials with real coefficients, degree <n (P₁(R),+,., °), where, P₁ = {p(x)=anx¹ +...+a₁x +ão | a¡¤R, iɛ {0,1,...,n}}, 0: : Pn-Pn →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 the projection of the vector r(x) = 2x5-x onto W and then write it as a sum of polynomials r(x) = s(x) + m(x), s(x)=W, m(x)= W¹.
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