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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 48E
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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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