Given the inner product space of polynomials with real coefficients, degree
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 47E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4d74cef-f64d-4ed0-a004-41e9fb8cce2f%2Fb30111de-e9c0-447e-91d1-f3a8159297fb%2Fs8obyz_processed.jpeg&w=3840&q=75)
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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