Please solve problem 5 with information of problem 1 Problem 5. Consider the inner product space from Problem 1. Let V be the sub-space spanned by the functions h₁(x) = 1 and h₂(x) = 2x - 1. Find the best least squaresapproximation to the function f(x)=√ on [0, 1] by a function from V.[Hint: first show that h₁ and h₂ are orthogonal.] Problem 1. Consider the inner product space C[0, 1] with the inner product defined by(f.g) = f* f(x)g(x) dxand the induced norm. Find the angle between the functions h₁(x) = 1 and h₂(x) == x.

Given that V be subspace of C0,1 spanned by h1x=1 and h2x=2x-1. We need to find the least square…

Answered: Problem 5. Consider the inner product…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 46E

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Problem 5. Consider the inner product space from Problem 1. Let V be the sub- space spanned by the functions h₁(x) = 1 and h₂(x) = 2x - 1. Find the best least squares approximation to the function f(x)=√ on [0, 1] by a function from V. [Hint: first show that h₁ and h₂ are orthogonal.]