Numerical AnalysisPart C only Problem 1:Here is a set of polynomials{1,1-x}.Is this a linearly independent or dependent set, and why?Show that this collection of polynomials is orthogonal with respect tothe weight function w(x) = exp(-x) on (0, ∞). Show your working, you should notjust plug integrals in to a software-solver.(c)Hence find the least squares polynomialP(x) = aogo(x) + aigi(x)for f(x) = e, where {go(x), g1(x)} = {1,1-x}. Show your workings.(a)(b)

Inner product in the polynomial space defined by<f(x),g(x)>=∫0∞e−xf(x)g(x)dxLeast square…

Answered: Problem 1: Here is a set of polynomials…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 21CM

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