Part Cc please Solve the following problems(a) Find the eigenvalues and eigen-functions for the problemƒ” (x) + \ƒ(x) = 0, ƒ(0) = 0, ƒ'(2) = 0(b) Discuss the orthogonality relation for the eigen-functions in part (a)(c) Find the general solution of the problemut (x, t) =9uxx (x, t), 0≤x≤2, t>0u(0, t)=0, ux (2, t) = 0

(a) f''(x)+λfx=0, f0=0, f'2=0 Let λ=0 fx=ax+b⇒f0=0⇒b=0f'(2)=0⇒a=0 Therefore f(x)=0 For λ=-μ2…

Answered: (a) Find the eigenvalues and…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 66E: Show that A=[0110] has no real eigenvalues.

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(a) Find the eigenvalues and eigen-functions for the problem ƒ” (x) + \ƒ(x) = 0, f(0) = 0, ƒ'(2) = = 0 (b) Discuss the orthogonality relation for the eigen-functions in part (a) (c) Find the general solution of the problem ut (x, t) =9uxx (x, t), 0≤x≤2, t>0 u(0, t) =0, ux (2, t) = 0