(a) Consider the eigenvalue problem -X" = AX, 0< x < / X'(0) + X(0) = 0, X(I) = 0. %3D i. Show, without calculating the eigenvalues and eigenfunctions explicitly, that the eigenfunctions corresponding to distinct eigenvalues are orthogonal. (You may assume that all eigenvalues are real and all eigenfunctions are real-valued.)

Linear Algebra: A Modern Introduction
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Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
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(a) Consider the eigenvalue problem
-X" = AX, 0< x < /
X'(0) + X(0) = 0, X(I) = 0.
%3D
i. Show, without calculating the eigenvalues and eigenfunctions explicitly, that the
eigenfunctions corresponding to distinct eigenvalues are orthogonal. (You may
assume that all eigenvalues are real and all eigenfunctions are real-valued.)
Transcribed Image Text:(a) Consider the eigenvalue problem -X" = AX, 0< x < / X'(0) + X(0) = 0, X(I) = 0. %3D i. Show, without calculating the eigenvalues and eigenfunctions explicitly, that the eigenfunctions corresponding to distinct eigenvalues are orthogonal. (You may assume that all eigenvalues are real and all eigenfunctions are real-valued.)
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