Matrix Analysis practice question please show clear thanks！ 1. Let p¹, p² be eigenvectors of a matrix A, that correspond to distincteigenvalues A₁, A2, respectively. Further, let p³, p4 be linearly independenteigenvectors associated with the eigenvalue X3. If λ3 ‡ λ₁ and λ3 ‡ λ2,does it follow that {p¹, p², p³, p¹} is linearly independent?

Answered: Image /qna-images/answer/9bc82804-e84b-468e-a6ac-819e34a7db7e.jpg

1. Let p¹,p² be eigenvectors of a matrix A, that correspond to distinct eigenvalues A₁, A2, respectively. Further, let p³, pª be linearly independent eigenvectors associated with the eigenvalue λ3. If λ3 ‡ A₁ and λ3 ‡ λ2, does it follow that {p¹, p², p³, p^} is linearly independent?

1. Let p¹,p² be eigenvectors of a matrix A, that correspond to distinct eigenvalues A₁, A2, respectively. Further, let p³, pª be linearly independent eigenvectors associated with the eigenvalue λ3. If λ3 ‡ A₁ and λ3 ‡ λ2, does it follow that {p¹, p², p³, p^} is linearly independent?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 26EQ

See similar textbooks