Which of the following statement about eigenvalue is false? (i) λ is an eigenvalue of A if and only if (λI−A)x=0 has nontrivial solutions. (ii) λ is an eigenvalue of A if and only if det(λI−A)=0. (iii) λ is an eigenvalue of A if and only if there exists infinitely many u such that Au=λu. (iv) λ is an eigenvalue of A if and only if (λI−A)x=0 is consistent.

Which of the following statement about eigenvalue is false? (i) λ is an eigenvalue of A if and only if (λI−A)x=0 has nontrivial solutions. (ii) λ is an eigenvalue of A if and only if det(λI−A)=0. (iii) λ is an eigenvalue of A if and only if there exists infinitely many u such that Au=λu. (iv) λ is an eigenvalue of A if and only if (λI−A)x=0 is consistent.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Which of the following statement about eigenvalue is false?

(i) λ is an eigenvalue of A if and only if (λI−A)x=0 has nontrivial solutions.

(ii) λ is an eigenvalue of A if and only if det(λI−A)=0.

(iii) λ is an eigenvalue of A if and only if there exists infinitely many u such that Au=λu.

(iv) λ is an eigenvalue of A if and only if (λI−A)x=0 is consistent.

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