Which of the following statements are true? 1 i) If A is invertible and V is an eigenvector for A corresponding to an eigenvalue A, then V is an eigenvector for A corresponding to the eigenvalue A. ii) If A is an eigenvalue for A, then -13A2 is an eigenvalue for -13A?. iii) If zero is an eigenvalue for A, then A is not invertible. iv) If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues.
Which of the following statements are true? 1 i) If A is invertible and V is an eigenvector for A corresponding to an eigenvalue A, then V is an eigenvector for A corresponding to the eigenvalue A. ii) If A is an eigenvalue for A, then -13A2 is an eigenvalue for -13A?. iii) If zero is an eigenvalue for A, then A is not invertible. iv) If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues.
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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Transcribed Image Text:Which of the following statements are true?
1
i) If A is invertible and V is an eigenvector for A corresponding to an eigenvalue A, then V is an eigenvector for A corresponding to the eigenvalue A.
ii) If A is an eigenvalue for A, then -13A2 is an eigenvalue for -13A?.
iii) If zero is an eigenvalue for A, then A is not invertible.
iv) If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues.
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