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3. (a) Show that an eigenvector cannot be associated with two distinct eigenvalues. (b) Let A be such that Ar = 0, for some positive integer r. Show that A has only zero as an eigenvalue. (c) Give an example of a 2 × 2 matrix such that A² = 0.

3. (a) Show that an eigenvector cannot be associated with two distinct eigenvalues. (b) Let A be such that Ar = 0, for some positive integer r. Show that A has only zero as an eigenvalue. (c) Give an example of a 2 × 2 matrix such that A² = 0.

Advanced Engineering Mathematics
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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Matrix Analysis practice question.  please show clear thanks 

Throughout, we let A ∈ C^nxn

 

3. (a) Show that an eigenvector cannot be associated with two distinct eigenvalues. (b) Let A be such that A” = 0, for some positive integer r. Show that A has only zero as an eigenvalue. (c) Give an example of a 2 × 2 matrix such that A² = 0.
Transcribed Image Text:3. (a) Show that an eigenvector cannot be associated with two distinct eigenvalues. (b) Let A be such that A” = 0, for some positive integer r. Show that A has only zero as an eigenvalue. (c) Give an example of a 2 × 2 matrix such that A² = 0.
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