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Suppose A is an n x n matrix given by A = 7 (5 ) where is a nonzero column vector in R". (a) Show that = ||||² is an eigenvalue of A with corresponding eigenvector u. (b) Show that 0 is an eigenvalue with geometric multiplicity n 1. (Hint: What is rank(A)?)

Suppose A is an n x n matrix given by A = 7 (5 ) where is a nonzero column vector in R". (a) Show that = ||||² is an eigenvalue of A with corresponding eigenvector u. (b) Show that 0 is an eigenvalue with geometric multiplicity n 1. (Hint: What is rank(A)?)

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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Suppose A is an n x n matrix given by A = 7 (5 ) where is a nonzero column vector in R". (a) Show that = ||||² is an eigenvalue of A with corresponding eigenvector u. (b) Show that 0 is an eigenvalue with geometric multiplicity n 1. (Hint: What is rank(A)?)
Transcribed Image Text:Suppose A is an n x n matrix given by A = 7 (5 ) where is a nonzero column vector in R". (a) Show that = ||||² is an eigenvalue of A with corresponding eigenvector u. (b) Show that 0 is an eigenvalue with geometric multiplicity n 1. (Hint: What is rank(A)?)
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