6. Consider the matrix 0 -[1] a A = (a) For what value(s) of a does A have an eigenvalue of multiplicity 2? What is the value of the eigenvalue in this case? (b) For what value(s) of a does A have -1 and 2 as eigenvalues? (c) For what value(s) of a does A have a complex eigenvalues?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
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6. Consider the matrix
A
0
[21]
a
(a) For what value(s) of a does A have an eigenvalue of multiplicity 2? What is the value of
the eigenvalue in this case?
(b) For what value(s) of a does A have -1 and 2 as eigenvalues?
(c) For what value(s) of a does A have a complex eigenvalues?
Transcribed Image Text:6. Consider the matrix A 0 [21] a (a) For what value(s) of a does A have an eigenvalue of multiplicity 2? What is the value of the eigenvalue in this case? (b) For what value(s) of a does A have -1 and 2 as eigenvalues? (c) For what value(s) of a does A have a complex eigenvalues?
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