Let 20 0 4 0 0 A = 0 0 7 -3 0 2 2 (a) Find the characteristic polynomial of A and all eigenvalues of A. (b) What are the algebraic and geometric multiplicites of each eigenvalue. (Keep in mind the geometric multiplicity is always at least one and at most the algebraic multiplicity) (c) Is A diagonalizable?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
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Please explain step by step how to do parts a, b ,c with the solution

Let
20 0
4
0
0
A =
0
0
7 -3
0 2 2
(a) Find the characteristic polynomial of A and all eigenvalues of A.
(b) What are the algebraic and geometric multiplicites of each eigenvalue. (Keep in mind
the geometric multiplicity is always at least one and at most the algebraic multiplicity)
(c) Is A diagonalizable?
Transcribed Image Text:Let 20 0 4 0 0 A = 0 0 7 -3 0 2 2 (a) Find the characteristic polynomial of A and all eigenvalues of A. (b) What are the algebraic and geometric multiplicites of each eigenvalue. (Keep in mind the geometric multiplicity is always at least one and at most the algebraic multiplicity) (c) Is A diagonalizable?
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