only need help on parts d-e

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
Problem 29EQ
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only need help on parts d-e 

3. Suppose that the characteristic polynomial of a square matrix A is
fA(A) = –X³ + 3A
(a)
What is the size of A?
(b)
What are the eigenvalues of A?
(c)
What is tr(A)?
(d)
Is A invertible? Why or why not?
Is A diagonalizable? If so, determine a diagonal matrix that is similar to A.
(e)
If not, explain why not.
Transcribed Image Text:3. Suppose that the characteristic polynomial of a square matrix A is fA(A) = –X³ + 3A (a) What is the size of A? (b) What are the eigenvalues of A? (c) What is tr(A)? (d) Is A invertible? Why or why not? Is A diagonalizable? If so, determine a diagonal matrix that is similar to A. (e) If not, explain why not.
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