3. Suppose that the characteristic polynomial of a square matrix A is fA(^) = –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.
3. Suppose that the characteristic polynomial of a square matrix A is fA(^) = –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.
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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Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51ba1ab0-5c9b-4874-b436-0ee9f47864fd%2F083f9160-d775-4a16-81cb-514c2c3e5933%2F4tcs57i_processed.png&w=3840&q=75)
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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