Consider that matrix A 12 24-2 36-3 (a) Find the eigenvalues of A. Also find the corresponding eigenspaces and their dimensions. (b) Explain why A is diagonalizable. Calculate A2021 (c) Your friend claims "I think if P diagonalizes A, then P diagonalizes every integral power of A." Is his statement correct? If not, under what condition(s) the statement holds true? Can you prove it in general?
Consider that matrix A 12 24-2 36-3 (a) Find the eigenvalues of A. Also find the corresponding eigenspaces and their dimensions. (b) Explain why A is diagonalizable. Calculate A2021 (c) Your friend claims "I think if P diagonalizes A, then P diagonalizes every integral power of A." Is his statement correct? If not, under what condition(s) the statement holds true? Can you prove it in general?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 38EQ
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Question
![Consider that matrix
1 2
-
A =
2 4 -2
36
-3
(a) Find the eigenvalues of A. Also find the corresponding eigenspaces and their
dimensions.
(b) Explain why A is diagonalizable. Calculate A2021.
(c) Your friend claims
"I think if P diagonalizes A, then P diagonalizes every integral power of A."
Is his statement correct? If not, under what condition(s) the statement holds true?
Can you prove it in general?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55012d47-76b1-4db5-aa6c-d62c11fce584%2Fea5e0495-db99-460d-b2f0-4c8119ebeaf6%2F1vkhz79_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider that matrix
1 2
-
A =
2 4 -2
36
-3
(a) Find the eigenvalues of A. Also find the corresponding eigenspaces and their
dimensions.
(b) Explain why A is diagonalizable. Calculate A2021.
(c) Your friend claims
"I think if P diagonalizes A, then P diagonalizes every integral power of A."
Is his statement correct? If not, under what condition(s) the statement holds true?
Can you prove it in general?
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