Consider the following. -7 24 3 -4 A = P = -1 (a) Verify that A is diagonalizable by computing P-AP. p-'AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (1,, A2) :
Consider the following. -7 24 3 -4 A = P = -1 (a) Verify that A is diagonalizable by computing P-AP. p-'AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (1,, A2) :
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
PLEASE, answer the following 2 problems, thanks.
![Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-'AP is the diagonal form of A. Prove that
-6 -11
Ak = PBkp-1, where k is a positive integer.
Use the result above to find the indicated power of A.
10
A =
18
AS
-1/3
1
AS =
1
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1f02723-d9e1-4704-83ab-f90dc08f102d%2F54bd890a-2d9d-4244-8689-9811d1d7198f%2Fn063zb_processed.png&w=3840&q=75)
Transcribed Image Text:Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-'AP is the diagonal form of A. Prove that
-6 -11
Ak = PBkp-1, where k is a positive integer.
Use the result above to find the indicated power of A.
10
A =
18
AS
-1/3
1
AS =
1
1
![Consider the following.
-7 24
-3 -4
A =
P =
-1 -1
(a) Verify that A is diagonalizable by computing P-AP.
p-1AP =
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
Similar Matrices Have the Same Eigenvalues
If A and B are similar n x n matrices, then they have the same eigenvalues.
(1, 12) = (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1f02723-d9e1-4704-83ab-f90dc08f102d%2F54bd890a-2d9d-4244-8689-9811d1d7198f%2Fvhsryg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following.
-7 24
-3 -4
A =
P =
-1 -1
(a) Verify that A is diagonalizable by computing P-AP.
p-1AP =
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
Similar Matrices Have the Same Eigenvalues
If A and B are similar n x n matrices, then they have the same eigenvalues.
(1, 12) = (
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