Consider the following. A = 18 −80 4 −18, P = −4 −5 −1 −1 (a) Verify that A is diagonalizable by computing P−1AP. 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 × n matrices, then they have the same eigenvalues. (?1, ?2) =
Consider the following. A = 18 −80 4 −18, P = −4 −5 −1 −1 (a) Verify that A is diagonalizable by computing P−1AP. 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 × n matrices, then they have the same eigenvalues. (?1, ?2) =
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
Consider the following.
A =
,
|
|
18 | −80 |
|
||
| 4 | −18 |
P =
|
|
−4 | −5 |
|
||
| −1 | −1 |
(a) Verify that A is diagonalizable by computing
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
P−1AP.
| 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 × n matrices, then they have the same eigenvalues.
If A and B are similar n × n matrices, then they have the same eigenvalues.
(?1, ?2) =
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