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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) =

Linear Algebra: A Modern Introduction
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 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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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) = 
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