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

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Question

Consider the following.

A =

−80

−18

P =

−4

−5

−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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