1. (9pts) Diagonalize the matrix below by the following steps: 2 2 A: 1 3 -1 eigenvalues are λ = 5, 1. -1 -2 2 (a) (5pts) Find the matrix P. (b) (2pts) Find the diagonal matrix D. (c) (2pts) Check that AP = PD.
1. (9pts) Diagonalize the matrix below by the following steps: 2 2 A: 1 3 -1 eigenvalues are λ = 5, 1. -1 -2 2 (a) (5pts) Find the matrix P. (b) (2pts) Find the diagonal matrix D. (c) (2pts) Check that AP = PD.
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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
Transcribed Image Text:1. (9pts) Diagonalize the matrix below by the following steps:
2
2
A:
1
3 -1
eigenvalues are λ = 5, 1.
-1
-2 2
(a) (5pts) Find the matrix P.
(b) (2pts) Find the diagonal matrix D.
(c) (2pts) Check that AP = PD.
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