We are given a 2x2 matrix A (shown in the attachment), and we need to find a diagonal matrix D and an orthogonal matrix P such that A = P'DP. Thus far, I found the following:Trace of A is 10The determinant of A is 24.From there, A has a characteristic polynomial of λ2 - 10λ + 24. Finding the eigenvalues from that results in the following eigenvalues: λ1 = 4, λ2 = 6. Because the eigenvalues here are distinct, A should be diagonalizable. diagonal matrix D is: [[6 0] [0 4]].I know we need to then find the eigenvectors and normalize them, am unsure of how to do that. I know the general format would look something like this though, With I representing the identity matrix.A - λ1I = A - 4IA - λ2I = A - 6IHow would we go about finding these eigenvectors and normalizing them? 5. Let A: =15Find a diagonal matrix D and an orthogonal matrix P such thatA = P'DP.

Given : A=5115 To Find : D Diagonal matrix and P Orthogonal matrix

Answered: 5. Let A 15 Find a diagonal matrix D…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

We are given a 2x2 matrix A (shown in the attachment), and we need to find a diagonal matrix D and an orthogonal matrix P such that A = P'DP. Thus far, I found the following:

Trace of A is 10
The determinant of A is 24.
From there, A has a characteristic polynomial of λ²- 10λ + 24. Finding the eigenvalues from that results in the following eigenvalues: λ₁ = 4, λ₂ = 6. Because the eigenvalues here are distinct, A should be diagonalizable.
diagonal matrix D is: [[6 0] [0 4]].

I know we need to then find the eigenvectors and normalize them, am unsure of how to do that. I know the general format would look something like this though, With I representing the identity matrix.