Find the eigenvalues Find the eigenvalues A₁ < ₂ and associated unit eigenvectors ₁, ₂ of the symmetric matrixThe smaller eigenvalue >₁=has associated unit eigenvector ₁ =The larger eigenvalue >₂=Note: The eigenvectors above form an orthonormal eigenbasis for the column space of A.has associated unit eigenvector ₂A =13 -21]-21 -43

Given matrix is A=13-21-21-43 The characteristic equation of matrix A is |A-λI|=0…

Answered: Find the eigenvalues X₁

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

Find the eigenvalues

Expert Solution

Step 1

Given matrix is

$A = [\begin{matrix} 13 & - 21 \\ - 21 & - 43 \end{matrix}]$

The characteristic equation of matrix A is $| A - λ I | = 0$

$|\begin{matrix} 13 - λ & - 21 \\ - 21 & - 43 - λ \end{matrix}| = 0 (13 - λ) (- 43 - λ) - 441 = 0 λ^{2} + 30 λ - 559 - 441 = 0 λ^{2} + 30 λ - 1000 = 0 λ^{2} + 50 λ - 20 λ - 1000 = 0 λ (λ + 50) - 20 (λ + 50) = 0 (λ - 20) (λ + 50) = 0 λ = 20, - 50 .$