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(10 Let A = 3 X-L with eigenvalues A, dq. Find xe ¢ such that a) A,+Qq = 3 %3D c) 2,?+ 2 = (Hint: a?+82 = (a+8)²_2 al) %3D

(10 Let A = 3 X-L with eigenvalues A, dq. Find xe ¢ such that a) A,+Qq = 3 %3D c) 2,?+ 2 = (Hint: a?+82 = (a+8)²_2 al) %3D

Advanced Engineering Mathematics
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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**Problem 10:** Let \( A = \begin{bmatrix} x+1 & 9x \\ 3 & x-1 \end{bmatrix} \) with eigenvalues \(\lambda_1, \lambda_2\). Find \( x \in \mathbb{C} \) such that: a) \(\lambda_1 + \lambda_2 = 3\) b) \(\frac{1}{\lambda_1} + \frac{1}{\lambda_2} = 1\) c) \(\lambda_1^2 + \lambda_2^2 = 1\) (Hint: \(a^2 + b^2 = (a+b)^2 - 2ab\))
Transcribed Image Text:**Problem 10:** Let \( A = \begin{bmatrix} x+1 & 9x \\ 3 & x-1 \end{bmatrix} \) with eigenvalues \(\lambda_1, \lambda_2\). Find \( x \in \mathbb{C} \) such that: a) \(\lambda_1 + \lambda_2 = 3\) b) \(\frac{1}{\lambda_1} + \frac{1}{\lambda_2} = 1\) c) \(\lambda_1^2 + \lambda_2^2 = 1\) (Hint: \(a^2 + b^2 = (a+b)^2 - 2ab\))
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