The answer has been given, please prove whether it is correct,Be sure to explain what you are doing in terms of the meaning of the words in the problems. Let A be an n X n diagonal matrix. Find conditions on A guaranteeing thatlim x(t) 0for all solutions to x' = Ax.Adiag {a₁,an} and ai < 0, i = 1,1, ..., n.

Answered: Image /qna-images/answer/2e4b42fd-6ec4-44a6-9747-7be37862dc73.jpg

Answered: Let A be an n X n diagonal matrix. Find…

Let A be an n X n diagonal matrix. Find conditions on A guaranteeing that lim x(t) = 0 - for all solutions to x' Ax. A diag {a₁, - an} and ai < 0, i = 1, ..., n.

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

The answer has been given, please prove whether it is correct,

Be sure to explain what you are doing in terms of the meaning of the words in the problems.

Let A be an n X n diagonal matrix. Find conditions on A guaranteeing that
lim x(t) 0
for all solutions to x' = Ax.
A
diag {a₁,
an} and ai < 0, i = 1,
1, ..., n.

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