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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.

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
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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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.
Transcribed Image Text: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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