. Let b ^= (²8) A C be a nonsingular matrix (det A # 0). (a) Show that, if a = 0, then b ‡ 0 and c = 0. (b) Suppose a = 0. Use the result of part (a) to show that the origin is the only equilibrium point. Along with the verification given in the section, this result shows that, if det A = 0, then the only equilibrium point for the system dY/dt = AY is the origin.
. Let b ^= (²8) A C be a nonsingular matrix (det A # 0). (a) Show that, if a = 0, then b ‡ 0 and c = 0. (b) Suppose a = 0. Use the result of part (a) to show that the origin is the only equilibrium point. Along with the verification given in the section, this result shows that, if det A = 0, then the only equilibrium point for the system dY/dt = AY is the origin.
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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Transcribed Image Text:14. Let
b
^- (²8)
-($)
A =
d
be a nonsingular matrix (det A = 0).
(a) Show that, if a = 0, then b ‡ 0 and c ‡ 0.
(b) Suppose a = 0. Use the result of part (a) to show that the origin is the only
equilibrium point.
Along with the verification given in the section, this result shows that, if det A = 0,
then the only equilibrium point for the system dY/dt = AY is the origin.
15. Let
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