14. Let be a nonsingular matrix (det A # a b A = (**) c d 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.
14. Let be a nonsingular matrix (det A # a b A = (**) c d 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.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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