Consider an n x n matrix A with m distinct eigenvalues ^1 * km. a. Show that the initial

Chapter 9, Problem 48

(choose chapter or problem)

Consider an n x n matrix A with m distinct eigenvalues ^1 * km. a. Show that the initial value problem= Ax, with x(0) = x q,dt has a unique solution Jc(r). b. Show that the zero state is a stable equilibrium solution of the systemdt if and only if the real part of all the X, is negative. (Hint: Exercise 47 and Exercise 8.1.45 are helpful.)

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