Consider the system x = Ax, and suppose that A has one zero eigenvalue.(a) Show that
Chapter 9, Problem 18(choose chapter or problem)
Consider the system x = Ax, and suppose that A has one zero eigenvalue.(a) Show that det(A) = 0.(b) Show that x = 0 is a critical point and that,in addition, every point on a certain straightline through the origin is also a critical point.(c) Let r1 = 0 and r2 = 0, and let (1) and (2) be corresponding eigenvectors. Show thatthe trajectories are as indicated in Figure 9.1.8. What is the direction of motion on thetrajectories?
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