HW3Problem.pdf x Sy |-1-2i] - Probability Calcul X Wolfram Alpha Examples x C Mathematical Statistics V X b.edu/courses/pluginfile.php/5465279/mod_resource/content/1/HW3Problem.pdf Problem 2: Solve the system i = AT with initial data (0) = To for A Find the stable, unstable and equilibrium subspaces and sketch (roughly) the phase diagram. Problem 3*: (Optional) Consider the solution r(t; To) = etsTo of the equation i = AT, F ER?, as a function of both time t and the initial data F(0; To) = To. Denote for To # 0 by ri(t: Fo)= i(t; Fo) the unit tangent vector to the orbit. Prove that if the origin is a stable node then the following limit exists for all To # 0. N(Fo) = lim n(t: 10). Show that the function N of Fo ( R" \\(0) is continuous if A is diagonalizable, and bring an example of non-diagonalizable A such that N is discontinuous. Interpret your results graphically. 9 RN DELL PS F7 F10 F11 7 R T Y U O F G H K