6. (6 points) For the system of equations x' ² x B 3] (a) (1 point) Show that the eigenvalues of the matrix A = are l =

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6 6 Points For The System Of Equations X X B 3 A 1 Point Show That The Eigenvalues Of The Matrix A Are L 1 (46 KiB) Viewed 27 times

6. (6 points) For the system of equations x' ² x B 3] (a) (1 point) Show that the eigenvalues of the matrix A = are l = 4, 12 = -1. (b) (2 points) Find corresponding eigenvectors for the eigenvalues found in (a). (c) (1 point) From your results in parts (a) and (b), construct the general solution for the system (1 point). (d) (1 point) Classify the type of equilibrium which resides at the origin as one of: stable node, unstable node, stable spiral, unstable spiral, center or saddle (circle the appropriate response) and give a rough sketch of the phase portrait.