This problem shows how small changes in the coefficients of a system of linear equations can affect a critical point that is a center. Consider the system x = (0 1 -1 0) x. Show that the eigenvalues are plusminus i so that the origin (0, 0) is a center. Now consider the system x = (epsilon 1 -1 epsilon)x, where |epsilon| is arbitrarily small. Show that the eigenvalues are epsilon plusminus i. Thus, no matter how small | epsilon | notequalto 0 is the center becomes a spiral point. Under what conditions is the critical point asymptotically stable and when is it unstable for this perturbed system? This is why the system is called "the critical case". The sensitivity to perturbations have deep consequences for numerical procedures