Question: (a) Given a homogeneous linear dynamical system with invariant stable, unstable, and center subspaces S, U,C, explain why the origin is asymptotically stable if and

(a) Given a homogeneous linear dynamical system with invariant stable, unstable, and center subspaces S, U,C, explain why the origin is asymptotically stable if and only if C = U = {0}.

(b) Is the origin stable if U = {0} but C ≠ {0}?

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