Classify the following systems according to whether the origin is (i) asymptotically stable, (ii) stable, or (iii) unstable: (a) $\frac{d u}{d t}=-2 u-v, \frac{d v}{d t}=u-2 v$;
(b) $\frac{d u}{d t}=2 u-5 v$, $\frac{d v}{d t}=u-v$
(c) $\frac{d u}{d t}=-u-2 v, \frac{d v}{d t}=2 u-5 v ;$
(d) $\frac{d u}{d t}=-2 v, \frac{d v}{d t}=8 u$;
(e) $\frac{d u}{d t}=-2 u-v+w, \frac{d v}{d t}=-u-2 v+w, \frac{d w}{d t}=-3 u-3 v+2 w$;
(f) $\frac{d u}{d t}=-u-2 v, \frac{d v}{d t}=6 u+3 v-4 w, \frac{d w}{d t}=4 u-3 w$;
(g) $\frac{d u}{d t}=2 u-v+3 w, \frac{d v}{d t}=u-v+w ; \frac{d w}{d t}=-4 u+v-5 w$;
(h) $\frac{d u}{d t}=u+v-w, \frac{d v}{d t}=-2 u-3 v+3 w, \frac{d w}{d t}=-v+w$.