Let be a nonsingular matrix (detA ≠ 0).(a) Show that, if a = 0, then b ≠ 0 and c ≠ 0.(b) S...

Let be a nonsingular matrix (detA ≠ 0).

(a) Show that, if a = 0, then b ≠ 0 and c ≠ 0.

(b) Suppose a = 0. Use the result of part (a) to show that the origin is the only equilibrium point.

Along with the verification given in the section, this result shows that, if detA ≠ 0, then the only equilibrium point for the system dY/dt = AY is the origin.