Problem

Let be a nonzero matrix. That is, suppose that at least one of its entries is nonzero. Sho...

Let be a nonzero matrix. That is, suppose that at least one of its entries is nonzero. Show that, if det A = 0, then the system dY/dt = AY has an entire line of equilibria. [Hint: First consider the case where a ≠ 0. Show that any point (x0, y0) that satisfies x0 = (−b/a) y0 is an equilibrium point. What if we assume that entries of A other than a are nonzero?]

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Solutions For Problems in Chapter 3.1

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