3. Consider the system of DES X = AX, where A is a constant matrix. (a) Show that if v is an eigenvector for X, then vet is a solution. (b) Show that if v is an eigenvector for A and v = = (A - AI)u, then vte + ue is also a solution. (c) Find another solution if v = (A — \I)u = (A − \I)²w. (Hint: for a solution s(t) you know that s(t) = As(t); equivalently ( – XI)s(t) is equal to (A - XI)s(t).)

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