A state equation is given below: d dt *(t) = Ax(t) Suppose that the eigenvalues of the matrix A are multiple (i.e., several roots equal to each other) This state equation can be writen as Jordan canonical form by using similarity transformation. y) pell(t) = P-'APy(t) = Jy() J is the Jordan canonical form. As an example, new state equation transformed to Jordan canonical form is given below: 1 [yi() d y2(t) dt [y3(t) = 01[y (t)] 0 1 1 ||yz(t) lo 012) [yz(t)] a-) Solve this equation and write down in a form given below. y(t) = S(t)@(t)y(0) The matrix S(t) contains no exponential terms. The matrix Q(t) has only exponential terms. b-) Similarly, extend the result obtained here to a more general form of the same analysis. Use the system given below. , 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 (t) =| 0 0 0 14 1 0 oly(t) 0 0 0 0 14 0 0 0 0 0 0 0 16 0