For the following time invariant linear system, x t = - x t +x t tut x t) = - 2x t) y(t = x t-x t+ut A=[ B=[ ] , c=[1 -1] , D=[1] sI - A)- (1) calculate (2) determine the transition matrix for the system by calculating the inverse Laplace transform of (SI - A)-i D(t) =L-1 (sI - A)-1] (3) Write its characteristic equation for matrixA explicitly as a polynomial of A det ( X] - A) =0 (4) Find out the eigenvalues (), and ),) of matrix A by solving the characteristic equation [5) Obtain vectors & and &, by solving the linear equations (AI - A =0 ( AI - A) =0 (6) Let T =$ 52 calculate Ti (7) Calculate transition matrix: D(t) = ett = TextI-1