9.4 Reducing a Markov model to a linear dynamical system. Consider the 2-Markov model xt+1 =A1xt +A2xt−1, t=2,3,..., where xt is an n-vector. Define zt = (xt, xt−1). Show that zt satisfies the linear dynamical system equation zt+1 = Bzt, for t = 2, 3, . . ., where B is a (2n) × (2n) matrix. This idea can be used to express any K-Markov model as a linear dynamical system, with state (xt, . . . , xt−K+1).