Reducing a Markov model to a linear dynamical system. Recall the definition of a Markov model (if you need a refresher, see §9.1). Consider the 2-Markov model xt+1 = A1xt + A2xt−1, t = 2, 3, . . . , where xt is an n-vector. In class, we studied systems where the next state is a linear function of the current state. Note here that the next state now depends on the states at the two previous time steps. 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).