The system described by the equations 1.1 x(k+1)= -0.3 | x(k) + [ ]μ(K), y(k) ‚y(k) = x₁(k) − x₂ (k) is excited by the initial conditions x(0) = [-12]", with input u(k) = 0. a) Solve the state equation for x(k), using the expression (k) = Z¹ [z(zI - A)¹] to compute (k) = A*. b) Find the output y(k). c) Show that the D(k) computed in part a) satisfies (0) = 1. d) Show that the solution in part (a) satisfies the initial conditions.