6. The system described by the equations 1.1 x(k+1)= 0.3 0 | ] x(x) + [ ]u(K), y(k); u(k), y(k) = x(k)-x₂ (k) is excited by the initial conditions x(0) = [-1 2], with input u(k) = 0. a) Solve the state equation for x(k), using the expression (k) = Z¹|z(z1-4)¹| to compute (k) = A*. b) Find the output y(k). c) Show that the (k) computed in part a) satisfies (0) = 1. d) Show that the solution in part (a) satisfies the initial conditions. e) Use an iterative or sequential solution using a matlab program running a for-loop to show that the values of y(k), k = 0, 1, 2 and 3 in part (b) are correct.