\text { 6. Consider the dynamical system, } x_{t+1}=A x_{t}, \text { when } A=\left[\begin{array}{cc} 0.80 & 0 \\ 0 & 0.64 \end{array}\right] \text { a. If } x_{0}=(3,3), \text

{ what are } x_{1}, x_{2}, \text { and } x_{3} ? \text { b. If } x_{0}=(-3,3) \text { what are } x_{1}, x_{2}, \text { and } x_{3} ? \text { c. If } x_{0}=(-3,-3) \text { what are } x_{1}, x_{2}, \text { and } x_{3} \text { ? } \text { d. If } x_{0}=(3,-3) \text { what are } x_{1}, x_{2} \text { and } x_{3} \text { ? } e. Plot all 4 trajectories. f. What is the steady state vector, x', for this system? g. What are the eigenvalues of A? h. Is x asymptotically stable?