Alinear time$-$invariant system is described by the equations: $$ x $=1101$ x$+12$ u y $=21$ x $($a$)$ Identify any fixed controllable modes. $($b$)$ Is the system stabilizable? Is the system completely controllable? $($c$)$ Determine the gain matrix K for which the non$-$fixed controllable modes of A BK are located at $2.($d$)$ Identify any fixed observable modes. $($e$)$ Is the system detectable? Is the system completely observable? $($f$)$ Determine the gain matrix L for which the non$-$fixed observable modes of A LC are located at $6.($g$)$ If it is possible, determine a controller based on estimated state feedback using an observer to guarantee that the origin of the closed loop is asymptotically stable. Give the closed loop state equations. What are the eigenvalues of the closed loop?