linear 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 arelocated 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 ALC are locatedat $6.($g$)$ If it is possible, determine a controller based on estimated state feedback using an observerto guarantee that the origin of the closed loop is asymptotically stable. Give the closed loopstate equations. What are the eigenvalues of the closed loop?