Given G$($s$)=$ s $1$ s $3+2$s $2$ s $2($a$)3$ points. Find a three$-$dimensional controllable realization. Is it observable? Is it detectable? $($b$)3$ points. Find a three$-$dimensional observable realization. Is it controllable? Is it stabilizable? $($c$)2$ points. What causes the apparent difference in controllability and observability of the same system? Derive an irreducible transfer function for G$($s$).($d$)4$ points. Please derive a realization that is both controllable and observable, represent it in both controllable canonical form and observable canonial form