Consider the system described by the transfer function, G$($z$)=$ Y$($z$)/$U$($z$)=($z$^2+0\mathrm{.}9*$z$)/($z$^2-1\mathrm{.}5*$z $+0\mathrm{.}5)($a$)$ Find two different state space representations for G$($z$).($b$)$ Find the state transition matrix $($k$)$ for this system.