$[4$ pts$]$ Transform the system into modal form $($see instructions for $1$h$).$ Let the transformed

state variable be z $=$ V $1$x$.$ For the rest of this problem, we will work in z

coordinates unless otherwise stated.

$($b$)[5$ pts$]$ Compute the zero$-$state and zero$-$input responses Lu and Lo$.$

$($c$)[5$ pts$]$ Find the adjoint system, and its zero$-$state and zero$-$input responses Pu and Po$.$

$($d$)[4$ pts$]$ Show that L$$o $=$ Pu$.$

$($e$)[4$ pts$]$ Show that L$$

u $=$ Po$.$