$10\mathrm{.}20.$ Consider a system whose input x$[$n$]$ and output y$[$n$]$ are related by

y$[$n $-1]+2$y$[$n$]=$ x$[$n$].$

$($a$)$ Determine the zero$-$input response of this system if y$[-1]=2.$

$801$

$($b$)$ Determine the zero$-$state response of the system to the input x$[$ n$]=(1/4)$n u $[$ n$].$

$($c$)$ Determine the output of the system for n $2$: $0$ when x$[$n$]=(114)$nu$[$n$]$ and

y$[-1]=2.$