$2.($Total: $30$ points$)$ A Adapted from $[$Am$]17\mathrm{.}28$: Find the zero$-$state response, the zero$-$input response, and the total response $($all in the time domain$)$ of the following systems using the z$-$transform: $($a$)(15$ points$)$ y$($n$]+1\mathrm{.}5$y$$n $-1]+0\mathrm{.}5$y$($n $-2)=(-0\mathrm{.}5)"$u$[$n$]$ with y$(-1)=0$ and y$(-2)=-4.($b$)(15$ points$)$ y$[$n$]-$ y$$n $-1]+0\mathrm{.}5$y$/$n $-2)=(0\mathrm{.}5)"$un with yl$-1)=-1$ and y$(-2)=2.$