$7\mathrm{.}23$ An LTI system has zeros $\{3,4\}\backslash \{3,4\backslash \}\{3,4\}$ and poles $\{1,2\}\backslash \{1,2\backslash \}\{1,2\}.$ The transfer function H$($z$)$H$($z$)$H$($z$)$ has H$(0)=6$H$(0)=6$H$(0)=6.$ Compute the following:

$($a$)$ The transfer function H$($z$)$H$($z$)$H$($z$).$

$($b$)$ The response to x$[$n$]=\{1,3,2\}$x$[$n$]=\backslash \{1,-3,2\backslash \}$x$[$n$]=\{1,3,2\}.$

$($c$)$ The impulse response h$[$n$]$h$[$n$]$h$[$n$].$

$($d$)$ The difference equation.