$7\mathrm{.}25$ An LTI system has the transfer function

H$($z$)=$z$($z$1)($z$2).$H$($z$)=\backslash$frac$\{$z$\}\{($z $-1)($z $-2)\}.$H$($z$)=($z$1)($z$2)$z$.$

Compute the following:

$($a$)$ The zeros and poles. Is the system stable?

$($b$)$ The difference equation.

$($c$)$ The response to input x$[$n$]=\{2,6,4\}$x$[$n$]=\backslash \{2,-6,4\backslash \}$x$[$n$]=\{2,6,4\}.$

$($d$)$ The response to input x$[$n$]=\{1,1\}$x$[$n$]=\backslash \{1,-1\backslash \}$x$[$n$]=\{1,1\}.$

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