$2.(12\%)$ Suppose that the step response of a linear time$-$invariant system is s$[$n$]=(1$

$2)$nu$[$n $2],$ in other words,

s$[$n$]$ is the output when the input is x$[$n$]=$ u$[$n$].$

$($a$)$ Determine the system function H$($z$)$ for the system.

$($b$)$ What are the poles and zeros?

$($c$)$ Write a difference equation for the system