Problem $3.(1$ point$)$ Consider a discrete$-$time LTI system whose response to the input

x$[$n$]=2((1)/(3))^($n$+1)$u$[$n$]$

is

y$[$n$]=3((1)/(2))^($n$+1)$u$[$n$]-2((2)/(3))^($n$)$u$[$n$]$

$($a$)(0\mathrm{.}4$ points$)$ Find the frequency response H$($e$^($j$\backslash$omega $))$ of this system.

$($b$)(0\mathrm{.}4$ points$)$ Determine the system's unit impulse response h$[$n$].$

$($c$)(0\mathrm{.}2$ points$)$ Find the difference equation relating the input and the output of this system.