$(12$ points$)$ Consider an LTI system with input x$[$n$]$ and out y$[$n$].$ The following relations are known between

x$[$n$]$ and y$[$n$]$: $($i$)$ If x$[$n$]=(1)$n for all n$,$ then y$[$n$]=0$ for all n; $($ii$)$ If x$[$n$]=(1/2)$n$[$n$]$ for all n$,$ then

y$[$n$]$ takes the following form:

y$[$n$]=$ $[$n$]+$

$(1$

$4$

$)$n

$[$n$]$

Answer the following questions:

$($a$)$ What is the value for $?$

$($b$)$ If x$[$n$]=1$ for all n$,$ what will be the corresponding y$[$n$]$