For each of the three systems below specify whether or not the system is $1)$ linear. $(2)$ shift$-$invariant, $(3)$ causal. $(4)$ BIBO stable. The system input is x$[$n$]$ and the system output & vinj Provide a short reasoning in case the system does not have a particular property

$($a$)(4$ points$)$ y $=12(1)$

$($b$)(4$ pomts$)$ y$[$n$]=$ x$[$n$]+$ x $*[$n $-1]^($sqrt$($n$))$

$($c$)(4$ points$)$ y$\backslash \{$n$\backslash \}=$ x $^2*\backslash \{-|$n$|\backslash \}$

$($d$)(4$ points$)$ v$\backslash \{$n$\backslash \}=$ nx$\backslash$ n$-3]$ x$[2]$