Consider a system defined by the transformation defined as

$T(x[n])={\displaystyle \underset{k=n-n_0}{\overset{n+n_0}{}}}x[k]$

Determine whether the system is

$($a$)$ stable

$($b$)$ causal

$($c$)$ linear

$($d$)$ time invariant

$($e$)$ memoryless