$3\mathrm{.}18.$ Consider three discrete$-$time systems $S_1,S_2,$ and $S_3$ whose respective responses to a complex exponential input $e^{j\frac{n}{2}}$ are specified as

$S_1$:$e^{j\frac{n}{2}}longrightarrow{e}^{j\frac{n}{2}}u[n]$

$S_2$:$e^{j\frac{n}{2}}longrightarrow{e}^{j3\frac{n}{2}}$

$S_3$:$e^{j\frac{n}{2}}$longrightarrow$2e^{j5\frac{n}{2}}$

For each system, determine whether the given information is sufficient to conclude that the system is definitely not LTI.