where all initial conditions are zero.

Question $12(40pts)$ : The following equations describe the input$/$output relationships of different systems

System A: $y(t)=Ay(t),A0$

System B: $y(t)=x(-2t)$

System C: $y[n]=e^{3x[n]}$

System D: $y[n]=Ax[n]+B,A,B0$

System E: $y[n]={\displaystyle \underset{k=-}{\overset{n}{}}}x[k]$

For each of these systems A$,$ B$,$ C$,$ D and E$,$ determine whether it is

$($i$)$ linear, $($ii$)$ time$-$invariant, $($iii$)$causal$,($iv$)$stable by explaining the reasons of your choices.