Part A: Can the system be time invariant?
The system cannot be time invariant.
For instance, the input
$ \,X_0[n]=\delta [n]\, $
yields the output
$ \,Y_0[n]=\delta [n-1]\, $
Thus,
$ \,Y_0[n-1]=\delta [n-2]\, $
However, the input
$ \,X_0[n-1]=\delta [n-1]=X_1[n]\, $
yields the output
$ \,Y_1[n]=4\delta[n-2]\, $
Since these two are not equal
$ \,\delta [n-2]\not= 4\delta[n-2]\, $
the system is time variant (by not fitting the definition of time invariance).
Part B: Find input given output
LAWL
