Is the System Time-Invariant?
No, the system is NOT time-invariant. It's not time-invariant because the output is simply scaled by the time-shift T.
Linearity: What input X[n] will yield the output Y[n] = u[n-1]?
If we put a unit step function into the input of the system, then the system will output a step function that is shifted one unit to the right.
