Linearity and Time Invariance
For the system
Xk[n]=d[n-k]
The output is defined as
Yk[n]=(k+1)2 d[n-(k+1)]
a) Time Invariance
This system is not time invariant because it is dependent on the time shift $ k $. If the time is shifted before being put through the system, there will be a different output than if it is put through the system and then time shifted.
b) Linearity
Looking at the examples on Mimi's homework page[[1]], the x[n] to produce the output Y[n]=u[n-1] would be u[n].
