System
Input: $ X_k[n]=\delta [n-k] $
Output: $ Y_k[n]=(k+1)^2 \delta [n-(k+1)] $
For any non-negative integer k
Question 6a
$ x[n] \rightarrow \mbox{Time Delay} \rightarrow y[n]=x[n-n_0] \rightarrow System \rightarrow Y_k[n-n_0]=(k+1)^2 \delta [n-n_0-(k+1)] $
$ x[n] \rightarrow System \rightarrow Y_k[n]=(k+1)^2 \delta [n-(k+1)] \rightarrow \mbox{Time Delay}\rightarrow Y_k[n-n_0]=(k+1)^2 \delta [n-n_0-(k+1)] $
So the system is time invariant.
Question 6b
$ x_0[n]= u[n] $ will yield the output $ y[n]=u[n-1] $
