Problem 6a
This system cannot be time-invariant because the function of the output has a constant k that gets changed everytime one selects a value of k. This changes the amplitude of the output function, making it not correspond to the input function and therefore cannot be time-invariant.
Problem 6b
The table indicates that if the input is $ \delta[n] $ then the output is $ \delta[n-1] $. Therefore, if the system is linear, for the output to be $ u[n-1] $, the input then needs to be $ u[n] $.
