How is it possible to tell if systems are linear, non-linear or time-invariant?

How is it possible by looking at systems to tell whether a system is linear, non-linear and time invariant? For example how would you tell with these systems, (a) y[n] = sin(x[n]) (b) y[n] = 3x[2n] (c) y[n] = 5x[n – 3]

Answer 1

[Wayne King]

This is not a MATLAB question. You can simply tell in these cases by checking whether the operator satisfies the superposition and scaling properties of a linear operator and whether the operator commutes with the shift operator (time invariance)