Given the following time varying model: $Z(t) = \alpha*t*z(t-1)$, how do I go about proving linearity? The issue I keep running into with a number of approaches is that because Z(t) is dependent on Z(t-1), I always end up with some inscrutable function within the function.
For transparency this is homework, some I'm happy for general guidance over a full solution.
Edit: The question explicitly says "Prove linearity" not "prove or disprove linearity." And the professor has used these homework's for years. So... take that for what it's worth. This is in the context of time series.