well, this is not Maple ...
You need to define an equation, i.e. it should read after
RSolve x[t+1] == a[t] ... In a notebook both operators (
==) look very similar.
Regarding your question on multivariate recurrence: I may be completely wrong, but to me this seems equivalent to your first problem. In the solution there is nowhere stated that every element needs to be a scalar.
Regards -- Henrik