  We study two families of (matrix versions of) generalized Volterra (or
Bogoyavlensky) lattice equations. For each family, the equations arise as
reductions of a partial differential-difference equation in one continuous and
two discrete variables, which is a realization of a general integrable equation
in bidifferential calculus. This allows to derive a binary Darboux
transformation and also self-consistent source extensions via general results
of bidifferential calculus. Exact solutions are constructed from the simplest
seed solutions.
