  In a recent paper, a distributed algorithm was proposed for solving linear
algebraic equations of the form $Ax = b$ assuming that the equation has at
least one solution. The equation is presumed to be solved by $m$ agents
assuming that each agent knows a subset of the rows of the matrix $[A \; b]$,
the current estimates of the equation's solution generated by each of its
neighbors, and nothing more. Neighbor relationships are represented by a
time-dependent directed graph $N(t)$ whose vertices correspond to agents and
whose arcs characterize neighbor relationships. Sufficient conditions on $N(t)$
were derived under which the algorithm can cause all agents' estimates to
converge exponentially fast to the same solution to $Ax = b$. These conditions
were also shown to be necessary for exponential convergence, provided the data
about $[A \; b]$ available to the agents is "non-redundant". The aim of this
paper is to relax this "non-redundant" assumption. This is accomplished by
establishing exponential convergence under conditions which are the weakest
possible for the problem at hand; the conditions are based on a new notion of
graph connectivity. An improved bound on the convergence rate is also derived.
