(a) Write down the incidence matrix A for the indicated digraph.

(b) What is the rank of .4?
(c) Determine the dimensions of its four fundamental subspaces.
(d) Find a basis for its kernel and cokemel.
(e) Determine explicit conditions on vectors b which guarantee that the system Ax = b has a solution.
(f) Write down a specific nonzero vector b that satisfies your conditions, and then find all possible solutions.