For the the graph G(V,E) shown above, find the following :

- The matrix giving the number of 3 step walks in G : [A
^{k}]_{ij}is the number of paths of length k from i to j. So, the answer is A^{3}.

- The generating function for walks from point i to j : The generating function is as follows. Here are more examples of generating functions.

- The generating function for walks from points 1 to 3 : Simplify the above formula using cramer's rule for i=1 and j=3.