Project 2, 20 points Math 314H, Spring 2000 Due: 3/10 Problem Description: Refer to Example 3.5 and Section 3 for background. As a social scientist you have studied the influence factors that relate seven coalition groups which, for simplicity, we will simply label $1,2,3,4,5,6,7.$ Based on an empirical studies, you conclude that the influence factors can be well modeled by a dominance directed graph with each group as a vertex. The meaning of the presence of an edge $(i,j)$ in the graph is that coalition group $i$ can dominate, i.e., swing coalition group $j$ its way on a given political issue. The data you have gathered suggests that the appropriate edge set is the following: E = {(1,2),(1,3),(1,4),(1,7),(2,4),(2,6),(3,2),(3,5),(3,6), (4,5),(4,7),(5,1),(5,6),(5,7), (6,4),(6,5),(6,1),(7,2),(7,6)} Determine the power rating of each coalition group. Now suppose you were an advisor to one of these coalition groups and, by deal making and currying certain favors, this group could gain influence over another coalition group (thereby either adding an edge to the graph or reversing an existing edge of the graph.) In each case, if you could pick the best group for your client to influence, which would that be? Explain your results in the context of matrix multiplication if you can. Methodology: You should use Maple commands to build a notebook that takes the list or array of edges as input and computes the desired results. Try to mechanize the entire process. This will likely involve "for" loops in Maple. See the LinAlgMaple5.ms notebook for an example. It might also involve if..then..else statements. See the Maple Help for details on how to do this. Output: Return your results in the form of an annotated Maple notebook, which should have the name of the team members at the top of the file and an explanation of your solution in text cells interspersed between input cells, that the user can happily click his/her way through. This explanation should be intelligible to your fellow students, which should constitute your target audience.