Monthly Archives: March 2013

Exercise 2.6.1. Specify the 2 by 2 matrix that has the following effects: Rotating all vectors 90 degrees. Projecting the resulting vectors onto the axis. Answer: From the discussion in the first part of section 2.6 we know that the … Continue reading →

Exercise 2.5.19. Verify that Euler’s formula (nodes – edges + loops = 1) is valid for a square mesh with 10 nodes on each side. Answer: If the mesh has 10 nodes on each side there are 10 times 10 … Continue reading →

Exercise 2.5.18. Consider a directed graph of nodes, where every node has a edge connecting it to every other node. How many edges are in this complete graph? Answer: Each of the nodes has a connection to the other nodes. … Continue reading →

Exercise 2.5.17. In the scheme described in section 2.5 for ranking football teams, is strength of opposition accounted for, or must it be considered separately? Answer: The ranking system described calculates potential values for each team based on score differences … Continue reading →

Exercise 2.5.16. Suppose we have a directed graph with four nodes and five edges as follows: edge 1 from node 1 to node 2 edge 2 from node 2 to node 3 edge 3 from node 1 to node 3 … Continue reading →