Monthly Archives: March 2013

Linear Algebra and Its Applications, Exercise 2.6.1

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

Posted in linear algebra | Leave a comment

Linear Algebra and Its Applications, Exercise 2.5.19

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

Posted in linear algebra | Leave a comment

Linear Algebra and Its Applications, Exercise 2.5.18

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

Posted in linear algebra | Leave a comment

Linear Algebra and Its Applications, Exercise 2.5.17

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

Posted in linear algebra | 2 Comments

Linear Algebra and Its Applications, Exercise 2.5.16

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

Posted in linear algebra | Leave a comment