40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Matrices Lesson: MAT-4 Networks Networks Learning Outcome L-4 MAT-L4 Objectives: To rewrite network diagrams in matrix form and solve network problems using matrix operations.

40S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Matrices Lesson: MAT-4 Networks The diagram below shows the roads connecting five towns in Saskatchewan. You can drive from Carlyle to Oxbow directly, but you must drive through one other town when driving from Carlyle to Bienfait. The route from Carlyle to Bienfait is an indirect route. This network may be represented in table form. A '1' represents a direct connection, and a '0' represents no direct connection. Theory – Intro to Network Diagrams

40S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Matrices Lesson: MAT-4 Networks Test Yourself – Write a Network Matrix The network may also be represented in matrix form as matrix A. Note: The elements in the main diagonal are all zeros. This indicates that there are no roads connecting towns to themselves. Quiz question: Write the information represented in the network diagram in matrix form as matrix N. Write all matrix entries in alphabetical order.

40S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Matrices Lesson: MAT-4 Networks Matrix B is a communication network matrix that shows the connections between six computers in a classroom network. Draw a network diagram that illustrates the matrix. Theory – Network Diagrams Note: Normally we draw the sites in a communication network diagram in a circular fashion as shown in the first diagram, because it may be more convenient to draw the connecting lines or arrows.

40S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Matrices Lesson: MAT-4 Networks Quiz Question: Sketch a network diagram that illustrates communication network C. Test Yourself – Draw a Network Diagram

40S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Matrices Lesson: MAT-4 Networks The network diagram shows the bus routes between five Manitoba centres. The arrowheads indicate the directions that the busses travel. This network may be represented by matrix A where '1' represents a direct link and '0' indicates that a direct link does not exist. We can now write matrix B that shows all the connections between towns with exactly one stopover. Note: Boissevain is now connected to itself via Brandon in a Boissevain-Brandon- Boissevain link. Similarly, Boissevain is connected to Virden via Brandon. Theory – Intermediate Routes; One Stopover

40S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Matrices Lesson: MAT-4 Networks On the previous page, the direct routes for five centres was Matrix A and the route matrix between the centres using one intermediate stopover was Matrix B. Theory – Intermediate Routes; Multiple Stopovers A 2 is the same as matrix B. Therefore, matrix A 2 indicates the number of routes between centres when travelling through exactly one intermediate centre. Similarly, A 3 will show the number of routes between centres when traveling through exactly two intermediate centres.

40S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Matrices Lesson: MAT-4 Networks Six towns, M, A, T, R, I, and X, have a communications network as shown. Test Yourself – Intermediate Routes