1. Math III Warm Up9/4/13

4. What is the multiplicative identity of a 3x3 matrix? The additive identity?

5. A collection of points and line segments connecting some (possibly empty) subsets of the points Vertex Edge AB C D F

6. Goal: Use vertex-edge graphs to represent real-life situations Transportation:

7. Goal: Use vertex-edge graphs to represent real-life situations Example 1 An airline serves four cities: Bedford, Columbia, Dunwich, and Exton. There are flights between Bedford and Columbia, Bedford and Dunwich, and Columbia and Exton. Draw a simple undirected vertex-edge graph to represent this situation. STEP ONE: REPRESENT STEP TWO: DRAW

8. Goal: Use vertex-edge graphs to represent real-life situations Example 2 An airline serves five cities: Lowell, Montour, Atlanta, Orlando, and Peoria. There are flights between Lowell and Montour, Lowell and Orlando, Montour and Orlando, Atlanta and Orlando, and Atlanta and Peoria. Draw a simple undirected vertex-edge graph to represent this situation.

9. Goal: Use vertex-edge graphs to represent real-life situations

10. CONNECTION ALERT! Example 3 Use a MATRIX to represent the vertex edge graph from example 1.

11. By taking the square of the matrix, you can find out the number of 2 route possibilities between 2 cities.