Math III Warm Up 9/4/13

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

•A collection of points and line segments connecting some (possibly empty) subsets of the points

Vertex

EdgeA B

C

D F

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

Transportation:

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

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.

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

CONNECTION ALERT!Example 3

Use a MATRIX to represent the vertex edge graph from example 1.

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