Networks and Matrices

Networks and Matrices

Students use matrices to represent and manipulate data from network diagrams.

Objective

Multiple Choice

simplify the radical

 $\sqrt{75}$  

•  $3\sqrt{25}$  

•  $3\sqrt{5}$  

•  $5\sqrt{3}$  

•  $75$  

Multiple Choice

simplify

 $\sqrt{24x^3}$  

•  $24x$  

•  $4x^2\sqrt{8x}$  

•  $2x\sqrt{6x}$  

•  $3x+2$  

Multiple Choice

simplify the radical

 $\sqrt{8}$  

•  $4\sqrt{2}$  

•  $2\sqrt{2}$  

•  $4$  

•  $\sqrt{2}$  

Poll

 What do you think of when you hear the word network?

• social network

• computer network

• television network

• network with professionals and career field

For our purposes, a network is a system of interrelated objects (such as people

or places) that we can represent using a network diagram, as shown below

Networks

Multiple Choice

• 3 ways

• 4 ways

• 7 ways

• 5 ways

There are three ways to travel from City 1 to City 4.

According to the arrows, you can travel from City 1 to City 2 to City 4, from City 1 to City 3 to City 4, or from City 1 to City 3 to City 2 to City 4.

Multiple Choice

• two possible ways

• Three possible ways

• one possible way

• four possible ways

There is only one reasonable way. You must go from City 4 to City 2 to City 3 to City 1. The arrows indicate that there is only one route to City 1, which comes from City 3. However, it is possible to travel from City 4 to City 2 to City 3 as many times as desired before traveling from City 4 to City 2 to City 1.

Multiple Choice

How many ways can you travel from City 1 to City 4 if you want to stop in City 2 and make no other stops?

• There are three bus routes from City 1 to City 2 and two bus routes from City 2 to City 4, so there are 𝟔 possible ways to travel from City 1 to City 4.

• There are two bus routes from City 1 to City 2 and two seven routes from City 2 to City 4, so there are 14 possible ways to travel from City 1 to City 4.

• There are four bus routes from City 1 to City 2 and three bus routes from City 2 to City 4, so there are 12 possible ways to travel from City 1 to City 4.

How many possible ways are there to travel from City 1 to City 4 without repeating a city?

City 1 to City 4 with no stops: no routes

City 1 to City 4 with a stop in City 2: 𝟔 routes

City 1 to City 4 with a stop in City 3: 𝟏 route

City 1 to City 4 via City 3 then City 2: 𝟐 routes

City 1 to City 4 via City 2 then City 3: 𝟔 routes

Total ways: 𝟎 + 𝟔 + 𝟏 +𝟐 + 𝟔 = 𝟏5 possible ways to travel from City 1 to City 4 without visiting a city more than once.

As a transportation network grows, these diagrams become more complicated, and keeping track of all of the information can be challenging. People that work with complicated networks use computers to manage and manipulate this information.