

Networks and Matrices
Presentation
•
Mathematics
•
12th Grade
•
Hard
+2
Standards-aligned
Ismael Galicia
Used 3+ times
FREE Resource
14 Slides • 7 Questions
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Networks and Matrices

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Students use matrices to represent and manipulate data from network diagrams.
Objective
3
Multiple Choice
simplify the radical
75325
35
53
75
4
Multiple Choice
simplify
24x324x
4x28x
2x6x
3x+2
5
Multiple Choice
simplify the radical
842
22
4
2
6
Poll
What do you think of when you hear the word network?
social network
computer network
television network
network with professionals and career field
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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
8
Multiple Choice
3 ways
4 ways
7 ways
5 ways
9
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.
10
Multiple Choice
two possible ways
Three possible ways
one possible way
four possible ways
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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.
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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.
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How many possible ways are there to travel from City 1 to City 4 without repeating a city?
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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.
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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.
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Networks and Matrices

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