Transcript of Essential Question: How do we use matrices to solve problems? How do we relate matrices to...
- Slide 1
- Essential Question: How do we use matrices to solve problems?
How do we relate matrices to vertex-edge graphs? Standards: MM3A7:
Students will understand and apply matrix representations of
vertex-edge graphs. MM3A7a: Use graphs to represent realistic
situations. MM3A7b: Use matrices to represent graphs, and solve
problems that can be represented by graphs.
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- Math 3 Activating Strategy Vertex-Edge Graph Adjacency Matrix A
B C D E F G A B D C E F G ABCDEFGABCDEFG
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- Math 3 Activating Strategy Vertex-Edge Graph Adjacency Matrix A
B C D E F G A B D C E F G ABCDEFGABCDEFG 0 1 1 1 0 1
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- AN OKEFENOKEE FOOD WEB Learning Task Recent weather conditions
have caused a dramatic increase in the insect population of the
Okefenokee Swamp area. The insects are annoying to people and
animals and health officials are concerned there will be an
increase in disease. Local authorities want to use an insecticide
that would literally wipe out the entire insect population of the
area. You, as an employee of the Environmental Protection Agency
(EPA), must determine how detrimental this would be to the
environment. Specifically, you are concerned about the effects on
the food web of six animals known to populate the swamp.
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- Consider the following directed vertex-edge graph (digraph) of
a food web for the six animals and the insects that are causing the
problem. Here each vertex represents an animal or insects. The
direction of the edges indicates whether an animal preys on the
linked animal. For example, raccoons eat fish. (Note: The food web
shown is simplified. Initial producers of nutrients, plants, have
not been included.)
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- Adjacency matrices can be used in conjunction with digraphs. If
we consider just the relationships between raccoons, fish, and
frogs in the food web shown, an adjacency matrix would be
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- 1.Construct the associated matrix F to represent this web. B M
I C FT M F R B M I C FT F R B M I C FT F R
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- 1.Construct the associated matrix F to represent this web. What
does a row containing a single one indicate? What does a column of
zeros indicate?
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- 2. Which animals have the most direct sources of food? How can
this be determined from the matrix? Find the number of direct food
sources for each animal.
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- 3. The insect column has the most ones. What does this suggest
about the food web?
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- More Practice with Vertex-Edge Graphs Worksheet To save paper,
an office administrator is trying to deliver messages through oral
communication between coworkers. The administrator tells one
employee the message; the administrator then considers the message
to be deliverable to every worker who has direct contact (talking
directly to the designated employee) or second-hand contact
(talking to someone who had direct contact with the designated
employee). The vertex-edge graph below summarizes the direct
contacts made between the six employees supervised by the
administrator. Complete the adjacency matrix below to summarize the
direct contacts made between the six employees. Ann Ann Bob Caf Dan
Eve Fin Ann Bob Caf Bob Caf Dan Eve Dan Fin Eve Fin
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- Ann Ann Bob Caf Dan Eve Fin Ann Bob Caf Bob Caf Dan Eve Dan Fin
Eve Fin Administrator tells:Who gets the message?Who doesnt get the
message? Ann Bob Caf Dan Eve Fin Complete the table below to show
which employees will and will not get the message if the
administrator tells the employee in the first column.