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# Operations with Matrices - PowerPoint PPT Presentation

Operations with Matrices. Dan Teague NC School of Science and Mathematics teague@ncssm.edu. Reasoning and Sense-Making. One key is to find a way of introducing new material that fits into the jigsaw puzzle created by what is already understood. Working with Units.

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### Operations with Matrices

Dan Teague

NC School of Science and Mathematics

teague@ncssm.edu

One key is to find a way of introducing new material that fits into the jigsaw puzzle created by what is already understood.

http://courses.ncssm.edu/math/talks/conferences/

If you are walking 2 miles per hour, how fast are you traveling in feet per hour?

We know there are 5,280 feet in a mile, so

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If you are walking 2 miles per hour, how fast are you traveling in miles per minute?

We know there are 60 minutes in an hour, so

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Think about the Mathematical Practices traveling in miles per minute?

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Now, on to Matrices traveling in miles per minute?

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What is a Matrix? traveling in miles per minute?

A matrix is a rectangular array of numbers.

A matrix as a model is

a rectangular array of

numbers with meaning.

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The Summer Woodworking Project traveling in miles per minute?

You and a Partner make 3 kinds of cutting boards:

Type I: alternating Oak and Walnut Strips

Type II: alternating Oak, Walnut, Cherry Strips

Type III: checkerboard pattern of Walnut and Cherry

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Creating a Matrix traveling in miles per minute?

During weekends in the month of April, you constructed 5 Type I, 8 Type II, and 3 Type III cutting boards. Your partner constructed 6 Type I, 4 Type II, and 10 Type III cutting boards.

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April and May Results traveling in miles per minute?

Dimensions of the Matrices

Interpretation of the Elements

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How many type II’s did your partner make in the 2 months? traveling in miles per minute?

How many type I’s did you make in the 2 months?

Can you create a matrix representing the work done by each person during the 2 months?

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http://courses.ncssm.edu/math/talks/conferences/ traveling in miles per minute?

Define this process as traveling in miles per minute?Addition

Notice the order. We didn’t define addition then practice. We asked what made sense, and used that for our definition.

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How many of each type did the partners make during June? traveling in miles per minute?

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Now We Can Define traveling in miles per minute?Subtraction

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Next Spring you want to Doubled your April Output traveling in miles per minute?

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Types and Wood traveling in miles per minute?

Interpret the elements in the Wood matrix.

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In April, how much Oak did You use? traveling in miles per minute?

In April, how much Cherry did the Partner use?

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http://courses.ncssm.edu/math/talks/conferences/ traveling in miles per minute?

http://courses.ncssm.edu/math/talks/conferences/ traveling in miles per minute?

Define Matrix Multiplication traveling in miles per minute?

Just like (ft/mile)∙(miles/hr) = ft/hr

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Cost Matrix traveling in miles per minute?

Each strip of Oak costs 2 cents.

Each strip of Walnut costs 4 cents.

Each strip of Cherry costs 5 cents.

What is the cost of the wood used by each person?

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Cost Matrix traveling in miles per minute?

Oak costs 2 cents/strip, Walnut costs 4 cents/strip, Cherry costs 5 cents/strip.

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Just like (ft/mile)∙(miles/hr) = ft/hr

http://courses.ncssm.edu/math/talks/conferences/ traveling in miles per minute?

One key is to find a way of introducing new material that fits into the jigsaw puzzle created by what is already understood.

http://courses.ncssm.edu/math/talks/conferences/

A fits into the jigsaw puzzle created by what is already understood.mouse is placed in the maze above. It is equally likely to pass through any open door. Each time it passes through a doorway is considered a transition.

What is the probability that the mouse will be in Room 4 after 2 transitions if it starts in Room 1?

Transition Matrix fits into the jigsaw puzzle created by what is already understood.

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What is the probability that the mouse will be in Room 4 after 2 transitions if it starts in Room 1?

From 1 to 2 after 2 transitions if it starts in Room 1?

and

then from 2 to 4

Or

From 1 to 3

and

then from 3 to 4

Can we create a transition matrix for the two-step probailities?

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Age Specific probailities?Growth

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Begin with [ 100 100 0 0 0 0 0 ] sheep. probailities?

How many sheep are in the [2, 4) age group in two years?

How many in the [6, 8) age

group in two years?

How many in the [0, 2) age

group?

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Photo by John Haslam probailities?

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After one transition, how many sheep in each group? probailities?

After two transitions?

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Matrix Multiplication probailities?

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Calculator probailities?

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Markov Chains probailities?

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### Operations with Matrices probailities?

Dan Teague

NC School of Science and Mathematics

teague@ncssm.edu

What is the probability that a taxi from Downtown will be again in Downtown after three fares?

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http://courses.ncssm.edu/math/talks/conferences/ again in Downtown after three fares?

http://courses.ncssm.edu/math/talks/conferences/ again in Downtown after three fares?