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Operations with Matrices

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

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  1. Operations with Matrices Dan Teague NC School of Science and Mathematics teague@ncssm.edu

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

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

  4. Working with Units 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 http://courses.ncssm.edu/math/talks/conferences/

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

  6. Think about the Mathematical Practices http://courses.ncssm.edu/math/talks/conferences/

  7. Now, on to Matrices http://courses.ncssm.edu/math/talks/conferences/

  8. What is a Matrix? A matrix is a rectangular array of numbers. A matrix as a model is a rectangular array of numbers with meaning. http://courses.ncssm.edu/math/talks/conferences/

  9. The Summer Woodworking Project 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 http://courses.ncssm.edu/math/talks/conferences/

  10. Creating a Matrix 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. http://courses.ncssm.edu/math/talks/conferences/

  11. April and May Results Dimensions of the Matrices Interpretation of the Elements http://courses.ncssm.edu/math/talks/conferences/

  12. How many type II’s did your partner make in the 2 months? 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? http://courses.ncssm.edu/math/talks/conferences/

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

  14. Define this process as Addition Notice the order. We didn’t define addition then practice. We asked what made sense, and used that for our definition. http://courses.ncssm.edu/math/talks/conferences/

  15. How many of each type did the partners make during June? http://courses.ncssm.edu/math/talks/conferences/

  16. Now We Can Define Subtraction http://courses.ncssm.edu/math/talks/conferences/

  17. Next Spring you want to Doubled your April Output http://courses.ncssm.edu/math/talks/conferences/

  18. Types and Wood Interpret the elements in the Wood matrix. http://courses.ncssm.edu/math/talks/conferences/

  19. In April, how much Oak did You use? In April, how much Cherry did the Partner use? http://courses.ncssm.edu/math/talks/conferences/

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

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

  22. Define Matrix Multiplication Just like (ft/mile)∙(miles/hr) = ft/hr http://courses.ncssm.edu/math/talks/conferences/

  23. Cost Matrix 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? http://courses.ncssm.edu/math/talks/conferences/

  24. Cost Matrix Oak costs 2 cents/strip, Walnut costs 4 cents/strip, Cherry costs 5 cents/strip. http://courses.ncssm.edu/math/talks/conferences/ Just like (ft/mile)∙(miles/hr) = ft/hr

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

  26. 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/

  27. A 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?

  28. Transition Matrix http://courses.ncssm.edu/math/talks/conferences/

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

  30. From 1 to 2 and then from 2 to 4 Or From 1 to 3 and then from 3 to 4

  31. Can we create a transition matrix for the two-step probailities? http://courses.ncssm.edu/math/talks/conferences/

  32. After 3, 4, 5 and 6 Transitions

  33. After 8, 10, 12 and 100 Transitions

  34. Age Specific Growth http://courses.ncssm.edu/math/talks/conferences/

  35. Begin with [ 100 100 0 0 0 0 0 ] sheep. 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? http://courses.ncssm.edu/math/talks/conferences/

  36. Photo by John Haslam http://courses.ncssm.edu/math/talks/conferences/

  37. After one transition, how many sheep in each group? After two transitions? http://courses.ncssm.edu/math/talks/conferences/

  38. Matrix Multiplication http://courses.ncssm.edu/math/talks/conferences/

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

  40. Markov Chains http://courses.ncssm.edu/math/talks/conferences/

  41. Operations with Matrices Dan Teague NC School of Science and Mathematics teague@ncssm.edu

  42. What is the probability that a taxi from Downtown will be again in Downtown after three fares? http://courses.ncssm.edu/math/talks/conferences/

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

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

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