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Matrices

Matrices. Mary Dwyer Wolfe, Ph.D. Macon State College MSP with Bibb County July 2010. Math III Standards. MM3A4. Students will perform basic operations with matrices. a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

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Matrices

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  1. Matrices Mary Dwyer Wolfe, Ph.D. Macon State College MSP with Bibb County July 2010

  2. Math III Standards • MM3A4. Students will perform basic operations with matrices. a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology. b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology. • MM3A5. Students will use matrices to formulate and solve problems. a. Represent a system of linear equations as a matrix equation. b. Solve matrix equations using inverse matrices. c. Represent and solve realistic problems using systems of linear equations.

  3. Basic Definitions • A matrix is an ordered set of numbers listed in a rectangular array with rows and columns. • A square matrix has an equal number of rows and columns. • A diagonal matrix has non-zero numbers on the diagonal of the rectangle going from upper left to lower right and all zeroes elsewhere. • The transpose of a matrix is a matrix with the where the columns consist of the rows of the original matrix.

  4. Basic Definitions • Examples of matrices 3 X 2 matrix diagonal matrix 3 x 3 square matrix Transpose of above matrix

  5. Addition and Subtraction • To add or subtract to matrices, the two matrices must be of the same size. • We just add or subtract the corresponding entries. • Example:

  6. Entering a Matrix into the TI84

  7. Addition and Subtraction It is probably just easier to add or subtract by hand.

  8. Multiplication • Example:

  9. Division We can multiply these 2 matrices but not divide them!

  10. Division Not a size error, hum.

  11. Division Let's try A x B-1 (like we do with real numbers.)

  12. Division A / B = A x B-1 Now lets proceed to a Learning Task. Candy? What Candy? Do We Get to Eat It? Learning Task

  13. Candy? What Candy? Do We Get to Eat It? Learning Task:

  14. Candy? What Candy? Do We Get to Eat It? Learning Task: Matrix form:

  15. Candy? What Candy? Do We Get to Eat It? Learning Task: Matrix form: So, x = -4, y = 1, z = 3

  16. Candy? What Candy? Do We Get to Eat It? Learning Task: Comment: UGH!!!!!!

  17. Candy? What Candy? Do We Get to Eat It? Learning Task: The general form is y = ax2 + bx + c

  18. Candy? What Candy? Do We Get to Eat It? Learning Task: (-3, 5), (1, 1), and (2, 10) are all on the parabola. The general form is y = ax2 + bx + c Substitution the x,y pairs, we get the following set of equations: 9a -3b + c = 5 a + b + c = 1 4a + 2b + c = 10 Solve this system! a = 2, b = 3, c = -4 So the equation is y = 2x2 + 3x - 4

  19. Candy? What Candy? Do We Get to Eat It? Learning Task Your bag tag: This bag contains Hersey's Milk Chocolate, Krackle and Mounds. This bag contains 2170 calories and 238 grams of sugar. The Nutrition Chart is on the next side.

  20. Candy Learning Activity W X Y Z

  21. Candy Learning Activity w + y + z = 9 270w + 210y + 230z = 2170 31w + 24y + 21z = 238 4 Milk Chocolate bars, 3 Krackle and 2 Mounds bars are in the bag.

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