Mary Dwyer Wolfe, Ph.D.

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Matrices

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

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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.

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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.

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Basic Definitions

• Examples of matrices

3 X 2 matrix
diagonal matrix
3 x 3 square matrix
Transpose of above matrix
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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

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Entering a Matrix into the TI84
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Addition and Subtraction
It is probably just easier to add or subtract by
hand.
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Multiplication

• Example

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Division
We can multiply these 2 matrices but not divide
them!
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Division
Not a size error, hum.
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Division
Let's try A x B-1 (like we do with real
numbers.)
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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
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Candy? What Candy? Do We Get to Eat It? Learning
Task
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Candy? What Candy? Do We Get to Eat It? Learning
Task
Matrix form
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Candy? What Candy? Do We Get to Eat It? Learning
Task
Matrix form
So, x -4, y 1, z 3
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Candy? What Candy? Do We Get to Eat It? Learning
Task
Comment UGH!!!!!!
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Candy? What Candy? Do We Get to Eat It? Learning
Task
The general form is y ax2 bx c
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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
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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.
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Candy Learning Activity
W X Y Z
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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.