The document provides information about matrices including how to define them, add and subtract them, and examples of performing these operations. A matrix is defined as a rectangular array of numbers arranged in rows and columns, where the number of rows and columns determines its dimensions. The document also explains how to name specific elements within a matrix using row and column notation.

1. Bell Ringer Find the average of each set of numbers. - add up and divide by # of items 12, 15, 7, 21, 18, 19, 20 25, 29, 33, 28, 28, 27 89, 95, 86, 81, 97, 82, 80, 81, 93, 95, 97, 80

2. What is a Matrix? A matrix is a rectangular array of data entries (elements) displayed in rows and columns and enclosed in brackets. The number of rows and columns in the matrix determines its dimensions .

3. Defined as: Row X Column Rows go across Columns go up and down Example: [ ] 2 4 6 9 5 3 This is a 3 x 2 matrix Because you have 3 rows and 2 columns

4. You try! Name These Matrices! [ ] 4 5 6 2 3 4 [ [ ] ] -4 12 6 12 –3 8 4 3 4 8 8 4 4 6

5. [ ] 4 5 6 2 3 4 [ [ ] ] -4 12 6 12 –3 8 4 3 4 8 8 4 4 6 Naming the Position 1. a21 2. a33 3. a11

6. [ ] -2 9 1 4 7 0 [ [ ] ] 2 -1 6 0 4 6 1 -8 3 6 9 8 2 1 10 You try! 1. a13 2. a24 3. a21

7. ADDING MATRICES To add 2 or more matrices , must have the same frame . “ same number of rows and columns” If you don’t , then they can not be added.

8. Definitions “ corresponding entries” - add the two numbers that are in the exact same position in each matrix.

9. EXAMPLE #1 ] [ [ ] 5.3 7.4 + 8.5 9.1 [ ] = = [ ]

10. EXAMPLE #2 [ ] [ [ ] ] 2 7 3 5 9 4 + 5 6 4 2 3 2 = = [ ]

11. YOU TRY [ ] [ [ ] ] 3 7 5 4 6 1 1 1 + 5 6 2 4 1 1 3 6 = = [ ] __ by __ matrix

12. SUBTRACTION The same rules as addition apply. [ ] [ [ ] ] 5 8 3 6 - 5 1 4 = = [ ]

13. SUBTRACTION The same rules apply as for addition [ ] [ [ ] ] 8 4 7 9 - -2 3 5 -11 = = [ ]

14. YOU TRY [ ] [ [ ] ] - = = [ ] __ by __ matrix 5 -7 9 2 4 -6 8 -7 5 2 -3 5 6 -3 7 -5 9 1

15. Homework Matrices WS