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

3. The number of rows is always reported before the number of columns.The number of rows is always reported before the number of columns. Rows go acrossRows go across Columns go up and downColumns go up and down Example:Example: [ ] 2 4 6 9 5 3 This is a 3 x 2 matrix Because you have 3 rows and 2 columns

4. Name These Matrices! [] 4 5 6 2 3 4 [ [ ] ] 16 -4 12 6 12 –3 8 4 3 4 8 8 2 4 4 6

5. Name These Matrices! [] 4 5 6 2 3 4 [ [ ] ] 16 -4 12 6 12 –3 8 4 3 4 8 8 2 4 4 6 2 x 3 matrix 2 x 3 matrix 3 x 4 3 x 4matrix 2 x 2 2 x 2matrix

6. Organizing Data into Matrices The table shows scores from the 2000 Olympics in Sydney, Australia. U.S. Women’s Olympic Gymnastics Team Qualification Scores GymnastFloor Exercise VaultBalance Beam Uneven Bars Amy Chow9.5259.4689.6259.400 Dominique Dawes 9.0879.3938.6009.675 Kristin Maloney 9.5259.2259.3129.575 Elise Ray9.2259.4689.687

7. Organizing Data into Matrices Write a matrix W to represent the information in the table. Use a 4x4 matrix. Which element represents Kristin Maloney’s score on the vault?

8. Organizing Data into Matrices Technology in Public Schools (millions) Type of School Videodisc Players ModemsNetworksCD-ROMs Elementary25.935.126.437.9 Junior High9.211.09.011.0 Senior High10.714.512.914.0 Write a matrix H to represent the data in the table. Find element h 23. What does this element represent?

9. ADDING MATRICES same dimensionsTo add 2 or more matrices, we must be sure that we have the same dimensions. same number of rows and columns.That is, the same number of rows and columns. If you don’t cannotIf you don’t have the same dimensions, then the question cannot be added.

10. ADDING MATRICES exact same positionWhen adding, you add the 2 numbers that are in the exact same position in each matrix. “corresponding entries”These two numbers are called “corresponding entries”

11. EXAMPLE [ ][[ ] ] 5.37.4 + 8.59.1 = 5.3 + 8.5 (5.3 + 8.5) 7.4 + 9.1 (7.4 + 9.1) = [ ] 13.816.5 2 by 1 matrix

12. EXAMPLE #2 [ ][[ ] ] 2 7 3 5 9 4 + 5 6 4 2 3 2 = 2+5) (7+6) (3+4) (2+5) (7+6) (3+4) (5+2) (9+3) (4+2) = [ ] 7 13 7 7 12 6 2 by 3 matrix

13. YOU TRY [ ][[ ] ] 3 7 5 24 6 1 1 1 + 5 6 2 64 1 1 3 6 = = [ ] __ by __ matrix

14. SOLUTION [ ][[ ] ] 3 7 5 2 4 6 1 1 1 + 5 6 2 6 4 1 1 3 6 = = [ ] 3 by 3 matrix 3+5) (7+6) (5+2) (3+5) (7+6) (5+2) (2+6) (4+4) (6+1) (1+1) (1+3) (1+6) 8 13 7 8 8 7 2 4 7

15. SUBTRACTION SUBTRACTION The same rules apply as for addition [ ][[ ] ] 5 8 3 6 - 25 1 4 = = [ ] 2 by 2 matrix (5-2) (8-5) (3-1) (6-4) 33 2 2

16. SUBTRACTION SUBTRACTION The same rules apply as for addition [ ][[ ] ] 8 4 7 9 - -2 3 5 -11 = = [ ] 2 by 2 matrix (8-(-2)) (4-3) (7-5) (9-(-11)) 10 1 2 20

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

18. SOLUTION [ ][[ ] ] - = = [ ] 3 by 3 matrix 5 -7 9 2 4 -6 8 -7 5 2 -3 5 6 -3 7 -5 9 1 5-2) (-7-(-3)) (9-5) (5-2) (-7-(-3)) (9-5) (2-6) (4-(-3)) (-6-7) (8- (-5)) (-7-9) (5-1) 3 -4 4 -4 7 -13 13 -16 4