2. What is a Matrices? 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. ADDING MATRICES same frameTo add 2 or more matrices, we must be sure that we have the same frame. same number of rows and columns.That is, the same number of rows and columns. If you don’t can notIf you don’t have the same dimensions, then the question can not be added.

7. 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”

8. 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

9. 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

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

11. 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

12. 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

13. 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

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

15. 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

16. CLASS WORK Do Lesson 31 worksheet