Bell RingerBell Ringer

Find the Find the averageaverage of each set of numbers. of each set of numbers. - add up and divide by # of items- add up and divide by # of items

4.4. 12, 15, 7, 21, 18, 19, 2012, 15, 7, 21, 18, 19, 20

6.6. 25, 29, 33, 28, 28, 2725, 29, 33, 28, 28, 27

8.8. 89, 95, 86, 81, 97, 82, 80, 81, 93, 95, 97, 8089, 95, 86, 81, 97, 82, 80, 81, 93, 95, 97, 80

What is a Matrix?What is a Matrix?

A A matrixmatrix is a rectangular array of data is a rectangular array of data entries (elements) displayed in entries (elements) displayed in rowsrows and and columnscolumns and enclosed in brackets. and enclosed in brackets.

The number of rows and columns in the The number of rows and columns in the matrix determines its dimensionsmatrix determines its dimensions..

Defined as:Defined as:Row X ColumnRow X Column

RowsRows go across go across ColumnsColumns go up and down go up and down

Example:Example:

[ ]2 4

6 9

5 3

This is a 3 x 2 matrixThis is a 3 x 2 matrix

Because you haveBecause you have

3 rows and 2 columns3 rows and 2 columns

You try!You try!Name These Matrices!Name These Matrices!

[ ]4 5 6

2 3 4 [ [] ]1 -4 12 6

12 –3 8 4

3 4 8 8

1 4

4 6

[ ]4 5 6

2 3 4 [ [] ]1 -4 12 6

12 –3 8 4

3 4 8 8

1 4

4 6

Naming the Position

1. a21 2. a33 3. a11

[ ]-2 9 1

4 7 0 [ [] ]2 -1 6 0

4 6 1 -8

3 6 9 8

1 2

1 10

You try!

1. a13 2. a24 3. a21

ADDING MATRICESADDING 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.

DefinitionsDefinitions

““corresponding entries”corresponding entries” --add the two numbers that are in the add the two numbers that are in the

exact same positionexact same position in each matrix. in each matrix.

EXAMPLE #1EXAMPLE #1

][[ ]5.35.3

7.47.4+ 8.58.5

9.19.1

[ ]= = [ ]

EXAMPLE #2EXAMPLE #2

[][[

]]2 2 77 33

5 5 99 44+ 5 5 66 44

2 2 33 22

= = [ ]

YOU TRYYOU TRY

[][[

]]3 7 53 7 5

22 4 64 6

1 1 11 1 1

+5 6 25 6 2

22 4 14 1

1 3 61 3 6

= =[ ]

__ by ____ by __

matrixmatrix

SUBTRACTIONSUBTRACTIONThe same rules as addition apply.The same rules as addition apply.

[][[

]]5 85 8

3 63 6-

11 55

1 41 4

= = [ ]

SUBTRACTIONSUBTRACTIONThe same rules apply as for additionThe same rules apply as for addition

[][[

]]8 48 4

7 97 9-

-2 3-2 3

5 -115 -11

= = [ ]

YOU TRYYOU TRY

[][[

]] -

= =[ ]

__ by ____ by __

matrixmatrix

5 -7 95 -7 9

2 4 -62 4 -6

8 -7 58 -7 5

2 -3 52 -3 5

6 -3 76 -3 7

-5 9 1-5 9 1

HomeworkHomework

Matrices WSMatrices WS