Warm-UpWrite an equation for the following information.

1. I bought sandwiches at $3.99 a piece and drinks at $1.99 a piece. I spent a total of $21.93.

2. At the school store, I bought notebooks for $2 and pencils for $.50 each. I received $8 change from a $20 bill.

3.99 x + 1.99 y = 21.93

2x + .5y = 12

Matrices Learning Task

Brookwood High School

Booster Club

Situation

• In order to raise money for the school, the Brookwood High School Booster Club offered spirit items prepared by members for sale at the school store and at games.

• They sold stuffed teddy bears dressed in school colors, tote bags and tee shirts with specially sewn and decorated school insignias.

• The teddy bears, tote bags, and tee shirts were purchased from wholesale suppliers and decorations were cut, sewn and painted, and attached to the items by booster club parents.

Cost

• The wholesale cost for each teddy bear was $4.00, each tote bag was $3.50 and each tee shirt was $3.25.

• Materials for the decorations cost $1.25 for the bears, $0.90 for the tote bags and $1.05 for the tee shirts.

Time

• Parents estimated the time necessary to complete a bear was 15 minutes to cut out the clothes, 20 minutes to sew the outfits, and 5 minutes to dress the bears.

• A tote bag required 10 minutes to cut the materials, 15 minutes to sew and 10 minutes to glue the designs on the bag.

• Tee shirts were made using computer generated transfer designs for each sport which took 5 minutes to print out, 6 minutes to iron on the shirts, and 20 minutes to paint on extra detailing.

The following is a__________, a rectangular array of values, showing the wholesale cost of each item as well as the cost of decorations. “Wholesale" and "decorations" are labels for the matrix ________ and "bears", "totes", and "shirts" are labels for the matrix ___________. The dimensions of this matrix called A are 2 rows and 3 columns and matrix A is referred to as a [_________] matrix. Each number in the matrix is called an ________.

Wholesale

DecorationsA =

bears totes shirts

matrix

rows

columns

2 x 3entry

4.00 3.50 3.25

1.25 .90 1.05

It is sometimes convenient to write matrices (plural of matrix) in a simplified format without labels for the rows and columns. Matrix A can be written as an___________.

A =4.00 3.50 3.25

1.25 .90 1.05

array

A =a11 a12 a13

a21 a22 a23

In this system, the entry a22 = _______, is the cost of decorations for tote bags.

.90

11 12 13 14

21 22 23 24

31 32 33 34

mn mn mn mn

a a a a

a a a a

a a a a

a a a a

Row 1

Row 2

Row 3

Row m

Column 1 Column 2 Column 3 Column 4

A=

A matrix of m rows and n columns is called a matrix with dimensions m x n.

That’s Row x Column

And a…

2 3 41.) 1

12

3 8 9

2.) 2 5

6 7 8

103.)

7

4.) 3 4

2 X 3 3 X 3

2 X 11 X 2

3 5

11.) 4

40

3 02.)

0 3

1 2 3

3.) 0 1 8

0 0 1

4.) 2

55.)

6.) 3

3 X 2 2 X 2 3 X 3

1 X 2 2 X 1 1 X 1

11

21

31

7

4

1

a

A a

a

21... 4So a

b34 = –7

b42 = – 5

b54 = 3

e32 = –2

g21 = –3

d21 = Does not exist

7 in X x21

0 in U u11

-5 in P p12

Amount of Time• Parents estimated the time necessary to complete a bear

was 15 minutes to cut out the clothes, 20 minutes to sew the outfits, and 5 minutes to dress the bears. A tote bag required 10 minutes to cut the materials, 15 minutes to sew and 10 minutes to glue the designs on the bag. Tee shirts were made using computer generated transfer designs for each sport which took 5 minutes to print out, 6 minutes to iron on the shirts, and 20 minutes to paint on extra detailing.

Cut/print

Sew/iron

Attach/dress/paint

B =

bears totes shirts

15 10 5

20 15 6

5 10 20

Number Produced

• The booster club parents made spirit items at three different work meetings and produced 30 bears, 30 tote bags, and 45 tee shirts at the first session. Fifteen bears, 25 tote bags, and 30 tee shirts were made during the second meeting; and, 30 bears, 35 tote bags and 75 tee shirts were made at the third session.

1st session

2nd session

3rd session

C =

bears totes shirts

30 30 45

15 25 30

30 35 75

Items Sold

• In the first month of school, 10 bears, 15 tote bags, and 50 tee shirts were sold at the bookstore. During the same time period, Booster Club members sold 50 bears, 20 tote bags, and 100 tee shirts at the games.

Bookstore

GameD =

bears totes shirts

10 15 50

50 20 100

Sale Price

• They sold the bears for $12.00 each, the tote bags for $10.00 each and the tee shirts for $10.00 each.

Sale PriceE =

bears totes shirts

12 10 10