Ch. 4-1 Organizing Data into Matrices

• Matrix: a rectangular array of numbers written within brackets

The dimensions of a matrix is determined by the number of horizontal rows and vertical columns.

Write the dimensions of each matrix.

Organizing Data Into Matrices

a. 7 –412 9

The matrix has 2 rows and 2 columns and is therefore a 2 2 matrix.

b. The matrix has 1 row and 3 columns and is therefore a 1 3 matrix.

0 6 15

Check understanding

• P. 164 # 1 A, B and C

Matrix Element

• Each number in a matrix is a matrix element.

• An element is identified by its position in the matrix.

Identify each matrix element.

K =

Organizing Data Into Matrices

3 –1 –8 51 8 4 98 –4 7 –5

a. k12 b. k32 c. k23 d. k34

Element k12 is –1. Element k32 is –4.

a. K =

k12 is the element in the first row and second column.

3 –1 –8 51 8 4 98 –4 7 –5

b. K =

k32 is the element in the third row and second column.

3 –1 –8 51 8 4 98 –4 7 –5

(continued)

K =

Organizing Data Into Matrices

3 –1 –8 51 8 4 98 –4 7 –5

a. k12 b. k32 c. k23 d. k34

Element k23 is 4. Element k34 is –5.

c. K =

k23 is the element in the second row and third column.

3 –1 –8 51 8 4 98 –4 7 –5

d. K =

k34 is the element in the third row and the fourth column.

3 –1 –8 51 8 4 98 –4 7 –5

4-1

Check understanding

• P. 165 #2 A - D

Three students kept track of the games they won and

lost in a chess competition. They showed their results

in a chart. Write a 2 3 matrix to show the data.

Let each row represent the number of wins and losses and each column represent a student.

Organizing Data Into Matrices

= Win X = Loss

Ed X X

Jo X

Lew X X X X

Ed Jo Lew

5 6 3

2 1 4

Wins

Losses

Check understanding

• P. 165 # 3 A and B

Refer to the table.

a.Write a matrix N to represent the information.

Organizing Data Into MatricesU.S. Passenger Car Imports

And Exports (millions)

Source: U.S. Department of Commerce.Use 2 3 matrix.

3.116 3.945 4.1150.617 0.794 0.989

N = Import Exports

1980 1990 1995

Each column represents a different year.

Each row represents imports and exports.

  1980 1990 1995

Imports 3.116 3.945 4.115

Exports 0.617 0.794 0.989

(continued)

b. Which element represents exports for 1995?

Organizing Data Into MatricesU.S. Passenger Car Imports

And Exports (millions)

Source: U.S. Department of Commerce.

Exports are in the second row.

The year 1995 is in the third column.

Element n23 represents the number of exports for 1995.

  1980 1990 1995

Imports 3.116 3.945 4.115

Exports 0.617 0.794 0.989

Check understanding 4

• P. 166 # 4 A and B.

Homework

• P. 166 # 1 – 25 eoo