4-1 Organizing Data
Into Matrices
Objectives : To identify matrices and their elements
To organize into matrices
Objectives
Identifying Matrices
Organizing Statistical Data
Vocabulary
A matrix is a rectangular array of numbers written
brackets.
3 Columns
Name of the Matrix
(represented with a capital letter)
2 Rows
2

6
3
7
4
 A
0
Dimensions - Matrix A is a 2 x 3 matrix
Writing the Dimensions of a
Matrix
Write the dimensions of each matrix.
a.
7 –4
12 9
The matrix has 2 rows and 2 columns and is
b.
0 6 15
The matrix has 1 row and 3 columns and is
therefore a 2  2 matrix.
therefore a 1  3 matrix.
Do Quick Check #1 (all) on Page 168
Vocabulary
Each number in a matrix is a matrix element. You can identify a matrix
element by its position within the matrix.
Use a lowercase letter with subscripts.
The subscripts represent the element’s row number and column number.
 a 11

a 21

A
 a 31

 a 41
a 12 

a 22

a 32 

a 42 
Identifying a Matrix Element
Identify each matrix element.
K =
3 –1 –8 5
1 8 4 9
8 –4 7 –5
a. k12
a. K =
b. k32
3 –1 –8 5
1 8 4 9
8 –4 7 –5
c. k23
b. K =
d. k34
3 –1 –8 5
1 8 4 9
8 –4 7 –5
k12 is the element in the first row
and second column.
k32 is the element in the third row
and second column.
Element k12 is –1.
Element k32 is –4.
Continued
(continued)
K =
3 –1 –8 5
1 8 4 9
8 –4 7 –5
a. k12
c. K =
b. k32
3 –1 –8 5
1 8 4 9
8 –4 7 –5
c. k23
d. K =
d. k34
3 –1 –8 5
1 8 4 9
8 –4 7 –5
k23 is the element in the second
row and third column.
k34 is the element in the third row
and the fourth column.
Element k23 is 4.
Element k34 is –5.
Do Quick Check #2 (all) on Page 169
Real World Example
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.
= Win
Ed
X = Loss
X
X
Jo
Lew
X
X
X X
X
Let each row represent the number of wins and losses and each
column represent a student.
Ed Jo Lew
Wins
Losses
5
2
6
1
3
4
Real World Example
Refer to the table.
a. Write a matrix N to represent
the information.
Use 2  3 matrix.
U.S. Passenger Car Imports
And Exports (millions)
1996
1998
2000
Imports
4.678
5.185
6.964
Exports
1.295
1.331
1.402
Source: U.S. Department of Commerce.
Each column represents a
different year.
N = Import
Exports
1996
1998
2000
4.678
1.295
5.185
1.331
6.964
1.402
Each row represents
imports and exports.
Continued
(continued)
b. Which element represents
exports for 2000?
U.S. Passenger Car Imports
And Exports (millions)
1996
1998
2000
Imports
4.678
5.185
6.964
Exports
1.295
1.331
1.402
Source: U.S. Department of Commerce.
Exports are in the second row.
The year 2000 is in the third column.
Element n23 represents the number of exports for 2000.