ALGEBRA 2 LESSON 41

1
Section 4.1
2
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
(For help, go to Skills Handbook page 842.)
Use the table at the right.
1. How many cars were imported to the United
States in 1980? How many were imported in
1995? 2. How many more cars were imported in
1990 than in 1980? 3. How many more cars were
imported than exported in 1995? 4. Compare the
percent increase of imports from 1980 to 1995
with the percent increases of exports from 1980
to 1995.
4-1
3
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
1. 1980 Imports 3.116 million cars 1995
Imports 4.115 million cars 2. 1990 Imports
1980 Imports 3.945 million 3.116
million 0.829 million cars 3. 1995 Imports
1995 Exports 4.115 million 0.989
million 3.126 million cars 4. Percent
increase of imports from 1980 to 1995
32.1 percent increase
of exports from 1980 to 1995
60.3
Solutions
4-1
4
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
Write the dimensions of each matrix.
7 4 12 9
The matrix has 2 rows and 2 columns and is
therefore a 2 ? 2 matrix.
a.
The matrix has 1 row and 3 columns and is
therefore a 1 ? 3 matrix.
b.
0 6 15
4-1
5
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
Identify each matrix element.
3 1 8 5 1 8 4 9 8 4 7
5
K
a. k12
b. k32
c. k23
d. k34
Element k12 is 1.
Element k32 is 4.
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6
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
(continued)
3 1 8 5 1 8 4 9 8 4 7
5
K
a. k12
b. k32
c. k23
d. k34
Element k23 is 4.
Element k34 is 5.
4-1
7
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
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 X Loss
Let each row represent the number of wins and
losses and each column represent a student.
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8
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
Refer to the table.
U.S. Passenger Car Imports And Exports (millions)
1980 1990 1995 Imports 3.116 3.945 4.115 Expor
ts 0.617 0.794 0.989
a. Write a matrix N to represent the information.
Use 2 ? 3 matrix.
Source U.S. Department of Commerce.
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Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
(continued)
b. Which element represents exports for 1995?
Exports are in the second row.
The year 1995 is in the third column.
Element n23 represents the number of exports for
1995.
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10
Organizing Data Into Matrices
ALGEBRA 2 LESSON 4-1
8 4 0 1 9 3 5 0 1
2 6 1
3 ? 4
1. Write the dimensions of the matrix. M
2. Identify the elements m24, m32, and m13 of the
matrix M in question 1.
0, 2, 0
3. The table shows the amounts of the deposits
and withdrawals for the checking accounts of
four bank customers. Show the data in a 2 ? 4
matrix. Label the rows and columns.
4-1