College Algebra 9th txtbk

460 CHAPTER 7 SYSTEMS OF EQUATIONS AND MATRICES
ZZZ EXPLORE-DISCUSS 1
Multiplication of two numbers can be interpreted as repeated addition if one of the
numbers is a positive integer. That is,
2a a a 3a a a a 4a a a a a
and so on. How does this apply to multiplication of a matrix by a number?
Matrix operations have many applications, particularly in business.
EXAMPLE 5 Sales and Commissions
Ms. Fong and Mr. Petris are salespeople for a new car agency that sells only two models.
August was the last month for this year’s models, and next year’s models were introduced
in September. Gross dollar sales for each month are given in the following matrices:
AUGUST SALES
SEPTEMBER SALES
Compact Luxury Compact Luxury
Fong
Petris
$36,000 $72,000
c d A
$72,000 $0
$144,000 $288,000
c
$180,000 $216,000 d B
For example, Ms. Fong had $36,000 in compact sales in August and Mr. Petris had $216,000
in luxury car sales in September.
(A) What were the combined dollar sales in August and September for each salesperson
and each model?
(B) What was the increase in dollar sales from August to September?
(C) If both salespeople receive a 3% commission on gross dollar sales, compute the commission
for each salesperson for each model sold in September.
SOLUTIONS
We use matrix addition for part A, matrix subtraction for part B, and multiplication of a
matrix by a number for part C.
(A)
(B)
(C)
Compact
Compact
$4,320 $8,640
c
$5,400 $6,480 d
Luxury
$180,000 $360,000
A B c
$252,000 $216,000 d
$108,000 $216,000 d Fong
September sales August sales
Petris
Fong Sum of sales for August and September
Petris
$108,000 $216,000
B A c
Fong
Petris
Luxury
(0.03)($144,000) (0.03)($288,000)
0.03B c
(0.03)($180,000) (0.03)($216,000) d
3% of September sales
MATCHED PROBLEM 5
Repeat Example 5 with
$72,000 $72,000
$180,000 $216,000
A c d and B c
$36,000 $72,000 $144,000 $216,000 d