MATH 166 Spring 2016
5.2
c
Wen
Liu
5.2 Matrix Multiplication
Definition:
• A matrix of order 1 × n (1 row and n columns) is called a row matrix or a row matrix of
dimension n.
• A matrix of order m × 1 (m rows and 1 column) is called a column matrix or a column matrix
of dimension m.
Order of AB: Given the two matrices A = (aij )m×p and B = (bij )p×n , the product matrix AB has
order m × n.
Technology Corner: The matrix operations can be carried out by MATRIX command.
Examples:
1. Compute the indicated product.

−9 1 5
5
10
 8 5 
10 4 9
4 1

2. Find the values of the variables.
x 2 1
0 y 3


1 1
 3 z = 6 0
6 4
4 2
3. Matrix A is order 8 × 6 and matrix B is order 2 × 8. Find the order of AB and BA, if they
exist. (If an answer does not exist, enter DNE.)
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MATH 166 Spring 2016
5.2
c
Wen
Liu
4. Matrix A shows the number of servings of each food that each person eats per day. Matrix B
shows the number of units of each nutrient in a serving of each food.
(a) Find the product matrix AB and label the rows and columns.
(b) What does the product matrix AB represent?
i. The total amount of each nutrient for each food.
ii. The total daily amount of each food each person eats.
iii. The total amount of each food each person has daily.
iv. The total daily amount of each nutrient for each person.
v. The product is meaningless.
5. Three network consultants, Alan, Maria, and Steven, each received a year-end bonus of $10000,
which they decided to invest in a 401(k) retirement plan sponsored by their employer. Under
this plan, employees are allowed to place their investments in three funds: an equity index fund
(I), a growth fund (II), and a global equity fund (III). The allocations of the investments (in
dollars) of the three employees at the beginning of the year are summarized in the matrix A.
The returns of the three funds after 1 yr are given in the matrix B. Which employee realized
the best return on his or her investment for the year in question? Which employee realized the
worst return on his or her investment for the year in question?
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MATH 166 Spring 2016
5.2
c
Wen
Liu
6. The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for
one feature at the Center is $4 for children, $6 for students, and $8 for adults. The attendance
for the Sunday matinee is given by the matrix
(a) Write a column vector B representing the admission prices.
(b) Compute AB, the column vector showing the gross receipts for each theater.
(c) Find the total revenue collected at the Cinema Center for admission that Sunday afternoon.
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