CP Algebra 2 10/8/15
Multiplying Matrices
Name______________
Matrices can be used to organize data and allow for quick computation. You have performed several matrix
operations: addition, subtraction and multiplication by a scalar. Under certain conditions, it is possible to
multiply matrices.
1. Below is a matrix for the number of ink cartridges used by each of the three printers and a matrix for
the cost of each cartridge.
P1
P2
P3
C
B
 4
 6


 3
3
2
5
cost ($)

 C 74.75
 B 52.90




c. The dimensions of the 1st matrix are

and the dimensions 2nd matrix are
.
 matrices, describe how to calculate the combined cost of cartridges for each printer.
b. Given the
c. Determine the combined cost of cartridges for each printer. Write your answer in the form of a
matrix.
d. What do you notice about the “inner” dimensions? Is this necessary for the process of matrix
multiplication? Why?
e. The dimensions of the matrix in part c are
. How do the “outer” dimensions of 1st
nd
and 2 matrix compare to the dimensions of the matrix in part c?
f. Let’s generalize our findings. Two matrices can be multiplied under these circumstances:
If the dimensions of Matrix A are a m x n and the dimensions of Matrix B are p x r:
a. [A]•[B] exists if
.
b. The dimensions of the resulting matrix are
.
3. Three teams competed in the final round of the Chess Club’s championships. For each win, a team was
awarded 3 points and for each draw a team received 1 point. Which team won the tournament?
a. Write a matrix that represents the number of wins and draws. Write a second matrix that
represents the number of points.
b. Multiply the matrices to determine the winner.
4. Multiply if possible.
1 2 
A  

3 4 
a.
A•B
0 1 3 
B  

1 5 2
b.
B•A
6 5 


C  4 3

2 1 

c.
0 1
D  

2 1 
C•D
d. D•C

5.
Based on your work in problems 10, is matrix multiplication commutative? Why or why not?
6.
Find the product if
a.
A(B + C)
1 2 
1 0 
3 1 
A  
,
B

,
and
C


3 2 
1 0 .
2
1






b.
AB + AC

c.
Compare the results of parts a and b. Generalize your findings.