The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 3.24: MULTIPLYING TWO MATRICES

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Follow the steps below to multiply two matrices:

1. Find the dimensions of the product matrix. The dimensions of the product matrix are
   the number of rows of the first matrix times the number of columns in the second
   matrix.


2. Find the product.
   
   
   • Multiply the elements in the first row of the first matrix by the elements in the first
     column of the second matrix and add. Place the element in the first row of the
     product matrix. Continue this process until the elements in the first row of the first
     matrix are multiplied by the elements in each column of the second matrix.
   
   
   • Multiply the elements in the second row of the first matrix by the elements in the
     first column of the second matrix and add. Place this element in the second row of
     the product matrix. Continue this process until the elements in the second row of
     the first matrix are multiplied by the elements in each column of the second matrix.
   
   
   • Continue until every row is multiplied by every column.
   
   
   
   

EXAMPLE

[

24

16

]

×

[

− 3 − 1

05

]

=

[

2 ×(−3)+ 4 × 02 ×(−1)+ 4 × 5

1 ×(−3)+ 6 × 01 ×(−1)+ 6 × 5

]

=

[

− 618

− 329

]

DIRECTIONS: Use the matrices below to find the product, if possible. If the matrices

cannot be multiplied, write ‘‘cannot be multiplied.’’

A=

[

1 − 1

25

]

B=

[

3

6

]

C=

[

12

0 − 4

]

D=

[

345

]

E=

⎡

⎢

⎣

26

84

31

⎤

⎥

⎦

1. A×B 2. A×C 3. C×A
   4. D×B 5. A×E 6. E×A

CHALLENGE:It is impossible to multiply the matrices in some of the

problems above. Select one of these problems and explain why the

matrices cannot be multiplied.

135

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.