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

Name Date

WORKSHEET 3.23: IDENTIFYING CONDITIONS

FOR MULTIPLYING TWO MATRICES

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To multiply two matrices, the number of columns in the first matrix must be the same as the

number of rows in the second matrix. (If this is not true, the matrices cannot be multiplied.)

The product of two matrices is a matrix that has the same number of rows as the first matrix

and the same number of columns as the second matrix. This is summarized by the formula:

Am×n×Bn×q=Pm×q.Pis a matrix that represents the product ofA×B.Phasmrows andq

columns.

EXAMPLE

Determine ifP, the product ofA×B, can be found. If it can, find the dimensions ofP.

A 2 × 3 ×B 3 × 1 =P 2 × 1 MatrixAhas three columns, which is the same as the number of

rows of MatrixB, therefore the product can be found. The dimensions ofPare 2 × 1.

DIRECTIONS: Use the matrices below to determine if the product of the matrices in each

problem can be found. If the product can be found, find the dimensions of the product. If the

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

L=

[

34

− 16

]

M=

[

− 34

25

]

C=

[

1

2

]

D=

⎡

⎢

⎣

314

6 − 15

−10 4

⎤

⎥

⎦

1. L×M 2. M×L 3. M×C
   4. C×M 5. C×D 6. L×C

CHALLENGE:Samantha said that if a matrix has the same number of rows

and columns, it can be multiplied by any other matrix that has an identical

number of rows and columns. Do you agree with her? Explain your

reasoning.

133

Copyright

©

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