Teaching Notes 3.24: Multiplying Two Matrices
Many students find multiplying two matrices to be a complicated process. Although the basic
procedure is relatively simple, students are often uncertain of where to place each element in the
product matrix.- Explain that only some matrices can be multiplied. Emphasize that in order to multiply two
matrices, the number of columns in the first matrix must equal the number of rows in the
second matrix. Only after students have determined that two matrices can be multiplied can
they move ahead and multiply them. You might find it helpful to review 3.23: ‘‘Identifying
Conditions for Multiplying Two Matrices’’ with your students. Also review, if necessary, how
students can find the dimensions of the product matrix. - Review the information and example on the worksheet with your students. Be sure that stu-
dents understand the precise steps for the multiplication of matrices. Caution them to pay
especially close attention to the order for multiplying the elements. Also remind them to pay
close attention to integers with negative signs.
EXTRA HELP:
Check the dimensions of the product matrix to be sure your elements are placed correctly.ANSWER KEY:
(1)[
− 3
36
]
(2)
[
16
2 − 16
]
(3)
[
59
− 8 − 20
]
(4)Cannot be multiplied(5)Cannot be multiplied (6)⎡
⎣
14 28
16 12
52
⎤
⎦
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(Challenge)Answers will vary. The matrices in numbers 4 and 5 cannot be multiplied. Students
should explain that the number of columns in the first matrix differs from the number of rows in
the second matrix.
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