Teaching Notes 3.22: Using Matrices—Addition, Subtraction,
and Scalar Multiplication
Many students find matrices confusing. Much of the confusion is a result of the specialized
vocabulary of matrices.- Explain that a matrix is a set of numbers arranged in rows and columns, usually enclosed in
brackets. Point out that a matrix is composed of rows and columns. A matrix is named by a
capital letter. - Explain that the number of rows and columns represent the dimensions of a matrix. For
example, a matrix with three rows and two columns is a 3×2 matrix. The number of rows
precedes the number of columns. - Explain that the numbers in a matrix are called the ‘‘elements,’’ or ‘‘entries,’’ of the matrix.
- Explain the steps for adding or subtracting matrices. Matrices must have the same dimen-
sions if they are to be added or subtracted. To add or subtract matrices, add or subtract cor-
responding elements to obtain a matrix of the same dimension. If matrices have different
dimensions, they cannot be added or subtracted. - Explain that to multiply a matrix by a number, which is called a ‘‘scalar,’’ students must mul-
tiply each element by the scalar. - Review the information and examples on the worksheet with your students. Remind them
that each element of a matrix is an integer. They must follow the rules for adding, sub-
tracting, and multiplying integers. They should be particularly careful when working with
negative numbers.
EXTRA HELP:
If two matrices have different dimensions, they cannot be added or subtracted, but every matrix,
regardless of its dimensions, can be multiplied by a scalar.ANSWER KEY:
(1)[
− 24
29
]
(2)
[
11
− 19
]
(3)
[
6 − 8
− 12 − 16
]
(4)
[
− 33
30
]
(5)Impossible(6)
⎡
⎣
39
− 924
−12 18
⎤
⎦ (7)
⎡
⎣
03
10 − 5
83
⎤
⎦ (8)Impossible------------------------------------------------------------------------------------------
(Challenge)Yes, provided they have the same dimensions.
------------------------------------------------------------------------------------------130 THE ALGEBRA TEACHER’S GUIDE