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TEKS
3.5
a.1, a.2
Key Vocabulary
• matrix
• dimensions
• elements
• equal matrices
• scalar
• scalar
multiplication
Perform Basic
Matrix Operations
Before You performed operations with real numbers.
AVOID ERRORS
Be sure to verify that
the dimensions of two
matrices are equal
before adding or
subtracting them.
Now You will perform operations with matrices.
Why? So you can organize sports data, as in Ex. 34.
A matrix is a rectangular arrangement of numbers in rows and columns. For
example, matrix A below has two rows and three columns. The dimensions
of a matrix with m rows and n columns are m 3 n (read “m by n”). So, the
dimensions of matrix A are 2 3 3. The numbers in a matrix are its elements.
4 21 5
A 5F 0 6 3G
3 columns
2 rows
Two matrices are equal if their dimensions are the same and the elements in
corresponding positions are equal.
KEY CONCEPT For Your Notebook
Adding and Subtracting Matrices
The element in the first row
and third column is 5.
To add or subtract two matrices, simply add or subtract elements in
corresponding positions. You can add or subtract matrices only if they
have the same dimensions.
Adding a b e f a 1 e b1f Matrices F c dG1F g hG5Fc1 g d1hG Subtracting a b e f a 2 e b2f Matrices F c dG2F g hG5Fc2 g d2hG E XAMPLE 1 Add and subtract matrices
Perform the indicated operation, if possible.
3 0 21 4 3 1 (21) 0 1 4 2 4
a. F 25 21G1F 2 0G 5F 25 1 2 21 1 0G 5F 23 21G
F
7
b. 0
21 6G
4
22 2F22
3
23 1G 5F
5 72 (22)
210
0 2 3
21 2 (23)
4 2 5
1G 5F
9 21
5G
22 2 (210) 23 8
6 2 2
3.5 Perform Basic Matrix Operations 187