guided practice - ABS Community Portal

REVIEW
PROPERTIES
For help with properties
of real numbers,
see p. 2.
E XAMPLE 3 Use matrix operations
Using
5F
the given matrices, evaluate the expression.
4 3
23 0
1 4
A 21 22 B 5F C 5F 1 22G,
23 21G
2 0G,
a. A(B 1 C) b. AB 1 AC
Solution
5F
4 3
23 0 1 4
a. A(B 1 C) 21 22
1
2 0GSF 22G 1F 23 21GD
5F
4 3
7
22 4
21 22
5F214
6 2
22
2 0GF 23G 8G 24
5F
4 3
23 0
b. AB 1 AC 21 22
1
2 0GF 22G 1F
4 3
1 4
21 22
23
2 0GF 21G
26
13
7
8G
5F29
1 4 5 22 6 2
26 0G1F25
2 8G5F214
24
MULTIPLICATION PROPERTIES Notice in Example 3 that A(B 1 C) 5 AB 1 AC,
which is true in general. This and other properties of matrix multiplication are
summarized below.
CONCEPT SUMMARY For Your Notebook
Properties of Matrix Multiplication
Let A, B, and C be matrices and let k be a scalar.
Associative Property of Matrix Multiplication A(BC) 5 (AB)C
Left Distributive Property A(B 1 C) 5 AB 1 AC
Right Distributive Property (A 1 B)C 5 AC 1 BC
Associative Property of Scalar Multiplication k(AB) 5 (kA)B 5 A(kB)
✓ GUIDED PRACTICE for Example 3
Using the given matrices, evaluate the expression.
2
3 2 24 5
A 5F21
23 0 B 5F C 5F 22 21G,
1 0G
4 1G,
4. A(B 2 C) 5. AB 2 AC 6. 2 1 } 2 ( AB)
3.6 Multiply Matrices 197