College Algebra 9th txtbk

466 CHAPTER 7 SYSTEMS OF EQUATIONS AND MATRICES
ZZZ CAUTION ZZZ
Example 9 and Matched Problem 9 illustrate an important point about matrix multiplication.
Even if you are using a graphing calculator to perform the calculations in
a matrix product, you will still need to know the definition of matrix multiplication
so that you can interpret the results correctly.
ANSWERS TO MATCHED PROBLEMS
1 5
1. (A) £ 0 2 § (B) Not defined 2. [1 1 4] 3. a 6, b 7, c 9, d 1
2 1
4.
13
£ $252,000 $288,000 $108,000 $144,000 $5,400 $6,480
2 § 5. (A) c (B) c (C) c
$180,000 $288,000 d $108,000 $144,000 d $4,320 $6,480 d
35
6. [8] 7. [6 1.5] c 10 or $72
8 d [72]
2 2 1 2
8. (A) Not defined (B) £ 1 6 12 4 § (C) c 0 0 (D) c 6 12
0 0 d
3 6 d
1 0 3 2
9. Assembly Finishing
PL [14,000 3,500] Labor hours
7-3 Exercises
1. What conditions must matrics A and B satisfy so that A B
exists?
2. What conditions must matrices A and B satisfy so that AB
exists?
3. What conditions must matrices A and B satisfy so that BA
exists?
4. What conditions must matrices A and B satisfy so that both AB
and BA exist?
5. What is the negative of a matrix?
6. How do you subtract two matrices?
7. How do you multiply a matrix by a number?
8. If A is a 1 n matrix and B is an n 1 matrix, how do you find
the product AB? What is the size of AB?
9. If A is a 1 n matrix and B is an n 1 matrix, how do you find
the product BA? What is the size of BA?
10. Describe the operation of matrix multiplication in your own
words.
Perform the indicated operations in Problems 11–24, if possible.
11. c 5 2
12. c 0 8
2 1 d c 9 4
3 0 d c 3 7
1 6 d
7 5 d
4 0 1 2
13. £ 2 3§ £ 0 5§
8 1 4 6
14.
15. £
16. c 6 2 3 3 6
4 8 7 d £ 9 2 §
1 4
17.
6 2 0 5
18. £ 4 1§ £ 7 2§
3 0 1 0
4 7
4 10 13
19. £ 10 11 § c
7 11 9 d
13 9
1
20. c
c 6 2 3
4 8 7 d c 3 9 1
6 2 4 d
4 0
2 3
8 1
c 5 1 0
4 6 3 d c 2 4 6
3 5 5 d
2 3 4
5
4 3 2
§ c 1 0 4
2 5 6 d
d c
9
2
7 4
1
4
1
2
d