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3.8 EXERCISES
EXAMPLE 1
on p. 210
for Exs. 3–12
EXAMPLE 2
on p. 211
for Exs. 13–18
EXAMPLE 3
on p. 211
for Exs. 19–24
SKILL PRACTICE
1. VOCABULARY Identify the matrix of variables and
the matrix of constants in the matrix equation.
2. WRITING
det A Þ 0.
Explain how to find the inverse of a 2 3 2 matrix A where
FINDING INVERSES Find the inverse of the matrix.
1 25
3. F 21 4G 22 3
4. F23 4G 6 2
5. F5 2G 27 29
6. F 2 3G
24 26
7. F 4 7G 6 222
8. F 212 20G
224 60
9. F 26 30G F
4 5
} }
10. 3 6
24 21G
11. ERROR ANALYSIS Describe and
correct the error in finding the
2 4
inverse of the matrixF
1 5G.
12. ★ TAKS REASONING
10 23
What is the inverse of the matrixF
3 21G?
210 3
AF 23 1G 21 3
B F23 10G
1 23
C F 3 210G D F
214 Chapter 3 Linear Systems and Matrices
HOMEWORK
KEY
F
21
2 4
1 5G
5 WORKED-OUT SOLUTIONS
on p. WS1 for Exs. 3, 25, and 47
5 TAKS PRACTICE AND REASONING
Exs. 12, 34, 41, 46, 51, 52, and 53
5 MULTIPLE REPRESENTATIONS
Ex. 45
F21 2
3 4GFx yG 5F 4
22G
5 24 30 224
5 6F 21 2G5F 26 12G
10 23
3 21G
SOLVING EQUATIONS Solve the matrix equation.
1 1 2 3
6 8 4 3
21 0 3 21
13. F 5F 14.
4 5GX
21 6G F 5F 15.
2 3GX
0 22G F 5F 6 4GX
4 5G
23 6 5 21
1 5 3 21 0 25 2 4 5 0
16. F 5F 17.
1 2GX
8 2G F 5F 18.
0 22GX
6 8 4G F 5F 29 3GX
3 1 6G
FINDING INVERSES Use a graphing calculator to find the inverse of matrix A.
Check the result by showing that AA 21 5 I and A 21 A 5 I.
5F
1 1
19. A 22 0
3 1
22
0G 3
5F
1
20. A 2
1
0
1
4
2
4G 3
5F
1 21 2
2G
21. A 22 3 10
3 21
22. A 5F22
0
12
5
8
25
21
0G 1
5F
3
23. A 2
21
28
4
0
0
1
26G 5F
4 1 5
6G
24. A 22 2 1
3 21