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EXAMPLE 1
on p. 203
for Exs. 3–21
✓ GUIDED PRACTICE for Examples 3 and 4
3.7 EXERCISES
SKILL PRACTICE
Use Cramer’s rule to solve the linear system.
5. 3x 2 4y 5215 6. 4x 1 7y 5 2 7. 3x 2 4y 1 2z 5 18
2x 1 5y 5 13 23x 2 2y 528 4x 1 y 2 5z 5213
2x 2 3y 1 z 5 11
1. VOCABULARY Copy and complete: The ? of a 2 3 2 matrix is the difference
of the products of the elements on the diagonals.
2. WRITING Explain Cramer’s rule and how it is used.
2 3 2 DETERMINANTS Evaluate the determinant of the matrix.
2 21
7 1
24 3
3. F 4.
4 25G F 5.
0 3G F 1 27G
1 23
6. F 2 6G
10 26
7. F 0 3
5 23G
9 23
9. F 7 2G 25 12
10. F 4 6G
27 5G 8. F
18.
3 3 3 DETERMINANTS Evaluate the determinant of the matrix.
F21 12
11. 0 2
3 0
4
1G F
1
25 12. 5
2
2 3
3G 28 1
4 F
5 0
13. 23 9
1 24
2
0G 22 14.
F
12 5
15. 0 6
1 10 4G
8 F24
28 16. 12
8
3
6
212
29
0G
F22
0 17. 8
4
6
7G
0
15 3
21
ERROR ANALYSIS Describe and correct the error in evaluating the determinant.
19.
⏐
2 0 21 2 0
4 1 6 4 1
23 2 5⏐ 23 2
5 10 1 0 1 (28) 1 (3 1 24 1 0)
5 2 1 27 5 29
HOMEWORK
KEY
20.
5 WORKED-OUT SOLUTIONS
on p. WS1 for Exs. 11, 23, and 43
5 TAKS PRACTICE AND REASONING
Exs. 21, 28, 38, 42, 45, 47, and 48
3 0 3 0 1
2 2 2 2 23
23 5 ⏐ 23 5 0⏐
F27 4
6G
5
1 2 24
210 1
F
5 7 6
7G 24 0 8
1 8
5218 1 0 1 0 2 (218 1 0 2 6)
5218 2 (224) 5 6
21. TAKS REASONING
Which matrix has the greatest determinant?
24 1
1 6
5 23
5 22
A F B
6 3G F C
3 8G F D
7 21G F 1 5G
3.7 Evaluate Determinants and Apply Cramer’s Rule 207