Intermediate Algebra (11th edition)

20.Concept Check Consider this system.

Match each determinant in parts (a) – (d) with its correct representation from choices A –D.

(a)D (b) (c) (d)

A. B.

C. D.

Use Cramer’s rule to solve each linear system. See Example 4.

(^3)

4

7

- 2

3

- 4

1

- 2

3

- 8

3 3

4

7

- 2

1

2

0

- 2

3

- 8

3

(^3)

4

7

- 2

3

- 4

1

1

2

0

3 3

1

2

0

3

- 4

1

- 2

3

- 8

3

Dx Dy Dz

• 2 x+ y- 8 z= 0

7 x- 4 y+ 3 z= 2

4 x+ 3 y- 2 z= 1

722 APPENDIX A Determinants and Cramer’s Rule

21. 22.

• 2 x+ 3 y= 16

3 x+ 5 y=- 5

4 x- 3 y=- 30

5 x+ 2 y=- 3

23. 24.

6 x- 5 y= 2

8 x+ 3 y= 1

2 x+ 5 y= 8

3 x- y= 9

25. 26.

5 x+ 6 y= 7

2 x+ 3 y= 4

7 x+ 8 y= 9

4 x+ 5 y= 6

27. 28.

x+ 2 y- 6 z=- 26

x- y+ 2 z= 5

2 x+ 3 y+ 2 z= 15

x+ 9 y+ 2 z=- 19

3 x+ 3 y- z= 1

x- y+ 6 z= 19

29. 30.

• 4 x+ 6 y- 8 z=- 16

6 x- 9 y+ 12 z= 24

2 x- 3 y+ 4 z= 8

• 6 x+ 9 y- 3 z=- 6

2 x- 3 y+ z= 2

7 x+ y- z= 4

31. 32.

• y+ 2 z=- 11

2 x+ 3 y= 1

3 x+ 5 z= 0

2 x+ z=- 1

3 x+ y=- 5

• x+ 2 y= 4

Use Cramer’s rule where applicable to solve each linear system. See Examples 5 and 6.

33. 34.

• x+ z=- 7

2 y+ z= 5

x- 3 y= 13

• y- 2 z=- 13

3 x+ 2 y+ z=- 3

• 5 x- y=- 10

Solve each equation by finding an expression for the determinant on the left, and then solving

using the methods of Chapter 2.

35. 36. 37. 38.`

5

x

3

x

^ =^20

x

x

4

- 3

^ =^0

- 2

x

10

6

^ =^0

4

2

x

3

(^) ` = 8