Intermediate Algebra (11th edition)

252 CHAPTER 4 Systems of Linear Equations

Complete solution available
on the Video Resources on DVD

4.4 EXERCISES

1.Concept Check Consider the matrix and answer the following.

(a)What are the elements of the second row?

(b)What are the elements of the third column?

(c)Is this a square matrix? Explain why or why not.

(d)Give the matrix obtained by interchanging the first and third rows.

(e)Give the matrix obtained by multiplying the first row by

(f )Give the matrix obtained by multiplying the third row by 3 and adding to the first row.

2.Repeat Exercise 1for the matrix.

Concept Check Give the dimensions of each matrix.

3. 4.

5. 6.

Use row operations to solve each system. See Examples 1 and 3.

D 384324

6

- 2

4

1

3

5

10

- 1

T

c

4

- 1

9

2

0

- 4

C d

3

4

- 1

- 7

5

0

S

C

- 7

3

0

0

2

1

1

- 2

6

S

-^12.

C

- 2

0

1

3

5

4

1

- 3

8

S

7. 8. 9.

3 x- y= 2

2 x+ 4 y= 6

x- y=- 2

x+ 2 y= 7

x-y= 3

x+y= 5

10. 11. 12.

3 x- y= 7

5 x+ 2 y= 8

2 x- 3 y=- 14

3 x+ 4 y= 13

x- y= 5

4 x+ 5 y=- 7

13. 14. 15.

4 x+ 2 y= 8

2 x+ y= 4

• 3 x+ 6 y= 5

2 x- 4 y= 8

x- 3 y= 9

• 4 x+ 12 y= 36

16. 17. 18.

7 x+ 2 y= 0

• 5 x+ 3 y= 0
  x- y= 0


• 3 x+ 2 y= 0
  6 x+ 8 y=- 2


• 3 x- 4 y= 1

Use row operations to solve each system. See Examples 2 and 3.

19. 
    
    
    
    20. 
        
        
        
        21. 
            
        
        
        
        
    
    
    
    

x- 2 y+ 3 z= 1

2 x- y+ z=- 9

x+ y- z= 6

x- 2 y+ 4 z= 14

3 x+ y- z=- 5

2 x+ 4 y- 3 z=- 18

3 x+y- 4 z= 8

2 x-y+ z= 9

x+y- 3 z= 1

22. 23. 24.

y+ 2 z=- 2

2 x- z= 0

x+ y= 1

x+z=- 1

y-z= 6

x-y= 1

x+ y+ 2 z=- 1

2 x- y+ 2 z= 0

x+ 3 y- 6 z= 7

25. 26.

3 x+ 9 y+ 3 z= 3

2 x+ 6 y+ 2 z= 2

x+ 3 y+ z= 1

• 2 x+ 4 y- 2 z=- 8

3 x- 6 y+ 3 z= 12

x- 2 y+ z= 4

27. 28.

5 x+ 10 y+ 5 z= 12

x+ 3 y+ 4 z= 10

4 x+ 8 y+ 4 z= 9

x- y+ 2 z= 6

2 x+ 4 y+ 6 z=- 5

x+ 2 y+ 3 z=- 2