Intermediate Algebra (11th edition)

The augmented matrix of the system is shown in the graphing calculator

screen on the left as matrix [A]. The screen in the middle shows the row echelon form for [A].

The screen on the right shows the “reduced” row echelon form, and from this it can be deter-

mined by inspection that the solution set of the system is 51 1, 5 26.

4 x+ 8 y= 44

2 x- y=- 3

CHAPTER 4 Summary 253

Use a graphing calculator and either matrix method illustrated to solve each system.

29. 
    
    
    
    30. 
        
        
        
        31. 
            
        
        
        
        
    
    
    
    
    
    
    • 3 x- 2 y+ 4 z= 3
    
    
    
    

2 x+ 3 y+ z= 5

5 x+ y- 3 z=- 6

7 x- 3 y=- 19

5 x+ 3 y= 7

2 x+y= 3

4 x+y= 5

32. 33. 34.

x+z=- 2

• y+z=- 2

x-y=- 1

x+y= 8

y+z= 3

x+z=- 3

x+ y+ 3 z= 11

3 x- 3 y- 4 z=- 1

x+ y+ z= 3

Evaluate each exponential expression. See Section 1.3.

35. 
    
    
    
    36. 
        
        
        
        37. 
            
        
        
        
        
    
    
    
    


36. 
    
    
    
    39. 40.a-
    
    
    
    

3

2

b

5

a

3

4

b

4

• 54

26 1 - 425 1 - 524

PREVIEW EXERCISES

4.1

system of equations
system of linear
equations
solution set of a linear
system

consistent system

independent equations

inconsistent system

dependent equations

elimination method

substitution method

4.2

ordered triple

focus variable

working equation

4.4

matrix

element of a matrix

row

column

square matrix

augmented matrix

row operations

row echelon form

KEY TERMS

SUMMARY

CHAPTER 4

1 x, y, z 2 ordered triple
c

a

d

b

e

c

f

d

NEW SYMBOLS

matrix with

two rows,

three columns