Chapter 4, Problem 17RE

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# In Exercises 7–18, solve the given system of linear equations. x = 1 2 y 1 2 x = − 1 2 z + 2 z = − 3 x + y

To determine

To calculate: The solution of the system of linear equations consisting of x=12y,12x=12z+2 and z=3x+y.

Explanation

Given Information:

The system of equations is

x=12y12x=ā12z+2z=ā3x+y

Formula used:

Elementary row operations:

Type 1: Replacing the row Ri by aRi, where a is a nonzero number.

Type 2: Replacing the row Ri by aRiĀ±bRj, where a is a nonzero number.

Calculation:

Consider the system of equation,

x=12y12x=ā12z+2z=ā3x+y

Rewrite the given equations in standard form,

xā12y=012x+12z=2ā3x+yāz=0

The augmented matrix for the given system of equations is

[1ā1200120122ā31ā10]

Apply Gauss Jordan reduction method to get the solution of the given system of equation.

Begin by simplification of first and second row in matrix by the operation R1ā2R1,R2ā2R2,

[1ā1200120122ā31ā10]ā[2ā1001014ā31ā10]

Select the first nonzero element of first row and clear its column

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