Chapter 4.2, Problem 63E

### 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

# Give an example of a system of three linear equations with the general solution x = 1 ,     y = 1 + z ,   z arbitrary. (Check your system by solving it.)

To determine

The example of a system of three linear equations with the general solution x=1,y=1+z;zarbitrary and check your system by solving it.

Explanation

Given Information:

The general solution is x=1,y=1+z;zāarbitrary.

Consider a general solution is x=1,y=1+z;zāarbitrary.

An example of three linear equations satisfying the given general solution is,

x=1yāz=1x+yāz=2

Verify the system by solving it using reduction method.

The augmented matrix for the given system of equations is,

[10010111ā1ā112]

Begin by pivoting the first nonzero element of the first row and clear its column.

Perform the operation R3āR3āR1,

[10010111ā1ā112]ā[10010011ā1ā111]

Next simplify the third row

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