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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
Section
BuyFindarrow_forward

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;zarbitrary.

Consider a general solution is x=1,y=1+z;zarbitrary.

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

x=1yz=1x+yz=2

Verify the system by solving it using reduction method.

The augmented matrix for the given system of equations is,

[100101111112]

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

Perform the operation R3R3R1,

[100101111112][100100111111]

Next simplify the third row

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