Chapter 4.2, Problem 58E

### 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

# Your other friend Hans tells you that because he is solving a consistent system of five linear equations in six unknowns, he will get infinitely many solutions. Comment on his claim.

To determine

Whether the claim of Hans that ‘a system of five linear equations in six unknowns will definitely have infinitely many solution’ is right or not.

Explanation

Given Information:

Your other friend Hans tells you that because he is solving a system of five linear equations in six unknowns he will definitely get infinitely many solutions.

Consider the claim that āa system of five linear equations in six unknowns will definitely have infinitely many solutionsā.

There are five linear equations so the augmented matrix will have five rows. Each row can have a maximum of one pivot. In total maximum five pivots can be formed, so at least one unknown has to be arbitrary.

For example,

Consider a matrix with greater number of unknowns than the equations,

[1ā3ā2ā1112301ā12123]

The solution

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