Chapter 4.2, Problem 57E

### 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 friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Comment on his claim.

To determine

Whether the claim of Frans that ‘a system of linear equations whose row reduced form has a row of zeroes cannot have a unique solution’ is true or false.

Explanation

Consider the claim that āa system of linear equations whose row reduced form has a row of zeroes cannot have a unique solutionā.

This claims turns out to be false when the number of equations is more than the number of unknowns. In such cases even if there is a row of zeroes in the reduced matrix, the system of equations can have a unique solution.

For example consider the system of equations,

ā0.3x+0.5y=0.1xāy=4x17+y17=1

The row reduced matrix of the system is:

[10

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