# Consistency Condition

1. Jun 22, 2005

### jdstokes

True of false. A homogeneous system of $r$ linear equations in $n$ unknowns is inconsistent if the number of equations, $n$ exceeds the number of unknowns, $r$. The questions seems to be implying that $n=r$, in which case the system is consistent. Is this true?

Thanks.

James

2. Jun 22, 2005

### geosonel

FALSE
any number of equations CAN BE consistent with any number of unknowns.

here are 5 consistent equations in 2 unknowns:

x + y = 2
2x + 2y = 4
3x + 3y = 6
4x + 4y = 8
5x + 5y = 10

or:

x + y = 0
2x + 2y = 0
3x + 3y = 0
4x + 4y = 0
5x + 5y = 0

etc.

Last edited: Jun 22, 2005