# Consistency Condition

#### 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

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#### geosonel

jdstokes said:
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
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.

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