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Consistency Condition

  • Thread starter jdstokes
  • Start date
True of false. A homogeneous system of [itex]r[/itex] linear equations in [itex]n[/itex] unknowns is inconsistent if the number of equations, [itex]n[/itex] exceeds the number of unknowns, [itex]r[/itex]. The questions seems to be implying that [itex]n=r[/itex], in which case the system is consistent. Is this true?

Thanks.

James
 
jdstokes said:
True of false. A homogeneous system of [itex]r[/itex] linear equations in [itex]n[/itex] unknowns is inconsistent if the number of equations, [itex]n[/itex] exceeds the number of unknowns, [itex]r[/itex]. The questions seems to be implying that [itex]n=r[/itex], 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.
 
Last edited:

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