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Consistency Condition

  1. Jun 22, 2005 #1
    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
     
  2. jcsd
  3. Jun 22, 2005 #2
    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
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