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Is a set with a 0 vector linearly independent?

  1. Nov 5, 2012 #1
    I don't know how to write out matrices nicely on this forum,

    but suppose you have some matrices:


    [1 0 3]
    [2 0 4]
    [0 0 5]

    This would, by definition, be linearly dependent, spanning a plane in r3..is this correct? Since c1=0, c2=anything, c3=0

    where c1v1+c2v2+c3v3=0

    With this:

    [1 0 3 5]
    [3 0 2 4]
    [2 0 1 4]

    Linearly dependent, spanning all of r3?

    [1 4 0 5 2]
    [2 3 0 2 4]
    [2 9 0 1 1]

    Linearly dependent, spanning all of r3?

    Are these correct? does the 0 vector hav any special properties with this?
     
    Last edited: Nov 5, 2012
  2. jcsd
  3. Nov 5, 2012 #2

    micromass

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    If a set contains the zero vector, then it is always linearly dependent.

    I think you made a typo when writing the title.
     
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