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Linearly indpendent

  1. Nov 16, 2006 #1
    Three vectors are linearly independent iff The vectors are not on the same plane. Three vectors are linearly dependent ⇔ The vectors are on the same plane. Is this true.
     
  2. jcsd
  3. Nov 16, 2006 #2

    radou

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    Yes, it is true, if you are talking about vectors in V^3(O), i.e. radius vectors.
     
  4. Nov 16, 2006 #3

    HallsofIvy

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    That's what "if and only if" (iff) means! "Three vectors are linearly independent iff The vectors are not on the same plane" means two things:
    If the vectors are not on the same plane then the vectors are linearly independent" and "Three vectors are linearly independent only if the vectors are not on the same" which is the same as "if three vectors are linearly independent, then they are not on the same plane", exactly the statement you are asking about.
     
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