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Bases of Vector Spaces

  1. Apr 18, 2007 #1
    Are these two sets:

    A = {(0,2,2)^T, (1,0,1)^T, (1,2,1)^T}

    B= {(1,2,0)^T, (2,0,1)^T, (2,2,0)^T}

    Bases of V3(R)

    I have found equations that show that they span V3(R)

    And that both set are linearly independant.

    So am I right in saying that they are both bases of V3(R).

    Cheers Ash
     
  2. jcsd
  3. Apr 18, 2007 #2

    matt grime

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    If you have three vectors in R^3 that span, then they must be linearly independent, and if you have three linearly independent vectors in R^3 then they must span. That follows from the definition of span and basis.
     
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