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Span question

  1. May 12, 2009 #1
    im given four vectors as a 1x4 matrices:

    [1,4,2,8]^t = v1
    [2,5,3,9]^t = v2
    [11,14,12,18]^t = v3
    [4,3,2,1]^t = v4

    How can i know which if any of these vectors can be removed without changing the span?
     
  2. jcsd
  3. May 12, 2009 #2

    dx

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    Gold Member

    Check if they're linearly independent. If they are, then you cannot remove any of them without changing the span.
     
  4. May 12, 2009 #3
    How can i tell if the vectors are a basis for R^4?
     
  5. May 12, 2009 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    A basis for an n dimensional vector space has three properties
    1) the vectors span the space
    2) the vectors are independent
    3) the set contains n vectors

    and, any two of those is sufficient to prove the third.

    You know you have four vectors here. If they are independent, then they must also span the space and are a basis. If they are not independent, they do not form a basis.
     
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