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Forming basis of R^3

  1. Sep 12, 2006 #1
    i have a question im trying to work but im not sure how to do it. i'm given 4 dirrerent answers to choose from (i wont post them because i want to try them myself)

    Only one of the following 4 sets of vectors forms a basis of R3.
    Explain which one is, and why, and explain why each of the other sets do not form a
    basis.


    S = {(1,1,1), (-2,1,1), (-1,2,2)}

    This one is not because it cannot be expressed as a linear combination right??
     
  2. jcsd
  3. Sep 12, 2006 #2
    S is not a basis for R^3 because it is not linearly independent.
     
  4. Sep 13, 2006 #3

    HallsofIvy

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    Because what "cannot be expressed as a linear combination"?
    Grammatically, the "it" in your sentence must refer to "this one", meaning the set of vectors- but it doesn't make sense to talk about expressing a set of vectors as a linear combination of anything.

    It is true that S is not a basis for R3 because one of the vectors in S can be expressed as a linear combination of the other two. For example, (1, 1, 1)= -1(-2, 1, 1)+ 1(-1, 2, 2).
     
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