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Subset? Basis?

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data

    After sorting out basis, now I encountered a new term, Subset. And I get all confused again, clearly I'm not good at these, but I am learning.

    Let S = {(1,-1,2,1) , (0,1,1,-2) , (1,-3,0,5)}
    Find a subset of S that is a basis for <S>

    2. Relevant equations

    3. The attempt at a solution

    I formed a matrix and row reduced it to row echelon form. Then the corresponding columns on the leading entry gives the basis which is {(1,-1,2,1) ,(0,1,1,-2)} . But now, to answer the question, how to find a subset ? and also, what does <S> mean ? Is that a symbol for a basis?
  2. jcsd
  3. Jan 25, 2009 #2


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    Homework Helper

    S is the original set of three vectors. <S> means the subspace spanned by the vectors in S. When you did your matrix exercise you found a basis for the subspace consisting of {(1,-1,2,1) ,(0,1,1,-2)}. That IS a subset of S. You are all done. The question was just to find a basis for the subspaces consisting of vectors from S. That's all.
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