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Math Help - Basis Problem

  1. #1
    Newbie
    Joined
    Mar 2010
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    Basis Problem

    I do not understand how to solve this problem:
    Let W = {(s+4t,t,s,2s-t)| s,t are elements are reals}. Where W is a subspace of R^4.

    Find the basis for W.


    I understand that a basis means that W spans R^4 and is linearly independent. But I fail to understand how to complete this problem. I think I am missing something small.

    Any help would be appreciated.
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  2. #2
    Super Member
    Joined
    Jun 2009
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    Africa
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    Smile

    you can see that,
    w=\left \{ s(1,0,1,2)+t(4,1,0,-1)\mid s,t\in \mathbb{R} \right \}=\texttt{Span}((1,0,1,2),(4,1,0,-1))
    which means ((1,0,1,2),(4,1,0,-1)) is a Basis of \mathbb{W}.
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