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Homework Help: Show whether it's a basis

  1. Sep 14, 2005 #1
    I have to show that for 2 distinct vectors u and v of a vector space V, for which {u, v} is a basis for V and a and b are nonzero scalars, then {u+v, a*u} is also basis for V.

    Please help!
     
    Last edited by a moderator: Sep 14, 2005
  2. jcsd
  3. Sep 15, 2005 #2

    quasar987

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    From memory (and common sense), u and v are a basis if they are linearly indep. and they span V right?

    So you need to show that provided that u & v satisfy these two conditions, then ([itex]\Rightarrow[/itex]) u+v & a*u also satisfy them.
     
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