1. Sep 14, 2005 #1

   loli12

   

   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

   loli12, Sep 14, 2005
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3. Sep 15, 2005 #2

   quasar987

   

   Science Advisor

   Homework Helper

   Gold Member

   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.

    

   quasar987, Sep 15, 2005

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