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Show whether it's a basis

  • Thread starter loli12
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  • #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!
 
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  • #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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