# Show whether it's a basis

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.

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quasar987
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 ($\Rightarrow$) u+v & a*u also satisfy them.