- #1

sana2476

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## Homework Statement

Prove (u,v,u+v) can not be a basis for <u,v,u+v>.

## Homework Equations

## The Attempt at a Solution

Let αu+βv+γ(u+v)=0

αu+βv=-γ(u+v)

α/γ(u)+β/γ(v)=-(u+v)

α/γ(u)+β/γ(v)+1*(u+v)=0

Since α/γ,β/γ,1 are not all zeros, therefore, (u,v,u+v) are linearly dependent. Hence it doesn't form basis for <u,v,u+v>.

Let me know if this is the right approach towards the proof.