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## Homework Statement

I need to prove that, if {u;v;w} is a linearly independent set in a

vector space, then the set

{2u + v + w; u + 2v + w; u + v + 2w}

is also linearly independent.

## Homework Equations

...

## The Attempt at a Solution

if {u;v;w} is a linearly independent set=> c1*u +c2*v+c3*w=0 and c1=c2=c3=0 and also u,v,w are distinct and different from 0.

=>c1(2u + v + w)+ c2(u + 2v + w)+ c3(u + v + 2w)=0,but if I create a system of equations based on this i get u=v=w=0...any help?