I had to prove the following notation: if $u1,u2,u3$ are linear depended then $u1+u2,u2+u3,u3+u1$ are also linear depended.
I tried to contradict saying that I assume that P is right but Q is wrong as for $u1,u2,u3$ are linear depended and $u1+u2,u2+u3,u3+u1$ are not linear depended.
I choose $u1 =(0,0,1), u2= (1,1,0), u3=(2,2,1)$ and show that both $u1,u2,u3$ and $u1+u2,u2+u3,u3+u1$ are linear depended.
- Is my proof is right?
- what is the reason that the notation is right?
Thanks a lot!!