Work Step by Step
If $a(1,-1,0)+b(0,1,-1)+c(1,1,1)=(0,0,0)$, then $a+c=0,-a+b+c=0,-b+c=0$. Thus $a=-c$, then $c+b+c=0,-b+c=0$, thus $3c=0$, thus $c=0$, thus $b=0$, thus $a=0$. Thus they are linearly independent.
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