设x(a1-a2-2a3)+y(a2-a3)+za3=0,则
xa1+(-x+y)a2+(-2x-y+z)a3=0,
向量组a1,a2,a3线性无关,
∴x=0,-x+y=0,-2x-y+z=0,
解得x=y=z=0,
∴向量组a1-a2-2a3,a2-a3,a3也线性无关.