设k1(a1+a2)+k2(a2-a3)+k3(a1-2a2+a3)=0(k1+k3)a1+(k1+k2-2k3)a2+(-k2+k3)a3=0因为向量组a1,a2,a3线性无关,所以k1+k3=0k1+k2-2k3=0-k2+k3=0解得k1=k2=k3=0所以向量组：a1+a2,a2-a3,a1-2a2+a3也线性无关.
