设k1(a1+2a2)+k2(a2+2a3)+k3(a3+2a1)=0,即证k1=k2=k3=0(k1+2k3)a1+(2k1+k2)a2+(2k2+k3)a3=0因为向量组a1,a2,a3线性无关,所以k1+2k3=02k1+k2=02k2+k3=0解得k1=k2=k3=0所以向量组b=a1+2a2,b2=a2+2a3,b3=a3+2a1线性无关...