证明题:设向量组a1,a2,a3,线性无关,证明向量组a1+2a2,a2+2a3,a3+2a1线性无关

设k1,k2,k3使得k1(a1+2a2)+k2( a2+2a3)+k3(a3+2a1)=0(k1+2k3)a1+(2k1+k2)a2+(2k2+k3)a3=0a1,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a1+2a2,a2+2a3,a3+2a1线性无关...