设向量组a1,a2,a3线性无关,证明:向量组B1=a1+2a2+a3,B2=a1+a2+a3,B3=a1+3a2+4a3

To prove : B1, B2, B3 is linearly independent
k1B1+k2B2+k3B3 =0
k1(a1+2a2+a3) + k2(a1+a2+a3)+k3(a1+3a2+4a3) =0
=>(k1+k2+k3)a1+(2k1+k2+3k3)a2+(k1+k2+4k3)=0
a1,a2,a3 is linearly independet, then
k1+k2+k3 = 0 (1)
2k1+k2+3k3 = 0 (2)
k1+k2+4k3=0 (3)
(3)-(1)
k3=0
(1)-(2)
k1=0
from (1)
k2=0
k1,k2,k3 =0
=> B1,B2,B3 is linearly independent.本回答被网友采纳