判别向量组的线性相关性?α1=(1,1,3,1)T,α2=(3,-1,2,4)T,α3=(2,2,7,-1)T
问题描述:
判别向量组的线性相关性?
α1=(1,1,3,1)T,α2=(3,-1,2,4)T,α3=(2,2,7,-1)T
答
k1(1,1,3,1)+k2(3,-1,2,4)=(2,2,7,-1)=>k1+3k2 =2 (1)k1-k2=2 (2)3k1-k2 =7 (3)k1+4k2 =-1 (4)from (1) and (2)(1)-(2)k2 =0k1=2but k1=2 and k2=2 does not satisfy (3)=>α1,α2,α3 线性无关