证:由i),有 α,=t,β,,i=1,2,,r要证α,αz,",α,线性相关,即证有不全为零的数k,k,..,k,, 使k,aα, +k,α,+...+k,a,=0作线性组合 xαi +x,α, +..+x,α,=x,α;B,=,=()B若能找到不全为0的xj,x2,…,x,,使Z = , j=1,.,.i=183.3线性相关性V§3.3 线性相关性 要证 1 2 , , , r 线性相关,即证有不全为零的数 k k k 1 2 , , , , r 使 证: 由i),有 1 , 1,2, , s i ij j j t i r = = = 1 1 2 2 0. r r k k k + + + = 作线性组合 1 1 r s i ji j i j x t = = = 1 1 s r i ji j j i x t = = = 1 1 2 2 r r x x x + + + 1 r i i i x = = 1 1 r s i ji j i j x t = = = 若能找到不全为0的 x x x 1 2 , , , r ,使 1 0, 1,2, , r i ji i x t j s = = =