k,α, +...+ kmαm + p,β +...+ Pn-mβn-m = 0由于αi,αz,,αm,β,β2,.…,βm-m线性无关，得ki = k, == km= P =..= Pn-m = 0所以, α1,α2,",αm,β1,β2,",βm-mY1,Y2,*,Yn-m线性无关．因而它是 Vi+V2 的一组基.:. dim(V +V2)= m+(n -m)+(n2 -m) = n +n, - m= dimV + dimV - dim(V NV2)86.6子空间的交与和区区§6.6 子空间的交与和 1 1 1 1 1 1 0 m m n m n m k k p p     + + + + + = − − 1 1 2 1 0 m n m k k k p p = = = = = = = − 由于       1 2 1 2 , , , , , , , m n m 1− 线性无关，得 1 2 1 2 1 2, 1 2 , , , , , , , , , , 所以，          m n m n m − − ∴ dim( ) ( ) ( ) V V m n m n m n n m 1 2 1 2 1 2 + = + − + − = + − 线性无关. 因而它是 V V 1 2 + 的一组基. = + − dim dim dim( ) V V V V 1 2 1 2