ni =(1,-1,0,...,0), n2 = (1,0,-1,0,..,0),.nn-1=(1,0,,0,-1)就是W,的一组基.而在W,中任取两个向量α,β，设α =(xi,x2,...,xn), β =(yi,y2,..",yn)则 α+β=(xi+ yi,X,+ y2,"",xn +yn)但是 (x, +yi)+(x, +y2)+...+(x, + yn)=(x +x, +...+xn)+(yi + y2 +...+ yn)=1+1=2：α+βW2，故W,不是Pn的子空间。86.5线性子空间K§6.5 线性子空间 就是W1 的一组基. 1  = − (1, 1,0, ,0), 1 (1,0, ,0, 1) n− = − , 2  = − (1,0, 1,0, ,0), 而在W2中任取两个向量  , ，设 1 2 1 2 ( , , , ), ( , , , ) n n   = = x x x y y y 1 1 2 2 ( ) ( ) ( ) n n 但是 x y x y x y + + + + + + 1 2 1 2 ( ) ( ) 1 1 2 n n = + + + + + + + = + = x x x y y y 1 1 2 2 ( , , , ) n n   + = + + + x y x y x y 2  +    W , 则 故W2不是Pn的子空间