证:1) V5eV, 设 5=X6+X6,+...+x,en于是 0()= x,o(e)+x,0(c,)+...+x,o(cn)E L(o(c)),0(c2),.,0(8n)即o(V)≤ L(α(c)),o(,),..,o(cn)又对 Vx,o(e))+x,0(c2)+...+x,o(en)有 Xo(c))+x,0(c2)+...+x,o(cn)=o(xe +Xe, + ...+xnen)eo(V)87.6线性变换的值域与核V§7.6 线性变换的值域与核 L( ( ), ( ), , ( ) 1 2 n ) 即 ( ) ( ), ( ), , ( ) V L ( 1 2 n ) 又对 1 1 2 2 ( ) ( ) ( ) n n + + + x x x 1 1 2 2 ( ... ) ( ) n n = + + + x x x V 证:1) V, 设 1 1 2 2 , n n = + + + x x x 1 1 2 2 ( ) ( ) ( ) ( ) n n 于是 = + + + x x x 有 1 1 2 2 ( ) ( ) ( ) n n x x x + + +