1、定义定义5.112,r 12,r 12,r 12,r ,W 1122,rrkkk 12(,)rk kk 12,r 12,r 12,r 12,r 1(1,1,1,1),12,n nK2(0,1,1,1),3(0,0,1,1),(0,0,0,1),n ,12(,)nb bb 1231 11 10 11 10 01 10 00 1n 10 1122nnxxx 111221233123nnxbxxbxxxbxxxxb 112213321,nnnxb xbb xbbxbb 121321(,)nnb bb bbbb 12,n 12,n nK12,s 12,r 12,s 12,r 12,s ii)sr ，1
2、2,s 12,sk kk 1122,jjjrjraaa 11220.sskkk 1122ssxxx 1sjjjx 11srjijijixa 11rsjijiijx a 11srjijijix a 常数常数1,2,.js ，12,sx xx121110sssjjjjjrjjjjx ax ax a11220.ssxxx 12,sx xx12,s 112211rsssjijiijxxxx a 121110sssjjjjjrjjjjx ax ax a111122121122221122000ssssrrrssa xa xa xa xa xa xa xa xa x 12,(),ssn 1(1,1,1,1
3、),2(0,1,1,1),3(0,0,1,1),(0,0,0,1),n ,nKnK12,s 12,n 1,s nK定理定理5.4 数域数域K上上n维向量空间维向量空间V的每个非的每个非0子空间子空间W都存在基。都存在基。证明证明12,r WW,12,r 12,r 12,r 12,r 12,s 12,r 12,s 12,r 12,s .sr 推论推论5.5则则.sr 12:,rA 12:,sB .rs.sr 定义定义5.2定义定义5.312,s 12(,)sL 12,s 命题命题5.7,WZ 命题命题5.6dim()dim().WZ 命题命题5.8WZ.WZ 1122iiiirraaa1,2,.
4、is 1,rijjja 1122rrxxx 1riiix 11rriijjijxa 11rriijjjix a 11rriijjijx a 112211rrrriijjjixxxx a 11220rrxxx 1122111()()()0rrriiiiiririiia xa xa x 121110rrriiiiiriiiia xa xa x 12,r 111212112122221122000rrrrrrrrra xa xa xa xa xa xa xa xa x 12,r 11220rrxxx 111212112122221122000rrrrrrrrra xa xa xa xa xa xa xa xa x 1121112222120rrrrrraaaaaaaaa 1112121222120rrrrrraaaaaaaaa 作业：作业：P168 Ex 1,2(2)
