1、浙江財經學院本科教學課程浙江財經學院本科教學課程-經濟數學經濟數學(二二)123nmnmO0.0.0.0記作4312045010245,2131 .74133126AB632114371534122010025143BA333441121247632114371534122010025143BA9151067321261567103421,321021BA)(23ABX32102110342123X222402233336038skkjiksjisjijiijbabababac12211.),.,2 , 1;,.,2 , 1(njmi9乘積乘積C的位于第的位于第i行第行第j列的元素列的元素ci

2、j等于等于A的第的第i 行與行與B的第的第j列列的對應元的對應元素素乘積之和乘積之和.111111121212212112111111.jnsjniiisssjsnmmmnjniijinmmjmnbbbaaabbbaaabbbaaaccccccccc 102305,1412A204121;375432B204230512127211.1412375597432AB11mnmnmmnnnnbxaxaxabxaxaxabxaxaxa22112222212111212111,.212222111211mnmmnnaaaaaaaaaA,21mbbbB,21nxxxXmnmmnnaaaaaaaaa212

3、222111211nxxx211mnnxaxaxa1212111xaxaxan2222121nmnmmxaxaxa2211mbbb2112232221131211aaaaaaA321BBB21AA332211qpqpqpB321BBB能耗單價33111111123321222211jjjjjjjjjjjja pa qccCcca pa q工廠工廠工廠工廠總收入總收入總能耗總能耗1A2AAB132142A6342B2142634222-16-32816634221422200001410000100.00100001nEE 15tsvuvutsABBAtvussvut,vuts1610,21A1

4、1122122,xxXxx111211122122112112221112111212212221222210;2221210.221xxxxAXxxxxxxxxxxxXAxxxxx1111121212111221221222222,22,2.xxxxxxxxxxxx112212,0.xxx112221,xxa xb0.aXba17().kkkABA B,kAO.AO000111,111AO 2000000.000AO.)( ,kllklklkAAAAA18OA1111反例：OA0000111111112但0001A反例：AA0001000100012則EAOA且但1001A反例：EA1001

5、100110012則EAEA且但BAAB19mnmmnnaaaaaaaaaA212222111211mnmnnnmmTaaaaaaaaaA212221212111nm例如：321021A則302211TA20（1）AATT)(（2）TTTBABA)(（3）TTkAkA)(（4）TTTABAB)(TTTsTsAAAAAA1221.).(推廣2122OBABA22由2)(BBAA得2)(BBAA則0B0)(BAABAA因此0A0, BA21Bn21Bn23反例0001A反例EA10111628223AA2425nnaaa2211200030005Annnnbababbaa111126aaa27nn

6、nnaaaaaaA00022211211nnnnbbbbbbB2122211100028BABABATTT)(kAkAkATT)(0311,;3212AB031136,321257AB29021201110A 30BBAATT,TTTBAABBAAB)()()(TTTTBAAB)()(BAAB)(ABBA )(BAAB BBEA2TTTBBEA)2(TTTBBE)2(TTTBBE)(2TBBE2A313210000100,32101201A132,12A212.EOAAE33mnmmnnaaaaaaaaaA212222111211),.,(112111naaa),.,(222212naaa),

7、.,(21mnmmmaaamA211m121111maaa222122maaamnnnnaaa21.nnA121,.,34351221103011,210320EAAAO1221103,011210,;320EAAO 1112214122,2002020BBBEO1112214,.122BBOEABABEBA)(222221121211026022001210361102020102,0053EEAOA12302120,010001BBBOE12121122.EEBBEBBABOAOAOE20220222;200222BE322122 .053AB37smmsmmssaaaaaaaaaA212

8、222111211nssnssnnbbbbbbbbbB212222111211.ijm nABCc),.,(),.,(2121nsCCCCAAAAsnssnnsbbbbbbbbbAAAABC21222211121121),.,(),.,(11211siiinsiiisiiiAbAbAb),.,2 , 1(1njAbCsiiijj)()()()()(BrBrABrABrABrTTTT而3812(,),tBB BB12(,)1,2, .TjjjnjBbbbjt1212(,)(,).ttABA B BBAB ABAB(1,2, ).jABOjt12( ,) .TnXx xx( ).r Bnr3940

9、nnnnnnAAAAAAAAA212221212111*ATijA5321A*A求5321A, 511A, 312A, 221A122A22122111*AAAAA132541EAnnnnnnaaaaaaaaa212222111211nnnnnnAAAAAAAAA212221212111*AAAA*nnnnnnAAAAAAAAA212221212111nnnnnnaaaaaaaaa212222111211AAA000000EAAAA1,0.nijsjjAisa Ais42*1|1AAA1AEAAAA11EAA10111AAAA0A0A*AAAA*EAEAAAAAA*)1(*)1(*11AAA4

10、31.ABAB0,0.AB1:A11,A ABA E1.BA1:B11,ABBEB1.AB.111BOOABOOA11BOOABOOA11BBOOAAEOOE.111BOOABOOA44)(2EAAAEAAAEAA2323222AEAA3)(2AEEAAEEAAAE21)(AE)()(22EAAAEAAE45412112013A412112013A54111) 1(1111A104212) 1(2112A01212) 1(3113A44101) 1(1221A124203) 1(2222A11213) 1(3223A11101) 1(1331A31203) 1(2332A11213) 1(33

11、33A*11AAA33231332221231211151AAAAAAAAA110312101455146因為因為A-1A= E,故故A-1也可逆也可逆, (A-1)-1= A;又又A*A=|A|E,故故A*(A/|A|)=E.因為因為(AB)(B-1A-1)= A(BB-1)A-1= AEA-1 =E,所以所以(AB)-1=B-1A-1 .11121121.).(AAAAAAss因為因為AT(A-1)T= (A-1A)T=ET=E,所以所以(AT)-1=(A-1)T . | /1|1AA,1EAA|111AAAAE| /1|1AA.|1*nAA,|,0|*EAAAA|*AAAAEA |nnA

12、EA|4713,.3AEA則已知.,1可逆證明且階方陣、設練習題：AOAnAAT;0,02AAAn證明滿足階方陣已知、48213,.3AAEA則已知.,1可逆證明且階方陣、設練習題：AOAnAAT;0,02AAAn證明滿足階方陣已知、0*, 02222212211inijiiininijijiiiiijijijaaaaAaAaAaAaAaAAAaOA所以，由存在，由矛盾與，可逆，則若因為0*0*0*,*AOAAOAAAOEAAAij495051100000010000001000000100000010000001E100000000010001000000100010000000001,ji

13、E521000001000001000001000001E100000100000000001000001k)(kiE53100000010000001000000100000010000001E10000001000000100000010000010000001k)(,kjiE54,jiEjiET)()(kiEkiET)(,)(,kijEkjiET,1jiEjiE)1()(1kiEkiE)(,)(,1kjiEkjiE5556BABAjiE,BABAkiE)(BABAkjiE)(,BABjiAE,BABkiAE)(BABkjiAE)(,57.)()()()(2112rnrmrrmrnrrts

14、OOOEQQAQPPPAnm 0011r.)()()()(rnrmrrmrnrrOOOE.)()()()(11rnrmrrmrnrrtsOOOEQAQPP582 112.stPP PAQQQE11121,sPPP11121,tQQQ11111111111112211221.ststAP PP EQQ QP PP QQ Q5912121121();().kkkAGG GGG GEAAGG GAE1212121()()() ().kkkGGG AEGGG AGGG EEA()A E1()E A60461351341A1011200110100013411211000110100453011211000110103220011AE1210113221A)(EA10046101035100134161754142310A100754010142001310)(EA120930010142001310123000014110200131