線代第三章習(xí)題解答

1、331第三章第三章行列式行列式習(xí)題習(xí)題3.1316.用定義計(jì)算行列式（1）??21000000000222211114???idcbadcbadcbaDiiii解：解：設(shè)則中第1行的非0元為，故444??ijaD4D113111baaa??113j?同法可求：234241324jjj???∵可組成四個(gè)4元排列1234，1432，3214，3412，4321jjjj故中相應(yīng)的非0項(xiàng)有4項(xiàng)，分別為，，4D2211dbca2211cbda?2

2、211dacb?2211cadb其代數(shù)和即為的值，整理后得4D????122112214dcdcbabaD???(2)010...0002...0000...000...0nDn?????解：解：由行列式的定義121212()12(1)nnnjjjnjjnjjjjDaaa???????僅當(dāng)分別取2，3…n1n1時(shí)，對(duì)應(yīng)項(xiàng)不為零，其余各項(xiàng)都為零12njjj?12121()(231)1212231(1)(1)(1)(1)(1)12(1)!n

3、nnjjjnnjjnjnnnnDaaaaaaann????????????????????習(xí)題習(xí)題3.23332110000100()(1)00010000nxxxaxx????????????????222222121221(1)(1)(1)(1)()(1)nnnnnnnnnnaaxaxaxxax?????????????????2211221nnnnnnaaxaxaxaxx?????????????右3=23計(jì)算下列行列式（1）11

4、111100((1))((1))00xaaaxaaxaxaxnaxnaaaxaaxxa?????????????????????????????])1([)(1anxaxn?????(2)????????????111(1)211111111()1(1)(1)111111nnnnnnnnnnnnnnnaaanaaanaaanDaaanaaanaaan???????????????????????????????????????（最后一行