线性代数本科习题解答一

1JINSW立信会计学院数统系立信会计学院数统系2JINSWJINSW线性代数线性代数习题解答3JINSW习题222151221032112321XXXXXXXX以千元为单位200221512021032121321XXXXXXXX215,35,654JINSW习题（）2545102040654321633241XXXXXXXXXXXX261521423122111020545CXCXCCXCXCXCCX654321367258925845XXXXXXS21693535CC5JINSW习题（）2312,CXCX3515MINS100,20021CC当0,2021CC时，取得最小值10,0,15,0,20,25,654321XXXXXX654321367258925845XXXXXXS21693535CC6JINSW习题（）NNNNLLLLLLLL21212110000001N11211111假定时，有KKKKLLLLLLLL21212110000007JINSW习题（）KKKKLLLLLLLL21212110000001KN000000121LLLLLLLK000000121111LLLLLLLKKK8JINSW习题（）000000121111LLLLLLLKKKKKKKKL212111111121211KKKL9JINSW习题（）333333222222111111ACCBBAACCBBAACCBBA121CC333333222222111111ACCBCAACCBCAACCBCA13CC333332222211111222ACCBAACCBAACCBA3333322222111112ACCBAACCBAACCBA（）10JINSW习题（）311CC3333222211112CCBACCBACCBA3333322222111112ACCBAACCBAACCBA（）231CC3332221112CBACBACBA333333222222111111ACCBBAACCBBAACCBBA11JINSW习题（）2222222222222222321321321321DDDDCCCCBBBBAAAA4,3,211JCCJ（）9644129644129644129644122222DDDDCCCCBBBBAAAA4,312JCCJ12JINSW习题（）（）9644129644129644129644122222DDDDCCCCBBBBAAAA423232CCCC62126212621262122222DDCCBBAA013JINSW习题（）12211000010000100001AXAAAAXXXXNNNLLLLLLLLLLLNNNNAXAXAX111L（）0X右左NNNNAA111114JINSW习题（）12211000010000100001AXAAAAXXXXNNNLLLLLLLLLLL211CXC（）0X左11000XAAXNNL15JINSW习题（）122111000010000100000AXAAXAAAXXXXNNNNLLLLLLLLLLLNNCXC11（）L121210000000000000000NNNNNXAXAXAAXAXXXLLLLLLLLLLLLL16JINSW习题（）121210000000000000000NNNNNXAXAXAAXAXXXLLLLLLLLLLLLL121211NNNNNXAXAXAAXXL（）NNNNNAXAXAXAX12211L右17JINSW习题（）NN222221222223222222222221LLLLLLLLLLL（）NJCCJ,4,3,112L2002003020001200002000021NNLLLLLLLLLLL18JINSW习题（）（）12002003020001200002000021NNLLLLLLLLLLL2000203002002020001200002NNLLLLLLLLLLL19JINSW习题（）（）2000203002002020001200002NNLLLLLLLLLLL22N20JINSW习题（）NNNAAAAAD11111111111111111111111111321LLLLLLLLLLL（）NJCCJ,4,3,211LNNAAAAAAAA00000000000013211111LLLLLLLLLLL21JINSW习题（）（）NNNAAAAAAAAAD0001000100010001113211111LLLLLLLLLLLNNAAAAAAAA000100010001000111321111LLLLLLLLLLLNNAAAAAAAAA000000000000000013211111LLLLLLLLLLL22JINSW习题（）（）NNAAAAAAAA000100010001000111321111LLLLLLLLLLLNNAAAAAAAAA000000000000000013211111LLLLLLLLLLL1000010000100001111111113121121LLLLLLLLLLLLNNNAAAAAAAANAAAL2123JINSW习题（）（）NIRRI,4,3,211L1000010000100001111111113121121LLLLLLLLLLLLNNNAAAAAAAANAAAL2111000010000100001000011113121121LLLLLLLLLLLLNNNIINAAAAAAAA11121NIINAAAAL24JINSW习题（）XYYXXYXYXDN0000000000000000LLLLLLLLLLL11100000000000000000100000000000000000NNNYXYYXYXYYXYXXYXYXXLLLLLLLLLLLLLLLLLLLLLL1111NNNYYXXNNNYX1125JINSW习题80661510420620225ZXYXZYX402062225D80661523综合除法18875610801552108520D8,5,226JINSW习题38005325004000600025005000YXYX职员主管YX7638242YXYX202YX27JINSW第二章总习题（）12125431432321NNNLLLLLLLLLNIRRI,4,3,211L121254314321111NNIIIININININILLLLLLLLL（）28JINSW第二章总习题（）121254314321111NNIIIININININILLLLLLLLL（）1212543143211111NNINILLLLLLLLL29JINSW第二章总习题（）2,2,1,11LNNNJCCJJ（）1212543143211111NNINILLLLLLLLL1111113111200011LLLLLLLLLNNNINI30JINSW第二章总习题（）（）1111113111200011LLLLLLLLLNNNINI11111111111NNINNILLLLLLLNIRRI,3,211L11111111111NNINILLLLLLL31JINSW第二章总习题（）（）NIRRI,3,211L111111111111111111NNINNILLLLLLLLL1100000000001111NNINNILLLLLLLLL32JINSW第二章总习题（）（）1100000000001111NNINNILLLLLLLLL22211111NNNNNINI121211NNNNN33JINSW第二章总习题（）NXAAAAAXAAAAAXAAAAAXAAAAAXNFLLLLLLLLLLL（）NJCCJJ,3,211LNXXAAAXAAXXAAAXXAAAXLLLLLLLLLLL000000000000034JINSW第二章总习题（）（）展开1CNXXAAAXAAXXAAAXXAAAXLLLLLLLLLLL000000000000010000000000000NXXAAAXAAXXAAAXXAAAXAXLLLLLLLLLLL112000000000000001NXXAAAXAAXXAAAXXAAXALLLLLLLLLLL35JINSW第二章总习题（）（）10000000000000NXXAAAXAAXXAAAXXAAAXAXNFLLLLLLLLLLL112000000000000001NXXAAAXAAXXAAAXXAAXALLLLLLLLLLL1NF36JINSW第二章总习题（）（）1NFAXNFAXAN11120000000000NXAXAAXXAAXXALLLLLLLLL22111NNNXAAXANFAX11NXAANFAXNF37JINSW第二章总习题（）（）2N11NXAANFAXNF122NNXAAXAANFAXAX1222NNXAAXAXAANFAXL121AXAAXFAXNN12NNAXAAXAAXL21AXAAXXAXNN12NNAXAAXAAXL38JINSW第二章总习题（）（）2N21AXAAXXAXNFNN12NNAXAAXAAXLAXAXAXAXAXAAXXAXNNN1112121NNAXAX（归纳证明略）39JINSW第二章总习题（）NNNNN111111111111LLLLLLLLL（）NIRRI,3,211LNNNN1111111111111LLLLLLLLL40JINSW第二章总习题（）（）NIRRI,3,211LNNNN1111111111111LLLLLLLLLNNNN0001001001001111LLLLLLLLL41JINSW第二章总习题（）（）NNNN0001001001001111LLLLLLLLL121111NNNN12111NNNN42JINSW第二章总习题NNCOSCOS211COS211COS211COSLLL（）1N右左COSCOSKN无解73JINSW习题4234321321321XBXXXBXXXXAXBABABAABA42110024110311时有唯一解且01BA，其余无解。时有无数解且501BA74JINSW习题32132132113101XXXXXXXXX222330030111A时无解0时有唯一解且30时有无数解3TTCX0,2,11,1,1RC75JINSW习题515454343232121AXXAXXAXXAXXAXX543211111111111AAAAAA4,3,2,115IRRI514321011111111IIAAAAA（）76JINSW习题515454343232121AXXAXXAXXAXXAXX514321011111111IIAAAAAA（）4ARARAR4AR051IIA有解77JINSW习题R矛盾02211RRLRRRNNKKKK0,21RLNKKKKNRN,21RLRR0KNNKKKKKKRLRRR22110K否则0,21RLNKKKAEEENN,2121RLRRRLRR1E1,21ANRLRRNRN,21RLRR78JINSW习题A组的极大无关组1,21RAAARLRRB组的极大无关组2,21RBBBRLRR121,1RAAARARRRLRR3,RBAR221,2RBBBRBRRRLRR3,RBAR321,MAXRRR而,3BARR,212121RRBBBAAARRLRRRLRR21RR21321,MAXRRRRR79JINSW习题组相关KSR,1121RLRRRLRRRKRRKR矛盾002211RVRRLRRLLLLRR0,2111RRRLRRRRLRRLLKRS0RRLK组无关组无关KSR,1121RLRRRLRRRKR002211RVRRLRRLKLKLKLRR0,2111RRRLRRRRLRRLLKRS0RRLRBR矛盾RKR80JINSW习题NNNNNNAAAAAAAAAALLLLLLL2122221112111,2,11NJCCNJL1NAR0002122211211LLLLLLLNNAAAAAA0000101LMO100MV,101NIANJIJ81JINSW习题8118510818101A,11RRB21,RR是OAX的两个不相关的非零解T0,1,85,811VT1,0,811,812VB不唯一1001811858181B82JINSW习题OBASNNMNBRARAA2OAA2OEAANEARARAERAREARARAEARNERNBRARBRARBAR83JINSW1011NARNARNARNAR第四章总习题A为N阶方阵EAAANAREARAARNNARAR,MINNAR1NAROAANARAR1AROA而1AR1AR1NAROA0ARA的所有1N阶子式皆奇异84JINSW习题3,2,10IEAII是A的特征根，则00IA0EAI01AAAI011AEAII011AEII1是1A的特征根；（）85JINSW习题3,2,10IEAII是A的特征根，则00IA0EAI01AAAAI0AEAAAII0AEAIIA是A的特征根；（）86JINSW习题3,2,10IEAII是A的特征根，则00IA0EAI0232331EEAI23I是EA23