线性代数期末考试试卷+答案合集

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XXᜧឋᦪὃ⚪ஹ⚪ᫀᙠ⚪஺⚪2ᑖᐳ10ᑖ#1-311.(05X=0,ᑣ.=—-12-2Ar,+x+x=0232.(45ឋ678<:+a2+<=0=ᨵ?@ᑣABCDX]++:=03.FGH▣4,B,஺=%#,ᑘCDAC=CB,ᑣA<8ᑖPQ▤H▣஺a\24.H▣A=aaḄTᔣV8ឋ஺2l225.஻▤6▣ACD42-34-5=0,ᑣX7=஺Zஹᑨ\]Ḅᙠ^_ᑁ“J"┯]Ḅᙠ^_ᑁ“X”஺⚪2ᑖᐳ10ᑖ#1.(Tᑡg஺hᐗjkᜧl?ᑣ஺ு0஺#2.?ᔣVnop⊤rᡂtu8ᔣVḄឋ8ᔠ஺#3.ᔣV8w,a,“᝞yq

1ট/§©¯?ᔣV3.°ᑡ±⚪ḄQ#஺জtu஻h஻+1ᔣVឋᐵঝtu஻h஻+1ᔣVឋᐵঞtu”+1h஻ᔣVឋᐵটtu”+1h஻ᔣVឋᐵ4.A,8ᙳ~n▤6▣°☢´µḄQ#0জ(A,8ᙳo⌮ᑣA+8o⌮ঝ(4,8ᙳo⌮ᑣA8o⌮ঞ(A+Bo⌮ᑣA—Bo⌮ট(A+Bo⌮¶ijA,Bᙳo⌮5.(ᓃv,ᓃᓃQឋ678AX=OḄ»Ạ@½ᑣᓃ+/+ᓃ+ᓃQ4*=0Ḅ#2জ@ᔣVঝ»Ạ@½ঞ¿@টAḄTᔣVஹÀÁ⚪⚪9ᑖᐳ63ᑖ#X+Qhcdax+bcd1.ÀÁTᑡgoabx+cdabcx+d@.x+abcdx+஻+/?+c+dhcdax-\-bcdx+o+O+c+dx+bcdabx+cdx+஻+/?+c+dhx+cdabcx+dx+o+6+c+dbcx+d1bcd\bcd1x+bcd0x00,=(X+Q+/?+c+d)=(x+஻+/?+c+d)=(x+a+b-^c+d)x31bx+cd00x01bcx+d000x’301ஹ2.A6=A+28,4=1I0,ÍBo1""2-1-f-5-2-2@.(A-2E)8=A(A-24=2-2-1,B^(A-2Ey'A=4-3-2-111-223_

2ஹ’1-100’2134ஹ01-103.5=C=ÑjÑÑH▣XCDᐵ½gX(C—B)=ÒÍX஺001-110001ஹ0002,74.Ó஺ÔÕÖ,×ᑡᔣV8ឋᐵ?Ax+x2+X3=A-3t5.4~ÕÖឋ678Øx+ÙÚ2+Û3=-2ᨵÜ@@ÝᨵÞß@àá678ᨵÞßX]+%2+Ù^3=-2@ÖÍᐸ¿@஺জá14H—2Ö678ᨵÜ@;ঝá7=-2Ö678@ঞá4=1ÖᨵÞß8@¿@~X=

3XXᜧឋᦪὃ⚪ᫀஹ⚪1.52.4w13.SXS,nxn4.ᐵ5.A-3EZஹᑨ\]1.X2.J3.V4.5.Xஹᓫ⚗⌱⚪1.ঞ2.ঞ3.ঞ4.ঝ5.জஹÀÁ⚪1.

4x+abedx+/?+c+dbcax+bcdx+q+/?+c+dx+bcdabx+cdx+஻+b+c+dbx+cdabcx+dx+஻+/?+c+dbcx+d\bcd[bed1x+bcd0x00=(x+஻+/?+c+d)=(%+Q+/?+c+d)=(%+Q+5+C+4)/1bx+cd00x01bcx+d000x2.-2-1-f-5-2-2-(A-2E)B=A(A-2E)-12-2-1,B=(A-2EY'A=4-3-2-111-2233.234-■)00O-01232100C-B=c-B)=00123210000l_4321-100O--100O-[(c-B)r=-2100[(ci)=-2100X=E1-2101-21001-2101-214.iici——22111cl1%,%Ḅl=——a——Z2஺+1#~2஺-2#á஺=—ᡈ஻=1ÖᔣV8᜜,a2,%ឋ2202__—1____—1zjU22ᐵ஺5.জá/Iwl/lw—2Ö678ᨵÜ@;ঝá4=2Ö678@

5ঞá4=1ÖᨵÞß8@,6.213121312134901001-4-201-4-2(%a2,%%)—»T-1-3-70-3-4-1000-16-160-3-1-70-3-1-700-13-13100-2010200110000%4)=3ᐸq,a2,%᪀ᡂ᩽ᜧᐵ84=-2þ+2ÿ+%7.2—100\AE-A\=0A-l0=(A-1)3=O0-22-10ᱯ4=4=4=1ᐭi=i—Ooஹ⚪\A+I\=\A+=|A|/+A[=-(/+A)'=-(/+A)'.2|(/+A]=0,V|(/+A)|=O$ஹ⌱&⚪('⚪ᐳ4)⚪*)⚪4ᑖ,ᑖ16ᑖ஺*)⚪/0Ḅ23⌱⚗56ᨵ$⚗8ᔠ⚪:⌕<)1ஹ=A,8?n▤B▣,DEFA8=0,GIJᨵ()(A)A=Oᡈ8=0;(B)A+B=0N(C)P=0ᡈQ=0;(D)|A+M=0஺

62ஹAT8ᙳ?஻▤W▣K)A+B*2=A2+2AB+B2,ᑣJᨵYZYAZA=E+YBZB=£NYCZA=B.YDZAB=BA.3ஹ=A?mx஻W▣^_B`aAx=0bᨵcdḄᐙ⌕ᩩghYZYAZAḄᑡᔣklឋnᐵNYBZAḄᑡᔣklឋpᐵNYCZAḄqᔣklឋnᐵNYDZAḄqᔣklឋpᐵ.4ஹ஻▤W▣A?᜻tW▣Ḅᐙ⌕ᩩghYZYAZAḄu)஻NYBZ|A|H0NY0AḄᱯwEcNYDZAḄᱯwxEcNyஹz{⚪Y'⚪ᐳ4)⚪*⚪4ᑖ,ᑖ16ᑖZ5ஹ}4▤W▣AḄqᑡFব=-5,A*hAḄW▣G!J|A*஺6ஹA?“X஻▤W▣—4-2E=0,GIJ(A+2E)T=21ஹY1Z7ஹB`a23a+2x3ndG=2a-248ஹy_/Y,2Z=2ᱏ+3¥+ᵨ+22+2/hḄᑣfḄhOஹ⚪Y'⚪ᐳ2)⚪*⚪8ᑖ,ᑖ16ᑖZl+x1119ஹqᑡFO=:y"J'111+y1111\-y10ஹ஻▤qᑡF᳝+3%…%2¥஽+3…%D”='.:X|x•••x„+322ஹ⚪Y'⚪ᐳ2)⚪*)⚪8ᑖ,ᑖ16ᑖ஺ᑏ0ª`Z11ஹ}ᔣka%,4,«3lឋpᐵᔣka4&3஺4lឋnᐵ஺Y1Z«¯ᨵ°±3lឋ⊤0;

7(2)%x¯ᵫlឋ⊤0஺12ஹ=Ah"▤WB▣Eh஻▤ᓫµW▣A+E¶⌮/(A)=(E-A)(E+A)T஺(1)(£+/(A))(£+A)=2EN(2)/(/(A))=4஺ஹd¸⚪('⚪ᐳ3)⚪*)⚪12ᑖ,ᑖ32ᑖ஺d¸¹ᑏ0ᦻ»¼ᡈ½¾¿)’200ஹ13ஹ=4=032,<$3ÁW▣ÂÃÄÂ$“Â?ÅW▣஺23,%1+x+x=02314ஹB`a-o25

8ஹ⚪9ஹd×$qØ×yq×qØ×2qÄ:xx0oI1-x1iD=00yy1il-yx0001-X10×yᑡØ×$ᑡ×2ᑡØ×ᑡÄ஺Y4ᑖZ00y010i-yᢥ×$qÚÛÄ-x10D-x0y00i-yᢥ×ᑡÚÛÄ$Xo22D=-xy]=xyoY4ᑖZy(n10ஹdÜᔜᑡÞᑮ×$ᑡᯠáâ×$ᑡḄÊãä+3,åÒªqᑡFḄæᣚᓄIi=l,7?éÅêqᑡF1(n\1D.=2᳝+3Y4ᑖZ\/=l71X2•••x஻+31x2%030=Ex/+3\/=1003=31ë,+3Y4ᑖZ

92ஹ⚪11ஹ(1)ஹã?a2,&3%lឋnᐵᡠî%ïlឋnᐵ஺ðJa2,a,lឋpᐵᦑJ¯ᵫa2,%lឋ⊤0஺(4ᑖ)ᔆ(q°°)=3,(2)ஹ(ôõ)}xᑣ%¯ᵫ24ölឋ⊤0123%=&J+ka+k3a3o22ᵫ(1)a,¯ᵫø«3lឋ⊤0xù=%=4%+t2ai°ᡠî஺4=ᓃ஺1%+2%)+A2a2+û3a3ü⊤&஺3&4lឋpᐵýþ஺12ஹ(1)(E+/(A))(E+A)=[E+(E-A)(E+A)T](E+A)=(E+A)+(E-A)(E+A)T(E+A)=(E+A)+(E-A)=2E(4ᑖ)(2)/(/(A))=[£-/(A)][£+/(A)rᵫ(1)[E+/(A)=(E+A),ᐭW(A))=[JET)(E+A)ὶ(E+4)=/+A)-3T)(E+Aᡷ+4)(E+A)(E-A)=A(4ᑖ)22!ஹ#$⚪13ஹ#(1)ᵫ|/IE—)=0AḄᱯ-./4=1,4=2,4=5஺(4ᑖ)

10ஹ0(2)4=1Ḅᱯ-ᔣ3/஺=-1,4=2Ḅᱯ-ᔣ3/4-4=5Ḅᱯ-ᔣ3/563ᑖ7(3)8/ᱯ-.9:;ᑣ&>?஺62ᑖ701647D஺2EᓫGᓄ0=62ᑖ70I0I1@P=(PBP2P3)=0C>f1a0>(\00(6)P-'AP^02061ᑖ7ஹ005714ஹ#IJKLMឋOPQAx=8TUḄKLOPQ/Ar=08R6A7=3,ᑣKLMឋOPQḄXẠ#Zᨵ1\J]#᪀ᡂ,ᓽabC\J]#cdeḄXẠ#Z஺65ᑖ7fCO☢hᔣ34=-6%+77,ᑣ-A(271-%-%)=2A஻|CA%-A%-2b-b-b-0lmnoJ=63,4,5,67qHO,JtdeḄC\XẠ#Z஺᪷vJKLMឋOPQ#Ḅw᪀xyOPQḄz#/

11’3ஹ2ஹ43x=4+7keRo(7ᑖ)546.15ஹ#Dজ~ঝὶJKLMឋOPQ:%1+x+x=0,23$+2X+ax=0,23x+4X+a2x=0,x23X]+2X+x=6Z-1.23JKLMឋOPQᨵ#ᑣজ~ঝᨵᐳ#ঞḄ#ᓽ/ᡠᐰᐳ#.TঞḄ▣N;ᣚ:’1110ஹ110ஹ12a001a-\0=->,(4ᑖ)14a2000(a—2)(஻—1)0J21a-1.ஹ001—aa-l>1°஺=1ᨵ(4)=ᔆᖪ)=2<3,OPQঞᨵ#,ᓽজ~ঝᨵᐳ#ᐸᐰᐳ#ᓽ/ঞḄz#f1010"|(0000)’-1ஹᑣOPQঞ/KLMឋOPQᐸXẠ#Z/0<1>Jpᡠ¦জ~ঝḄᐰᐳ#/§0,a/a¨©ᦪ.(4ᑖ)2°a=2ᨵr(4)=«Z)=3,OPQঞᨵ¬C#"1000ஹ0101001-1ஹ0000,

12ᦑঞḄ:1,ᓽজঝᨵᐳ=14ᑖ!ឋ#ᦪ%⚪&'ᫀ)*+,-ᑖ⌱/⚪0ᐳ28ᑖஹᓫ⚗⌱/⚪03ᜧ⚪ᐳ145⚪675⚪2ᑖ6ᐳ28ᑖᙠ75⚪ᑡ:Ḅ;<⌱⚗=>ᨵA.-6B.6

13C.2D.-24.¯AdO▣᝞ᨵ▣ᐵZAB=AC,ᑣ³ᨵ67A.A=0B.B*CA=0C.AwOB=CD.IAIWOB=C5.¶x3X4▣AḄᔣ3QMឋ·ᐵᑣ¸AT
;¹6)A.1B.2C.3D.46.¯º\ᔣ3Qa”a2,6^¾ᓽg…6,ᙳMឋ:ᐵᑣ6)A.ᨵ9ᐰ/0Ḅᦪ¼1A.2,ᐭsÃAIaÄX.2a2+…+ᐭsas=0¾ᐭτB1+ᐭ2B2+…As஺s=0B.ᨵ9ᐰ/0Ḅᦪ¼1ᐭ2,…3üτ(a|+61)+ᐭ2(a2+82)+…+ᐭs(as+B.)=0C.ᨵ9ᐰ/0Ḅᦪ¼1A2,…AsüB(aI)+82(az—B?)+…+ᐭs(as-3s)=0D.ᨵ9ᐰ/0Ḅᦪ¼”A2)—,L¾9ᐰ/0ḄᦪNIu2,…,Ãᐭia|+ᐭ2a2+…+ஹsas=O¾1B1+U272+…+u0=0ss7.¯▣AḄ¸/r,ᑣAË6)A.ᡠᨵr-l▤Îc9/0B.ᡠᨵr-1▤Îᐰ/0C.ÏÐᨵ•\r▤Î9;¹0D.ᡠᨵr▤Îc9/08.¯Ax=bdCJKLMឋOPQ,”dᐸa¨2\#ᑣÙᑡwÛ┯ÝḄd6)B.|Oi+gLdAx=bḄC\#A.ni+n2dAx=oḄC\#c.nqn2dAx=oḄC\#D.2nn>Ax=bḄC\#r29.¯n▤O▣A9×⌮ᑣ³ᨵ67A.¸6A7

14637▤O▣Ùᑡ▰àË>áḄd6)A.᝞âᙠᦪ¼¾ᔣ3aÃAa=ᐭa,ᑣadAḄä¹ᱯ-.¼Ḅᱯ-ᔣ3B.᝞âᙠᦪ¼¾J]ᔣ3a,Ã6¼E-A7a=O,ᑣᐭdAḄᱯ-.C.AḄ2\9åḄᱯ-.צᨵå•\ᱯ-ᔣ3D.᝞ᐭX,ᐭ3dAḄ3\æ9:åḄᱯ-.a6,a,5çLdAḄä¹A”X,ᐭ3Ḅᱯ222-ᔣ3ᑣa|,a,<13ᨵ×èMឋ:ᐵ211.¯ᐭ஺d▣AḄᱯ-OPḄ3é᪷AḄä¹ᐭoḄMឋ·ᐵḄᱯ-ᔣ3Ḅ\ᦪ/k,ᑣ³ᨵ6)A.kW3B.k<3C.k=3D.k>312.¯Ad>?▣ᑣÙᑡwÛ┯ÝḄd6)A.IAF³/1B.IA³/1C.A-I=ATD.AḄ6ᑡ7ᔣ3Qd>?ᓫGᔣ3Q13.¯AdëTì▣Cdë×⌮▣B=CTACᑣ6)A.A~B:íB.A~B9;îC.A~Bᨵ:åḄᱯ-.D.A~Bᔠå14.Ùᑡ▣Ëd>ð▣Ḅ/6)23341A.B.,34,26,

15n00ஹpirC.02-3D.120<0-35>J02>,-ᑖh⌱/⚪(ᐳ72ᑖ)ñஹòó⚪(ôᜧ⚪ᐳ10ö⚪÷ö⚪2ᑖᐳ20ᑖ)9ᑏ#$ùPD>áḄ$ᫀᑏᙠ÷ö⚪Ḅóûᑁ஺┯òᡈ9òᙳ·ᑖ஺11115.356=.9253616.¯A=(]B=C].ᑣA+2B=-------117.¯A=(aijbx3,IA1=2,Ajj⊤IAIᐗa.Ḅᦪ(i,j=l,2,3),ᑣ(aiiA2τ+a12A22+a13A23)~+(a21A21+a22A22+a23A23)~+(a31A2τ+a32A22+a33A23)~=.18.ᔣ(2,-3,5)ᔣ(-4,6,a)#ឋ%ᐵ'ᑣa=.19.A)3X4+▣'ᐸ./3,01'112/234#ឋ5678*=1)Ḅ2:;<Ḅ='ᑣ>Ḅ?=/.20.A)mXn+▣'AḄ./r«n),ᑣ34#ឋ567Ax=0ḄF:GẠ=IJᨵ=Ḅ:ᦪ/.21.ᔣaஹBḄNOP4/2Q3,ᑣᔣa+6a-BḄᑁT(a+B,a-0)=,22.3▤+▣AḄVᑡIAI=8,XYAᨵ2:ᱯ[\-1Q4,ᑣ]Fᱯ[\/.(0106](2ஹ23.+▣A=1-3-3,XYa=-1)>ḄF:ᱯ[ᔣ'ᑣaᡠ`aḄᱯ[\/F12;ஹF2108>24.de4ff(X|,X2,X3,X4,X5)Ḅ./4,ijឋᢣᦪ/3,ᑣᐸln/oஹpq⚪(sᜧ⚪ᐳ7w⚪'xw⚪6ᑖ'ᐳ42ᑖ)‘120ஹ3-125.A=340(-.{(1)ABT}(2)I4AL240,-121>31-126.pqVᑡ:132011-53ᑨa4)ᔲ/a”a,a3Ḅ#ឋ7ᔠ}9:,ᑣ{7ᔠIᦪ஺2

16'I-2-102-2426-629.+▣8=0,A2-1023ஹ33334,{1.A}2AḄᑡᔣ7ḄF:ᨬᜧ#ឋᐵ7஺‘0-22'30.+▣A=-2-34Ḅᐰᱯ[\/1,1Q-8.{i+▣TQ`+▣D,TAT=D.ஹ24-3,31.ᵨ5ᓄᑡe4f/᪗nfx],X2,X3=x}+2x5-3x+4xτx2-4xτxj-4x2^3'ᑏᡠᵨḄ.#ឋᣚ஺ஹ¡¢⚪sᜧ⚪ᐳ2w⚪'xw⚪5ᑖ'ᐳ10ᑖ32.5▣A£A3=0,¡¢E-A¥⌮'§E-A-1=E+A+A2.33.)234#ឋ567Ax=bḄF:ᱯ=''g2)ᐸª7Ax=0ḄF:GẠ=I¡¢1n«no+1,12=110+&2ᙳ)8*=1Ḅ=}2Ho,Hl,n?#ឋᐵ஺±ᫀFஹᓫ⚗⌱¶⚪sᜧ⚪ᐳ14w⚪'xw⚪2ᑖ'ᐳ28ᑖ1.D2.B3.B4.D5.C6.D7.C8.A9.A10.B11.A12.B13.D14.Ceஹ¸¹⚪sᜧ⚪ᐳ10¹'x¹2ᑖ'ᐳ20ᑖ15.617.418.-1019.ni+c஺2-nIᡈn2+c஺2-Qi'C/½¾¿ᦪ20.n-r21.-522.-223.124.zf4-Z2+Z3-Z4oஹpq⚪sᜧ⚪ᐳ7w⚪'xw⚪6ᑖ'ᐳ42ᑖ'12OY2-2ஹ25.=1ABT=3403421Ä—10;

17’86ஹ=1810<310>(2)I4AI=43IAI=64IAI,È120IAI=340=-2.-121ᡠÉ14Al=64•(-2)=-12831-11-11-51313-126.=2010101-53-530511=-111-1-5-505220=30+10=40.-5-5027.=AB=A+2Bᓽ(A-2E)B=A,È’223Í1-4-3ஹ(A-2E)■=1-101-5-3<-12-164;-4-3Y423ஹᡠÉB=(A-2E)-,A=1-5-31064;23>3-8-6ஹ2-9-6-2129>230]-53-2ஹ1-30-11-30-128.=Fm02240112<34-19;<013-1ফ035ஹ<1035ஹ020120088001<00-14-14}<0000}1002>01010011<0000>ᡠÉa4=2aj+a+a,7ᔠIᦪ/2,1,1).23—ὃa4=x]a1+X2a2+X3a3,

18—2x]+x2+3x3=0x]-3x2=-1ᓽ2x2+2x3=43X]+4x2-x3=9.567ᨵÐF=2,1,1Ñ'7ᔠIᦪ/2,1,1.29.=`+▣AÒVÓÔVᣚ-2-102ஹ0006-2A0328-2<0963-2>-2-102ஹ-2-102ஹ0328-30328-3=B.0006-20003F1<000-217><00000>(1).(B)=3,ᡠÉ.A=.(B)=3.2ᵫÖABḄᑡᔣ7ᨵ%<Ḅ#ឋᐵI'ÈB)▤×n'BḄØ1ஹ2ஹ4ᑡ)BḄᑡᔣ7ḄF:ᨬᜧ#ឋᐵ7'ᦑAḄØ1ஹ2ஹ4ᑡ)AḄᑡᔣ7ḄF:ᨬᜧ#ឋᐵ7஺AḄØ1ஹ2ஹ5ᑡᡈ1ஹ3ஹ4ᑡ'ᡈ1ஹ3ஹ5ᑡÚ)30.=AḄÛÖᱯ[\ᐭ=1Ḅ2:#ឋᐵḄᱯ[ᔣ/g1=2,-1,0T,&2=2,0,1T.‘2Ý/5ஹ’20/15ஹßi᪗ᓄ'à3=-V5/5,ã475/15.ஹ°>ஹä3,ᐭ=F8ḄF:ᱯ[ᔣ/1j(1/3ஹ2,ßᓫåᓄà113=2/3.1-2/3}’2ᵨ52715/151/3ᡠ{i+▣/T=-75/5475/152/30V5/3-213,00ஹ`+▣D=000-8;’2ᵨ52V15/151/3Ú¥æT=0-A/5/32/3.).75/5-475/15-2/331.=f(X],X2'x)=(X|+2x-2x3)2-2X22+4XX3-7X23223—(x]+2x2—2x3)2—2(X2-X3)5X?2.

19Y1=xi+2X-2X23X]=yi-2y2Y2=X-X,ᓽ.X2=Y2+Y323X3=Y3Y3=X3'1-2o'èᐸIᦪ+▣C=011¥⌮'ᦑé#ឋᣚ.஺<001>ßéᣚᓽàf(X|,X2,X3)Ḅ᪗nyi'--2y22-5y2.3ஹ¡¢⚪(sᜧ⚪ᐳ2w⚪'xw⚪5ᑖ'ᐳ10ᑖ)32.¡ᵫÖ(E-A)(E+A+A2)=E-A3=E,ᡠÉE-A¥⌮'§(E-A)-I=E+A+A2.33.¡ᵫᎷAn()=b,Ai=0,A&2=஺.(1)An|=A(Q()+^i)=An()+A&«b,<ᳮAn2=b,ᡠÉ2'112)8*=1>Ḅ2:=஺(2)ὃ⇋/()no+8ni+beO'ᓽ(lo+ll+(2)no+Ai+'2&2=0.ᑣ/o+/i+/2=O,ᔲᑣnoï)Ax=oḄ='ðñ஺ᡠÉl\K1+Z2&2=஺òᵫᎷ'"'&2#ឋᐵ'ᡠÉ/«0,/=0,ôÈ/o=O.2ᡠÉn(”Hi'n2#ឋᐵ஺