线性代数期末考试试卷答案合集

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2(1a--22j_4ஹÎaÏÐÑ,²ᑡᔣ\7ឋᐵ?஺2=a'221j_a<-2Ax1+%2+Ó=Ô35ஹÕÐÑឋ567᳝+஻2+Ö=—2ᨵ×>,¢>Nᨵ¢ØÙ>ÚÛ567ᨵ¢ØÙ>ᐗ1+%2+^^3=-2ÑÊᐸÃ>஺জÛX஺—2Ñ567ᨵ×>;ঝÛ4=2Ñ567¢>ঞÛ;I=1Ñ,ᨵ¢ØÙ7>,Ã>Xr2)’1ஹÞ3ஹ490106ஹ,=,a2=4=,«4=.Êàᔣ\7ḄáNl᩽ᜧ¢ᐵ7,ãᐸ¯ᔣ1-1-3-7aஹ3,ஹ-7µ\ᵨä᩽ᜧ¢ᐵ7ឋ⊤v஺’100ஹ7ஹA=010ÊAḄᱯå@Ḅᱯᔣ\஺ஹ021,æஹçè⚪´7ᑖµ'AQR஻▤5▣44T=/,=—1,çè.+4=0஺ᐸ/ᓫéH▣஺XXXᜧឋᦪὃ⚪ᫀஹ⚪1ஹ52ஹX¥13ஹsxs,nxn4ஹᐵ5ஹA-3E_ஹᑨab1ஹX2ஹV3ஹV4ஹV5ஹXஹᓫ⚗⌱⚪1ஹঞ2ஹঞ3ஹঞ4ஹঝ5ஹজ©ஹÄÅ⚪1ஹ

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)1ஹA,8n▤▣A3=0,ᑣᨵ()(A)A=0ᡈ8=0;(B)A+B=0©|=0ᡈើ=0;(D)|A+ᓽ=0஺2ஹA'6ᙳ஻▤+▣,(A+B)2=A2+2AB+82,ᑣᨵ()(A)A=E;(B)B=E;(C)A=Bஹ(D)AB=BA஺3ஹA/x஻+▣1234Ar=06ᨵ78Ḅᐙ⌕ᩩ<=>()(A)AḄᑡᔣABឋDᐵF(B)AḄᑡᔣABឋGᐵF(0AḄHᔣABឋDᐵF(D)AḄHᔣABឋGᐵஹ4ஹ஻▤+▣A᜻K+▣Ḅᐙ⌕ᩩ<=>()(A)AḄLMN஻F(B)|O஺0;(0AḄᱯQRSN7F(D)AḄᱯQRSTN7FUஹVW⚪(Y⚪ᐳ4M⚪,[⚪4ᑖ,ᑖ16ᑖ)5ஹ^4▤+▣AḄHᑡ_=-5,A"=>AḄbc+▣ᑣ|A*eo

56ஹA▤+▣,A2-A—2E=0,hi|(A+2E)T='121Yxi)rn7ஹlm3423஺+2x2=3D8,ᑣ஺=Ja-2r'7ஹ4,8ஹU2s/(xx,x)=2xv+3ὃ+x+2yz+2{|=>}~ḄᑣfḄR=p23>Oஹ⚪(Y⚪ᐳ2M⚪,[⚪8ᑖ,ᑖ16ᑖ)1+x1119ஹHᑡ,1!111+y1111\-y10ஹ஻▤Hᑡ{+32X”%%+3X,D஻=%%Z+3ஹ⚪(Y⚪ᐳ2M⚪,[M⚪8ᑖᑖ16ᑖ஺ᑏ3)11ஹ^ᔣA4%,%,BឋGᐵᔣA4஺2஺314BឋDᐵ஺v(1)ᨵa2,%Bឋ⊤F(2)%Tᵫ,%,Bឋ⊤஺12ஹA=>஻▤+▣£=>஻▤ᓫ+▣A+EnTi^,K/(A)=(E-A)(E+A)-1.(1)(E+/(A))(E+A)=2E;(2)_/V(A))=A஺ஹ8¡⚪(Y⚪ᐳ3M⚪,[M⚪12ᑖᑖ32ᑖ஺8¡¢ᑏᦻ¤¥ᡈ¦§¨)’200ஹ13ஹA=032
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8(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)f(f(A))=[E-f(A)][E+f(A)]-'ᵫপ¯v[E+/(4)í=g(E+A),ïᐭد«(ò)=Ï3-⚚᝞”]ᡷ+Ìᡷ+Ì(—)3+,᝞+&=<(E+A)-v(E-A)=A(4ᑖ)22ஹ8¡⚪13ஹ8v(1)ᵫ|øª=0¯AḄᱯQR4=1,4=2,4=5஺(4ᑖ)0ஹ(2)4=1ḄᱯQᔣA஺=-1=2ḄᱯQᔣAù=1o]=5ḄᱯQᔣAú(3ᑖ)(3)ÑᱯQRTGᑣ஺4ú}¬஺(2ᑖ)ভüý44ᓫᓄ¯(2ᑖ)P[ஹ01011一(5)P=(p],p2pj=0逝ªÿ11五0ஹV2

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P'AP0201ᑖ(0014ஹ:ឋAx=bḄAr=0R(A)=3,ᑣឋḄẠᨵ1᪀ᡂ!ᓽ#$%&'()ḄẠ஺5ᑖ+%☢,.ᔣ0J=2஻]%(%+6)!ᑣAJ=4<2=_஻3=2A஻i--^73=2b-b-b=0DEFGHJ=(3,4,5,6),/0,J''()Ḅ%Ạ஺᪷JឋḄK᪀L,MḄN3243x=4+=k,kGR஺7ᑖ546515ஹ:OজQঝὶTHឋ:Uτ+%+%3=°!᳝+2X2+ax3=0,x+4x,+a2x=0,]3%+2x,+x=a—1.3XYឋᨵ!ᑣজQঝᨵZᐳ!\ঞḄᓽᡠ_ᐰaZᐳஹঞḄbcd▣fghijkᣚHm0ஹ0ஹ200<7-104ᑖ400002a—1,01—aa—1,1°n”=1p!ᨵ(4)=«,)=2<3,ঞᨵ!ᓽজQঝᨵZᐳ!ᐸᐰaZᐳᓽঞḄN,Yp0ஹ000000000

101-1ஹᑣঞឋ,ᐸẠ0’-1ஹᡠজঝḄᐰ#$ᐳ&0,A'()ᦪஹ<4ᑖ,2°-஺=2/0ᨵrn-mDஹm-n'100ஹ2ஹbc▣A=0200ᑣAief<003>r1-Oo10o311A、0-OB、o-O22O011Oo-"11-Oo-oo231010D、o-O13oo-O012

113-12ஹ3ஹxd▣A=10-1,A*'(AḄz{d▣!ᑣA*|}~<1,2Ḅᐗ'(<ஹ-2I4>Aஹ-6Bஹ6Cஹ2Dஹ-24ஹxA'(▣!᝞ᨵd▣ᐵAB=AC,ᑣᨵ<AஹA=0BஹBrCpA=0CஹAwOpB=CDஹ|A|x0pB=C5ஹL3X4d▣AḄjᔣ0ឋᐵ!ᑣ312ஹxA'(¾Ïd▣!ᑣ±ᑡK³┯µḄ'(<Aஹ|A|21Bஹᑁ1CஹA-'=ATDஹAḄj<ᑡᔣ0'(¾Ïᓫ}ᔣ013ஹxA'(ÒÓd▣,C'(Òf⌮d▣,B=CTACஹᑣ<AஹAQBÕBஹAQBiÖCஹAQBᨵÇḄᱯÄÅ

12DஹAQBᔠÇ14ஹ±ᑡd▣|'(¾Ød▣Ḅ()233AஹBஹ00)’11nCஹ02-3Dஹ120<0-35;J02;=i#ᑖj⌱?⚪(ᐳ72ᑖ)ÚஹÛÜ⚪(Þᜧ⚪ᐳ106⚪,à6⚪2ᑖᐳ20ᑖ)ᑏâã!O¾¿Ḅâᫀᑏᙠà6⚪ḄÜåᑁ஺┯ÛᡈÛᙳᑖ஺11115ஹ356925361-1112316ஹxA=ஹᑣA+2B=11-I-1-24,17xA=(ajj)3x3,|A|=2,Aij⊤é|A||ᐗayḄëᦪì«(i,j=l,2,3),ᑣ(aτ]A21+a12A22+a]3A23)2+(a21A21+a22A22+a23A23)2+(a31A21+a32A22+a33A23)2Úஹ18ஹxᔣ0(2,-3,5)Qᔣ0(-4,6,a)ឋᐵ!ᑣa=ஹ19ஹxA'(3X4d▣,ᐸ3,X2ឋAx=bḄ2ÇḄ!ᑣ)ḄNஹ20ஹxA'(mXnd▣,AḄr(

13ûᑨýa4'(ᔲai,a2,a3Ḅឋᔠ;X'(!ᑣ_ÿᔠᦪ஺1-2-102'426-629ஹ▣A=*2-1023ஹ33334,:প(A);(2)AḄᑡᔣ!Ḅ"#ᨬᜧ&ឋ(ᐵ஺‘0-22ஹ30ஹ▣A=-2-34Ḅᐰ,ᱯ./01,11-8ஹ34▣T167▣D,9T-AT=Dஹஹ24-3,31ஹ:ᵨ<=>ᓄ@ᑡABC0᪗EF??f(Xi,X2,X3)=Xi+2xj-3X3+4X)X2"4X”3-4X3X3,HᑏJᡠᵨḄL&ឋMᣚ஺OஹPQ⚪(Sᜧ⚪ᐳ2U⚪,VU⚪5ᑖYᐳ10ᑖ)32ஹ=▣ALZA3=0,:PQE-A\⌮Y^(E-A)T=E+A+A2ஹ33ஹnobcdeB&ឋ=fAx=bḄ"#ᱯi,jY&2bcᐸmJAx=0Ḅ"#nẠiஹ:PQ(i)ni=no+gi,n2=no+&2ᙳbcAx=bḄis(2)no,Hi,n2&ឋ(ᐵ஺uᫀ"ஹᓫ⚗⌱|⚪(Sᜧ⚪ᐳ14U⚪,VU⚪2ᑖYᐳ28ᑖ)1ஹD2ஹB3ஹB4ஹD5ஹC6ஹD7ஹC8ஹA9ஹA10ஹB11ஹA12ஹB13ஹD14ஹCAஹ⚪(Sᜧ⚪ᐳ10YV2ᑖYᐳ20ᑖ)15ஹ616ஹ(11:17ஹ418ஹ-1019ஹni+c(n2-nD(ᡈn2+c(n2-n0),c0wxᦪ20ஹn—r21ஹ—522ஹ—223ஹ124ஹzs+z]+z—Z4ஹ⚪(Sᜧ⚪ᐳ7U⚪U⚪6ᑖ42ᑖ)20Y2-2186ஹ25ஹi(l)ABT=34034=1810ஹ21-10,ஹ310,(2)|4A|=43|A|=64|A|,W120ব=340=-2ஹᡠ14Al=64•(-2)=-128-121

1431-1-513226ஹi=30+10=40.201-51-5327ஹiAB=A+2Bᓽ(A-2E)B=A,(22(1-4-31(A-2E)-'=1-10=1-5-3.21J1-164>(1-4-3V423W3-8-6AᡠB=(A-2E)-'A=1-5-3110=2-9-6.1-164JI-123)1-2129s(-2130]-53-21p035)(1035)¡1-30-11-30-10112011228¢-....>---->---->0224011200880011U4-19J(013-112sVO0-14-14sVO00oj1002ஹ----IIlYᡠa4=2ai+iAὃ⇋a=xiaj+x2.000-217?<00000;প(B)=3,ᡠ(A´(B)=3ஹ(2)ᵫ¶A1BḄᑡᔣ!ᨵ·¸Ḅ&ឋᐵYBbc▤ºF,BḄ»1ஹ2ஹ4ᑡbcBḄᑡᔣ!Ḅ"#ᨬᜧ&ឋ(ᐵYᦑAḄ»1ஹ2ஹ4ᑡbcAḄᑡᔣ!Ḅ"#ᨬᜧ&ឋ(ᐵ஺(AḄ»1ஹ2ஹ5ᑡᡈ1ஹ3ஹ4½IJ,ᡈ1ஹ3ஹ5ᑡ¾bc)30ஹiAḄ¿¶ᱯ./ᐭ=1Ḅ2#&ឋ(ᐵḄᱯ.ᔣ!0"25/5/52Å/15ஹgi=(2,—1,0)T,&2=(2,0,1)TஹÃ34᪗EᓄYÄ5=-V5/5,஺2=475/151Æ3,01j(1/3ஹᐭ=-8Ḅ"#ᱯ.ᔣ!0€3=2YÃᓫÈᓄÄn3=2/3.1-2/3s

1526/52^/15/151/3)100ஹᡠ34▣0T=-75/5475/152/3ஹ67▣DA010ஹ0V5/3-2/3ஹ00"&;2Å/52V15/151/3ஹ(¾\ÊT=0-75/32/3ஹ)ஹÅ/5-4V5/15-2/3,31ஹif(X|,X2,X3)=(Xi+2X2-2X3)2-2X22+4X2X3-7X32=(X|+2X2-2X3)2-2(X2-X3)2-5X32^Y1=x1+2x2-2x3X1=Y1-2y2'1-2O'ÍÎ2=X?-X3YᓽYx2=Î2+Î3YÏᐸᦪ▣©=011\⌮YᦑÑ&ឋMᣚLx3=Y3ஹ00b)3=X3஺ÃÑMᣚᓽÄf(xi,X2,X3)Ḅ᪗EFyi2-2y2-5y2ஹ23OஹPQ⚪(Sᜧ⚪ᐳ2U⚪,VU⚪5ᑖYᐳ10ᑖ)32ஹPᵫ¶(E-A)(E+A+A2)=E-A3=E,ᡠE-A\⌮Y^(E-A)r=E+A+A2ஹ33ஹPᵫᎷAn()=b,Agi=0,A&2=0ஹ(1)AHi=A(n()+&i)=AHO+Agi=b,¸ᳮAq2=b,ᡠn1,n2bcAx=bḄ2#i஺ফὃ⇋/on()+/in1+/2n2=0,ᓽ(/0+/1+/2)n0+/1C1+/2C2=0ஹᑣ4)+/I+/2=0,ᔲᑣnoØbcAx=oḄi,ÙÚ஺ᡠh€1+Z242=0.ÛᵫᎷ,jYg2&ឋ(ᐵYᡠ/´0,/2=0,Ü4)=0.ᡠno,5,n2&ឋ(ᐵ஺