Bài giảng Hình học tuyến tính 2

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Bài giảng Hình học tuyến tính 2 gồm có những nội dung chính sau: Bài giảng Hình học tuyến tính 2 gồm có những nội dung chính sau: Bài 1: không gian xạ ảnh, bài 2: tọa độ xạ ảnh, bài 3: tỷ số kép, bài 4: nguyên tắc đối ngẫu. Mời các bạn cùng tham khảo để biết thêm nội dung chi tiết!

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Nội dung Text: Bài giảng Hình học tuyến tính 2

/ Hình hoc tuyên tính 2 . Chương 1. Không gian xạ ảnh Bài 1. Không gian xạ ảnh 1. Khai mein thing gianxaaeik truing -1-21 dim ✓ Coo d-qi ' V let k ' + fho lkgvt trees a so , = n+ ' [ V3 la-t.oipcaikgconm.it chiiiecua v kyihi.eu ✗ it I la-mi.tt?aph?opva- IT [ V3 → P la-m.it song oink : ' Khidr ta go.imoi.br 3 goin l P T V ) la-mi.it kgxqaeih ( hay Pta ' , w , , . kgxa triongiiug vs kgvt V1 nla-soichieiicuakgxa.aieh.ph air tri aid P , gotta diein . 2 Khong gian con cud kgxqaeih } cud EW ] la-t.apcaikgconm.it chien ' ✗ ét wea- 1 kg con Khai {E v . cud W ✓ w . Rciraug [ W] c [ V3 . Ta go.it ( [W 3) la-m.tt ± , kg xD con lphaiig ) trong P :* dim ltl [W ] ) ) = dim W - I ✓ ={tÑ < u→>w= → Cho phaing a : + Néu dim a = 0 → ✗ bi lotion Neil dim a + = A → a lot dieting thangka aich / . Neil dims = n - a → a lot siuephaug 3 Vi die vÉ kg ✗a. oink . hinh trees truing son ! ✗ it kla-ltniemglaid-a.is ' 1. ME s -1-21 " " Trier K l { 03 , xét wiptqhé tuong dieting ~ : (Koi ( yo ty.it/-i--O,nXetP=lk . - . ixn ) ~ , . . - syn ) F t E k SK Ki = chien lkét "" "" ) / la-m.it klgxq airs I { 03 ~ . P n - is K that va.is , xét : "" JT : I K ] → p ( it = l ko , . . . . sent > [ñ ] → top uing as qh ~ 1kg con a chute suis bin . recto ñ ) IT lñ aids Rirñy song . →
"" 2. Mei hiuhbo : Trong kg aggine A , xét 1 d- iein 0 ✓a- tap BCO) cat dieting thang di qua 0 . • la-mi.otkgxa.ae/rh,lieisketisAn+TXetsongairh 0 ' khido BCO ) : 17 : [ Ñi ] → BIO ) IF uiougtnaingotiqua 0 chip twig ' [ñ> → A- co leg ME hints sueie Cate : " 3. Trong kg Euclid E , xétmotsiieucaii S tain 0 , bk R la-t.apeaci.apd-i-einxayintainaias.khiotoseaekgxa.auk.tt IS ] µ÷* : BG ) → [ S] d + ⑨ n (d) 4. Boi sung phaiitivitgnva-okgajgui.de Ekg " ✗a. auth . a) didnt : ✗ it d-1- A ' vñediéin 0 nain ugoai An la-dotg-thayxa.at ' {A } ' • O P = { 0 } U it la-mpagginechiia-mva-ova-B.co ) lñbo ' M ✗ A ^ KE A Cai att di 0 A " qua trong ☐ : Pd → BIO ) " ME A H OM O µ d-tatiana Orci 11 is An b) dim = 2 . Trong A ' ✗e 't mp A " (✗ ) di qua O song song voi A! ✗ét Tho ) la-bcicaia.tt :p gpn y trong A } di qua B-to] lobo ' cat att (a) voi i. ✓a- O, trong - - - - - - - - . . . . . - . . di qua 0 . if those a- Amp ✗a. airs 2 chien P " \ B' 10 ) " " (a- a att ✗ a. aid P II A V { D } ) Taco song ' arik : tho ) → A ' v Is lo ) de Ico ) → d d ¢ Ñ lot→ ' d n A B- lol trong do Bicol " ' A la-mi.fmp a' h att gait d-c. go.ilad-uiohgvcita.es V ✗a. u , (a- a ✗ , A' ' Cua mp ✗ a. all = mp ayin u d-tapir U A diein -ÉÉdd ( Phair vs teen )
a'uh , phu.thu.io?aairh-yCheiig-.D--ieintiCCu-71c-Pnh?anula-m.ot vectodqidi.eu 4 . D- of Yap ✗ a. ' . Ichi do , tu , te o cxla-dvectod-a.edu?ncua'sTC5u' 7) eat otiéin ants rien caivectod-ai.de?enHuTio. . .i mla-dTttltou-o,. .,tmu?n D- In : P . , . Pm d-iu.io go.ila-ot.io Yap ✗ a. , . . . ( ti ⇐0 ) d- Ht ) * Trai la.icuad-o.tl?apxa.auhla-phu.thu.ocxqairh . Tink chief la-m.it/cgx.aaul.D:Xefmo?tho.eaikg ' : Giao ± 0 Cua Cai kg ✗a. anti con con ai = Tl I [ Wi 7) ' Taco : A [ Wi ] = [ h Wi ] I c- I IEI v5 Wi o n Wi [ Wi ] [ ¥ Wi ] ( → 3 . i c- I , ti ) c- [ Wi ] ii c- Wi i ñ c- nwi [ Wi ] C [A Wi ] i c-I win Jl ( n [ Wi ] ) = A Ji ( [ Wi ] ) itI I C- I trees 11 bin 17 I [A Wi 3) Fossil IEI Cheiy khoriggiauhenk-etaeacacpha-irggiaola-giaoueacaikq.ua ' +1 : 't . 5 khoirggianxa.airhsiukbo.im?ott.ap . +1 Cho s ta e t.ap-i-0.KGX.aaiehcouuhonhai-dueiasd-d.ee KH : < s > vñ d-c. go.ila-kgxauksuihbo.is NI : S = n x kg con choices +, Voi moi MES , taxét Tem let 1 recto d-a.id-ie.in cud M ( Mccuin > ) = M ) ' Ichi d-o : = 17 ( [< ñm : MESS ] ) kg con ✗ = M ( CWT ) Chia S ?Ég chieiiuiaw con 1
ME S ; M = 17 ( ( ie'm > ) E M ( ( WI) → Tim c- w → c- d. t) chines > = chin [ ñm : Mes > - 1- Ichi < Aoi thay cho S { Ao Am } Ky hie.ie ' + ) = , . . . . Oa . . . , Am > C { Aoi . . . Am} ) Taco do ahh ' doin ( Aoi . . . Ams = m ⇐ Aoi . . . . Am :c Yap ✗a. +, Cho 2 phasing a voi B. khi do ' ✗ + 13 :-. < ✗ up > dien la + B) = doin ✗ + dim B- dim Ian B) Neil ✗ A B = 0 , guy uÉc Him in B) = - 1 . D: Gia sci ✗ = Til CW ] ) , 13=17112 ] ) . ✗ + B = M K w v27 ] ) = Tl I [ Wt z] ) ✗ n B = Tl lcwnz ) ) = Taco dim dim @ dim dim dimlwnz -1 ' : ✗ + p = + 2) - l = w + z - = dim ✗ +1 + dim B. +1 - dim an p - l - l = dine ✗ + dein B - dein ✗ hp ☐ He quoi ? : Trong kg ✗a. ahh n Chien niu , hai keg con ✗ voi B citing si ' Chien > n thi ✗ np -1-0 . D-qibiét trong , mpxoi 2 d- wing , thang ✗a. ainhluoncé d-Ein Chung . 3 d-aim ' Dinh ly Desargues : Trong mp a. aish oho ✗ 2 b.ci 1A , B. c) , ( A :B:c 's . go.im , Ms P thing la-giaocuacaica.pd-uongtha-irglBC.BG , ( CA IA's , , ' coating ' CAB A'B' 1 , . Ichi do M . N . P thaiighañg ⇐ AA's BB , guy . e Goi . ' a- ii. E. of iii. É thing la-vectod-a.idie.ir and A , B C,, ' ' ' ' ' B A B , c , e . § AA ' = 17 ( [said ' > J) cc ' = 17 ( [ { E. E > 3) - - - - - - " M ¥ biib > 3) - - - ' - - - - BB ([ - - - ' M [ - - - - - = N A C AA'_É'=M([Caa'>ncb) D- orig guy ( k° gian con lchieii B ① :{ F- " + ' 7 F' ± o sic ' ' b→ ' r = y5 + y r = 2- E + ÉÉ
F F ' Cho yb→ 28 É i. in { ' b' ' -1-0 Sao + z y - = - = , ZÉ - ✗a- ' = - z 'É + riot : = ñ 'Ñ ' ✗ a→ - y b- = - stat + y : = p→ Cbt ' → in c- ( b- , E > n , É > voi to M= ti ccñi >) F- 145 > ) ' . N = IT Ccñ > 7 , P = Tl Hoh nita ein p→ ' < in ñ > ' , p = - + ñ I c- , P C- MN " " ⇐ ' ' b- ' ' a- ' I c- = ✗ a- + y - in j, - - iii. . - - - - - - - - . . - . in ñ ' ñi ñ Choy : + Bài 2. Toạ độ xạ ảnh 1. Mug time ahh a'uh nchiéie d-iém " ✗a. : Trong kg ✗a. P , moi he : goin n -12 So Sai , . . . . Sun Sao cho n -11 d-i-einbatky-trongohungd-eiid-i.cl?apx.aanh.d-u?oo go.ila-mu.ctieiexa.a.nu 2. Toa d-i. . ✗ a. auth : Xét lmiectieie ✗a. añh : 1 So , Se Se , , . . . , Sn ; E) . Ichi d-o ' , tin tai cai vectod-qidie.cn éo éi : . , . . . , En , é cud So , s, , . . . , Sn, E Sao Cho E' = to + . . . + e-n ' Lei Ei go.ilaboveetod-qidi.eu SÉ ' ' , , . .. . Ein , é ) d-info ma co ' ( so , - . . .sn E) , Trong mug tieienay : Si : d-ink F- d- iéiinotdn i. : v. Ichi oto voi ñ la-2d-a.idie.is bait Kyi cud ' ' " ✗ it lot M ' µ lñ trey y ma I . , it : u→= Xo ?eo + . - . + Xnéir ' I = yoéo + . . . + yuéu thi Ft to Sao Cho Yi = t ki ti Taavi la-toa.dz?thuaiinhai-aea'Md-oi-vsmu.ctieielSo....,9uiE : [ Xo :X , : . . . : kn ] I [ yo :-. . : yn ] voi goi Ix . : Ka : . . . : Ku ) ) Chui y ' : Alvi trees thing ph.uthe.iocva-ovi.ec big bo ? veitod-qidi.in Ceiiéi . . . . . ii. é ) ' .
D: Goi Ceci , - . . éii , É ) la-td-a.idi.eu Khai cud mug tou , I = Eéi ' éi iii. éii die { = ✗ éi . - + = . i - . . . + duéu : É ' = ✗é ' = do to + → An Eu éñ duet = do d) - I . + . . . + ( Xu d) En - = 0 \ É ' = d é ' Xo = - . . = Xu =D V§y hai be d-a.idi.in cuing 1 mug tide sé Sai Khai uhaun.io/-haiigsoinhais → Viii M bait kej co uectod-qidie.is ñ , Ñ ' : = Koei + . . . + kuéu yo ÑÉ Éu = + . . . + Yo → Ki = A yi Ki → ( Xo : . . . : Ku] = [ yo : . . . : yn] 3. To a. d-& sieur phasing ✗it siiu pending (a) . Trevi (a) ta laiy notion do Kip :c takin ✗ = n - e) , Ari . . . An vectootqidi.int/uiu-i,. . i nvoFuij=EaijeTi--OXetMla-ld-'baI- vii. cat xueii.la-lvectod-ai.de?euceedM. ' tag , ? Hato [ x . : : . . :xu ] . Ichi do ii = koéo + . . . + ' ME ñ (Tei ,u→u ka { ✗ Ku :/ ⇐ c- > ⇐ Ko . . - , . . . ↳^ "^^ " Am → - ÷ ÷ : . . Aou den - - - Ann phaiig ctoivoimuctieie ' aoko + air, + . . . + Anka =o : ptriuh wa Siete ✗ ban otiin . 4. Phiiingtniikeuaphaiig . Phaiig = giaocaisieiephairgneisptcudnoaidapgf.ie pt (B) : AK = 0 din 13 = Cnt d) - rank A -1 = n - rank A. Co ' men otiéin A , . . . Am . Boi sung Amen , . . . . , An . oteith-auloto.cl?ap . ( Ao Ibo Ai ) ) ' ✗i = , - . . . , Au → in = < Aoi - - - , Am > i=m+ ,
* D- iyhly Pappus : trongmipxa.auk.chohaiboibad-ieinlha-irgha-ycA.B.cl voi CA:B ' d) M= Bin B' C N= CA'M C' A- F- ABIA'B , . Goi . , , Minhplhñughairg ' khido , * ! ! % Chore niuctieiexqaerk ' ' ( A. B. A ; B ) N M p All :O :O) A' 10 :O 1) : 1310--1 :O) B' ( f. 1:17 13 i • ' ' ' A CEAB , c=tA+ÉB It -1-0 , vineii t=O→c=tB → ⇐ B) Clt :1 :O) choir -1=1 kiahiiimgvitoqdoxa ) ' → ( → A' B' c 'll ' c C- → :D : 1+5 ) ' Bc : ko ka ke 0 1 0 = 0 111-5776 - k=0 1 1 1+5 CB ' ko ka ka =D Xo - tx, + It 1) Kz- =O t 1 0 1 1 1 toa.at?aeciMla-nguia.nl--tci-mHuiiongcua { → Its ko - ka -0 - ko - txa -14--1194=0 { → xo=t . X , = tlstd ) - s Kz=t( Stl ) All ko ka Xu = 0 (1+5) Ki - Xz =O 1 O O l l 1+5 ' CA Ko H X, = 0 Ko - th =0 t 1 O O O 1
{ ' → N lñ no Cua 11+5774 → 2=0 Ko - t ✗ a =o → N ( t : 1 : its ) Choy 94=1 → Ko , Xu ' f ; ; 1=0 AB ×. - ×. -0 1 0 0 "B ; ; ;/ =o % -0 - 0 0 1 → P ( o : e : e) 3 otiiin * thang hairy → det =o ✗ it ° ^ ^ t 1 Its = t2 ( Stl ) - tcsel ) - tics -11 ) + ts tt t tls -11 ) - s thts ) = 0 → M , N , P thang hang
Bài 3. Tỷ số kép ' kép aid action thang hoeing ' n ti son laiyreeto-aib.ci uiy ' Cho Ai B. GD thairghang (A- B) ± . d- treeing d- qi die.ir Cho Ai B C , D , . ' tab ' ' Ichi do : E = Kia + of = Kia + lzb→ khido ÷ ¥ khoiigphee.fhe.ocv-aovie.ekiycacvectod-qidie.is ' : : . cud A , B i. D va-d-ie.ee go.ila-tisoikepaeciAIB.ci D. { Cj a- krait Abi ¥ Y÷ = → → KH : [ A, B C D ] , , = kraj + enbj , +1 Neil A Cao : an : : an ) ; C Koi : Cn ) { Yda¥ . . . . . . . ¥ " → = Blbo :b . but du , - . Dido . : : . . . . ; : . . . . : " Do A -1-13 → Fi ⇐ I ate bi f ai -1-0 9 ; bj f ai di f di ci Ichi d-6 [A,B C, D ] ai ai ai di , , = , bi di fbi bj Ci Cj \ / b; dj / Ichi IAB .ci D) la-lha-ngd-ieind-ieeihoa.2.ly = -1 , tana . A , B , C ,D soikepcua chain bin side ' phñirg ' Cho 4 sieiephaiig xp 8,8 , , ✗ -1-13 → dim ✗ np = n -2 I haiphñygiaonku . Neil 8,8 diii dive dim In : miinmp ✗ np , tauoi 8) B. ✗ is lñmotdeuin → dtiig . . . ) Hsien pending ✗ it ld-tisbatky-ligiaovoi.sn ' B , Kaido A D Coit 4s 'p ' kelp ' ' tag 4 d- pb AaB , voi ti son " " ' 1AM kleoingphu.C-va-ovi.tn DJ - a D, - . § - . ,§ . . . de-io.ugoila-ti.SE/apceea'4spapi8iS . E . - - , - , KH : Ed , P , J, S ] *
D: Trough mug tree xa.ae?ih,Xetx:aoKo-anXn-...tauxu--O { P bosco bake bnku :O : , -1 . . - + 8 : CoRot cake -1 . . . -1 CaXn=O 8: doxoi-daknt.it dnXn=0 Bibi :b d-o.tl?apc--kiA-iluV&W--kiA-e.v 1¥ → Alai : . . . . : ais , . ' : . . . : bit ( ftp.ec-vio → [ AIB.ci D) = : ¥ D) . Cnigtniiu [ ip.no ) 1¥ ¥ ✗ : = : . , Neii CAP .ci D) not A. = -1 , ta B. GD lñdhatrgdieiisdiieihoa Not Kip 810-1=-1 , . - rip , ✗ iQ laid claim - ③ ' . D- cauehtoañphais uihly ' 4 µ Cho Kot d- nñothaj ' A.B.CDSktrongduyk.co ' hat ctrgmpxad ) Q A Goi . M= AD ABC N , - - ABACK ,P=AcnBBQ p B MNABP [B, Pip , a) -- → = - y P C N D . Chm Muffin ✗a. all CAIBIGDI . A -11 :O :O) , 13/(0--1,0) , CCO :O : 1) , DCI :D : 1) . * / I % If / ⇐ "" =o → pie :O :p O O l BD : Xo - Ka -0 AD : Ka Ka -0 } - → M : co : 1:11 BC Ko MN : ko : = 0 → - ke -1×2--0 AB : Ko =L Q ( 1 : 2:17 } = → N ( 2=1 :o) CD = Ko - xz=o ' Taco : p= - B + D Q=B -117 . → [ 13,01%0-7 = f- -11=-1 : .
Bài 4. Nguyên tắc đối ngẫu d-of ✗a. Hong " 1. Phép P . 8 tap tali caiphaiig.co d-ui.hr " ' ' Troy " ' P lé mug true P voi xét , goi . ca cua , aid ✗ a. : f: 9 → I A- Cao ) :< Au 1→ JCA ) Ao ko -1 Ku : = . . . 1- An 20 A JCA ) ✗ to j( d) = AEL Neith oté : Neiixla-phaymchieielhi-gcaila-pha-irgn-michie.ie . Xét Aoi . . . . Am ea-m-td-ieindo.cl?aptroyd . Ta not : ✗ = ( Ao . . . - i Am> . Vary A " Viet chieh A = Cotto d the day ' A E ⇐ co : + . . . + em Am . pt alia of (A) lot 1 pt he ? gud cud f- CAN , . . . ,fCAn ) . ⇐ JIA ) 0 If y Uti ) ✓ciy gal ← of (Ai) Daddo : dim GCA ) = m - n -1 d-eeiiiemo.tm-phaiigtha-dcacsouphaiyaychuamo.tn j bris Héqud : cat phaiy - m - 1 2. Nguyeistaudoingau Qey riot trong lmeiih dei ÑE tried lies thuo.cva-tisoikep.talopbie.it - think vñ chita not ' theoecv the the loi " tri CVD : U ex co Ucv hoat.ve v1 d-t think dtiin • , ☐ M = ME ✗ ) Mignet Phép d-É " +7 troy P gut nguyen hei lien tuuoggiiia cat phñj : ✗ a. quan . ✗ C P y 43) c gon ) ( taught gcd ) Cjc B) ) Gia sit M la-mo.tn?uldeTna-oditrogPhnoiveicacphaiigva-giao aid eaiphaiigho.at ti so kép cud Cai ctiéin chin stew phaiig Neil trogm tathay ' ' . , phaiig that phaiig coñ care tui coin " la.ithigiuiuguyeikhid-itad-iu.io " t u " war r - n - r - - meet d-E.cl?goi.eaMD-doiugaiiaedM mei.is . haimefdd-e-d-ofuhaulhi-ho.a-oaigd-iyihoc.io ' * Acids ly : Troy kg ✗ a. anti , cut Sai .
pb ldttegthaiig d-eiyl-phaiytheo.ir zdtéinpbohotrc ' ' " Qua 2 d- ' VI ! co " : a) w = oingae Co d-iytno.tk 2) phñy thuoisieuphayckotoe ' D- " : - - ' Giao I sphaijpblñ 1h 2) phaif " • = aea - - 2) Pappas : chobo.3-dieinA.BE uy-c-ld-y-thcifd.i.A.B.ci auf, thro:c otejtd! thcyhg ? B. go.im let d- E Bira B' C N P ' ca ' , . - . . . . . . - MMP µ D-oingaii Cho 3-diiouglha-ya.bicay-diqnam.it dteiiso ' : " M P Cho ' ' dining :b :c ' b a city di qua ed O go.im la-d-uiigtna-ydiquabniv.ci ' cab * is E . u - and voi eine Ia b p - ans ' v a- ' a n to . P cctoiig guys ' m di ' ' b KL: eat a → m , nip wig qua . . C ① • . . u 31 Troyup tho 4ctg-aib.cidd-oiigauytai.ld-io.no?totg-tliajal0d-i qua O dat aibic , d tail 4 d- A Bic D ' , , . ' Ichi do [ Amici D) µ ju.EU: tri D . ld-uiigthaym.no?td-iein ' D- Ñngiie : Cho 4 d- Ai B. Cid aiy c- I 10 then.im . . lip ' Ichi do ' and IA IB IC ID , tj so , , , 10ft Evño I .
Think d- cud Klein ' hog theo quan (phil E) 3) Aah ✗a. x.aaeihbieiim.it he cai-di.in do:c ? Idp ✗a. aid trail the deities . A ✗ ✗ a bath ' ' a) m - phaj that mph g- 5) ' la- ais thi dim P ± doin p! j : p → p ax ✗ ' ' d-eiila-sogaisva-axqnqio.sc j ' " Ichi - 6) P= P thi tax oils P → P :P P ✗ a. g : → axttiisd-ai.de?enla-y-1 ' ' ki daxxa.co : V → V Dai bist , V-axxatuipua-pd-eiila-sougaisva-aiax.angui.ooexla-axxa.is Tip cat ax ✗ a tri P rat P la-tnhomd-oiupheptoanh.oplhout.at?uicgo.ila- nhoni bias d-of ais cud P ' ✗a. , ki h-i.eu PG ( P) . Neil y la-laxttd-a.idie.is aiglet dota.idi.in and g thi ' ' F) : v → V til (1--1-0) and g. Ngeipulai neil ya , ya ay-otai.de?enclwgthi4e--tyzCt--o) Kief d died die.ir céo eii e) ' ( mug true (so , - . . , Su , E) Cua Pis 1 , . . . , . In ii. ) v a- Quiet ) ay-d-a.idie.is do fcsi ) rien a = tickles ' turf tri : U, cé I = tilde's taco : if , I E) = tilde I = the Eli I ? = If t.lk (E) . it !Eéi I = i =0 É Yacéi ) = Ig till dei ) → -2¢ - ti) 42 Cei 1=0 → ti = t ti nhoincaitr.iataycaiic.at ' ma v → LG ( v ) Vématuhom : P G- ( Pcv ) ) ± { t . Idw tc-k.ly : g → iii. ] → axttd-a.edu?uchof ③ Dips by ' . ✗ at axa . ✗ a. dub . cinema A-✗ ✗ a htoa-nx-d.is Ichi biel-hmuc.to?u . Cho { So } let the ' ' lñ turns true cud P voi { so ' . . . . .su , Ey , . . . Su . E diein Cho ' ' chug d-eiiot.oila.p.uluyn-l.at nñy ' at b- ' f) P Sao nee at big c.)
' ' F ! ' gu.thuo.co Ichi do rag P → P sicko : Isil Si a ✗ ✗a g : j = . , ' (E) = E lily caida.idi.info?.. e-'u.e-')choCSoi.-.SuiE)leoi. .,eu.e9choCSo'i. .Sri E D. +, Tori tai : ' ) . F axtl Y: V → V ' sicko 4¥ - - et tho rats 4 lot d-oh ais il te, Ellie? Eé? =e→ ' ' voi = I = . go.iglee-axxaeket-isy.VN bei't laiju-d-ai.de?euckoMdtugcm)ldd-iiincod-ai.die.irla-U( M Kef , vii. ' Rf rig fl Si ) = Si i JCE ) = E ' . Day usÉet ' : Gls co fate Hmyk : ' Ichi di Hiei . ) vñ Hiei? 7 cujd-a.edu?udeof.lSi7--FilSi)--Si . Yeti } I title ceil → ti-tv-i.CH trail - - → . . F Ue IÉ I = tilde → Ye = t Ue → ge=fz . ④ Quan d- cud Klein velvet hog ' . Mit kin hay a trill droit d-c. ga la-boitbieisquaukouibi.in doi ? - : ✗ a. aid nai vii. lbieii dot ✗a. aid f bait tag neil kid H tlmaiikcui.in , his gut ) city H main bluefin + tis chat di ' to 1 do thi hay tk - at nlaiucaiklnva-cait.us droit bait bien ' ? - HH ✗a. qua uhoni beti dir xa? ⑤ lhetitoa.cl?cua'bieis-doixa.auk.ChoPla-lkgxan-chieei.xet1mu.c tieiexqauh Coig ( so , . . . . Su E) voi , . d-a.id.in ( lo ) . . . seu , e) . giasii : y : P → P lo meet bien did ✗ a. aid vñ ✗ a. out d- at d.in v → V to ma tra.ir A d-vs ' SE en en y : co . . . . ✗ it M GG t.cl d Cai ' : . - - . : Ku ) C- P . Cflsii JCM ) ai ? : . . . : Xu ) . 8 Ichi d- it = Koi . - . . ✗ a) la-ld-axdi.in cud M vñ : A | ÷;u ) la-toa.cl?gYCu-y
f :&;) / ÷ ) ' that =\ UM d- ai dii.es chosen > net t = A la-coigthiiotoa.d-s.ua ' f : , § Moi quauhfgeiiahiidho.caggeireva-xa.cat ⑨ Khong gianxqaulrbo-dinu.it siéeephaieg Cho aid P" phaiig " " kg ' voi d Siete (d) troy do Ta sé bi cho A =P H + ✗a. . trang wit caii truce og kg again + Choy mug tell Isa . . . . Su , E) Sao Cho Si , . . . . Su c- 2 . Ichi oto : ✗ : 96=0 diii ai the viet toa.to?diioEda.yll:ki.....:xu ! ✗it axa : A ✗ A → A . Mcd:X : :X uh NH : ya : ya ) → ( Yi -74 ; Yu - Xu) , . . , . . , . . . . . Ax frein ✗ Arif duo Amit cain true Agni . A xét a mere ton ( so Ei .in ) f) Kg Agin , , , . . in ski O Soi chi's tail aea R Ichi di voi " " ( ei ME A ' . . . . . , MH :X, : . . . : xD SIÑ Ihi Cia Kief i& Viqy neil A Hots ails ' Kul = , . . . . = . M C- w . ✗ a. Mlxo ' Ki :X a) thi m to a. do again M ( %-) ,÷ ?÷ ) : co , i . . . . . . . . (76-1-0) gut bait boil JIA leid bien ' +1 D- nifty : Cho g ki l bite's dtoixqauseua P, ✗ , Ichi di doi? ' dot agent cua A. Ngui.to lai moi bien ageing and A. tinted airs give bait ' i. bait dot ✗ bias a. of aea P, x voi of 1A = g. wgoa-ira.tiinguiye-iuoitreirgiuauhombieisdoi.iq giuibbxva-nhoinbieird-oiageivtuongtr.is aid phép hop is toan that , ai ughiñ : gtiga = gio gi .
glad µ any Ctu : ✗it mutton whit trees : jai ma train let A-= an - . . . ÷ Do ) neil Aoi m a- def A-1-0 an Ann get Aon = ✗ = - . . = = O . am - - -. heir doo 1=0 ' ✗ it M 114 Ichi do Mio toy out ' , . . . . Ku ) trey y thug Al . ate ✗a. M 11 : Xi . . . . : Ku ) . Do di j cm ) co ' fog D8 ✗a. aid ( ko ' : . .. : ai ) , . di g oi ai - - aoo Kal = Aao t dei ke t . . . -1 den Xu ' Xu = Ano t Aniket . . . + Ann Xu . vai.gg CM ) tog dnf aguila ' - co : 11 :÷H÷l ÷ ( ÷ :÷ . - . :÷ : ← : . . . to det ÷ :÷ ÷ - - - - Ning gl Ai kid bai's din? again ( ÷:/ +4¥;) i Ngieoolqi Nñigeñdbieii Aoi again f ) . ethno : " : Ibi;) i , ✗ it bieisdoi ✗a. aid alma train ) • 0 ( !! ( 1 0 . - . 0 bao bii ) Roo rag of (d) = ✗ voi theo phaii trees of 1 Aig . Tail ! I a- hair vxhienva-axxahoa-ntoairx-d.is Ichi beet and aid Invective give bait been ✗ geau-ygeiibatbieiiama-gi.ge ' Sui ' Gia ga ga, go . 9^2 ogt-gz.ge 1A, = gao ga . Héqua : Huis hog agin la-dhi-usho.com and hhxq ais Do di moi Ee't area aid hh ✗ a. ais cteiikéo that Kai ' ' au hh again .
hair dot xiingcua ' 82 : N 1 d- a digndeiiranhom con hate hay end so (3) 1. Nhoind-oixiiyaedmo.it heiik Cho heirs syne ( H) ea-uhonicaofhepdoihiisgie.ie bit it . Gori biéu ( DoE hid d-aihga.e-thu.am luéog ) H = ( Nhñn d- ✗ cua ' H) otao heiiig 2. D- a dii.ir otiie . D- In : Mft hid d-adi.eu nip trip lm.at cate d-c. go.ila-de.ie neii . : is Cai m.at (a- cai da giaédeii y cai-dieincuoiaeacacca.es aig xuéitpliat tie died cai-dieisogld-agiaid-e.ie . Trong ktgco 5 loaf d- a di.eu oteii : n tie die.is oteiie Hind a Yap photog 3) Bait diets cteii a) Th?ap uhi.cl2) die.es die luwi cnet.fla-ngeigia.es 5) Nhi.tn?apl2o)diei.r-deie.C-la-ogiaE ) * Going twice Euler : Troy Khoi d-adi.in . dtii : tiiih c- M.at - Coyle = 2 . Itoi again : Caig tain of cat meet vii. t Khoi noi tai . → hit dadte.is dtii ugaii Aoi . e) Hai d-a d-i.eu d-oingaeeeu-yn.in tip . m.at cate tain o , the dteioug not O voi d-iidogd-adie.u-deienayse.de tain da - ☒ qua q d-i.eu oteii dirt Yay I Khoi d-a deep d-eiid-o-iugaie.co auf nkomi xuij ' H H → o 1 (A) ' ' of = It fat ) = It
fail { → His flo ) -0 Tain mq-t-staimm.at fbñis lain caima.tthaltaincaim.at 0 to → ltuoñg thing not 0 is fain m-a.tt tainmat → D- g- H - is . ' M sm gbieiidg-uo-ioisd-iil.gr H ' did → g- not dins ' thais d- o is H of = f ' t g (8) o = S2 ( Fbi mcngooqitiépg H voi H ' ) Vafyfboiidti ' ties ' og H that g H ' H ais Vqig : haihiildoiingaiicoaynhomdoixiuy . • 0 si Sym LH) let Iulian Gute hay Hleilkkoi? d-ad.ee?ubat-kgB : is 1 c , I µ ? I \ , D jlo ) = 0 i://HH.ly#i----I----. 4 c'gccs-. (A) l it f = i "" - - 1 , I p 24 pheiplhua.it?huiig--24pheipotaohiuig . " " " " " "" " * ↳ "" Id : d-of nhiit . / " true d- cheol ( 120° 2g 8 phépquay quail g- voi 2400 ) . 901180,240 3 9 quay quot true D: ✗ = ☐ : D-i : 6 Frug Rot (Es ) toppling
Illy phañloqunhomi contain hay ' ' 3. Cua So (3) try tahini Khai fairs thwÉy aid SO (3) chico' the ' Ally : con her c- 1 Head loaf saw ¥1 d) : e) nhoindois-d-i.eu zn ( ut N n > 2) , 2) nhoinnhi.de?ees1DnCnEN u > 2) , . 3) Dhoni do-ihiisthua.is hiioj give bait bias tudieisdeii Rot CDs ) 4) Dhoni dot hits thua.is hairy gin bb his . Yap pluiiy Rot CID 5) - thuanhuég - his thgptlu-nhi.de?nd-eii Rot ( Dod) ④ ta't ' Haj cainhom ' ' mi ta ca con hhaea so (3) 6 nhim tain thing ☒ - - Suhani Kia : lift Keira , VD : Rot ( Ig ) - 24 phép thna.rs hairy tie digs quay cos otgcao 11207 alterman lletao > ( : . , d- xiy true 60 lhuie.rs , 60 dad . ① them dñs diets . Lai nhoincaipheipdoih.is/hua?nhiiiygiEbbs4haggui bd-itd.gora-gietbbme.it d-agiaodeii An Ac . . . An E- ¥ ld-g-tro-yvkhaudg-tm-nlohtreiss2.AZ - - • . . . nip - tteip f) - As 810 ) -0 . - Zu goin n phép quay quad true of Cfl tain a- dagiac got quegloi bin mop ¥ k ( k-0 vs k=u gioigufau , k- - l voi - - nut
* Dhoni nhi . digs Dn nhonicaipheipda-hiisgikbbs~cginibd.iq ) : 0 vie gbb 1 d-a giaodeii Aa Au nip top ldz-tro-nlmaea.gl . . . An ' pliep P ' Dn goin 2m do ai phép quay " , try n t anas tore 1- Au toy voi - ump Aa Az O ÉÉ . . . ' ai got qugea-bo.i.ua 2¥ . iv. -2 . true doing " phépdñixiiy qua cat ¥µ Voi " g) . n A] An gotagiacideii Doi xiiyqaadj : flx) =L • * " ° " " * •" ↳ " " not • " the £ " " • " " ca.bg d- giac - → n a ✗ dulia true do too? Khai tais thing ← Troi! 0 moi-nhoinconhiiuha.uvauisoedmoiois-diisota-igca.ir story otieiis * Cour : . is In Cn ¥4 - l w ñiiig not ?⃝