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W08_M136_Assn7_sols - A’SSKQNEMEENT:at’ 7 c099...

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Unformatted text preview: A’SSKQNEMEENT :at’ 7+ , c099. 2.008” /'03/I2. SfleC—ti‘m LL16) PP Jan-Sg—v’QS-fi‘: '1Tet af/ 6/ 8} IO, ’4”20’-2‘£Pl “2.6/30 Sect—Fen rinP PP 260 ”‘le “#4“! U”! ”112’32 4.4 EAERQl‘fDfiS ... ‘ -€r @) 63:: § 5' ivyii] ; [:18 ; Lag -=“- [ 3} gmd "vine vm‘w r X , defiermhedi , O . 9:“ b3, ix 365~ '4’ 1 H) T“;- 4.1% QZ'CJL‘M Lijfir'nijfitzl'\€3ffis U\F"O " 3~ ‘* wan-23 ' f.— -‘ 55’ ”5- '“ .— :2 3:: X “[6? L] :‘ngfl [-Swaomes ' »O+1bv-21 H ‘9 ”i 1'] J bfi‘flf] , x: [3] {5051 {the wbrfl‘u'nave 2x165 0+ x reiaL—Tue, w A." .90..) Mae has”: 65 = g b" bills \. Let X:EQ];C,b,+ Cabng. [321+ Cali] S; L“: CI+SC2 o . : “2'9"592. [3!) I}: chat ”f—Dr amend? (iflmp a: {363 h b ‘ a; rm h (.3 mp6: r49 r31;— fil ’ ._ A“, -‘. _y . H6063 , 1x 33 2. O H) Eva/mt fr.» tO) Find the change-"Cufir cmordTnai—fifi matrix 5‘.“sz (333 "E0 «the sfiancjard \ba 222 m R" ...-\l \2.._ , . 2 K % :— § '1 1 O , «2 35> Pg): _' O -,.2 Ln 7T? "RY £1143 rg'ju‘fu'f‘f‘x 4 '5" 9 c, "*5 El £4) The 53“" (8:31.221, *"ta‘z .2224:th b ca bests (par I7”; Find --{:}"1€E‘_ ¢¢or~dm ma “9% vector 0,5; th) : 31—11:..th raicwfl'ue w (E) \f? PM; 3% wag: q (Ml) c2 {we-2a) + c2c,2.2.22+t2~-) : qp CHI; +— C911 C1129” + C32 " 532-43 ‘V‘ 53132" ‘ :— {Cl 4- Q2615) 4" ti C2 *QCLS) +t9”(c:3..c;l 22(1) .5) Cl+9_C‘5—= 3 m (02:132.; (2,42: 3 42 w) Cara—C32: :L (9.] C3*C:“C~2_$”'é [3) (1.2).; (3-) 2-) C3": ”9' 53 Ct “H" “:3 he Ci 3 9’ C92WL¢ :2 L he C3515" 1 Hr . game; PR") : 5* U] ) P {2" H?! read a": ..2 ® CUM) p r: he.“ M L; Kneurlua, cperpenrfieanw spanr‘fincg, 591—5— '90,“ a UQQ-EOr sweet Q0) 52:99:95.2? §v,,.., U23 :5 a \\].Show that each uu in V can be, ewprafified 70 more than are way. ”‘6‘” w as at \mear cambmabTon 0,}. 4,“,ij {‘35 Ence §u, , , ”1,43 :5 “neat-ha, de'panclarrt, aware aerél scalar5 CH.‘..,.C£( racy—£762!!! 0,;— them aggro“ such that? 'l' . 1" r711- "' , " 3" al.2{'i“f,h‘\t" H! ‘Sm “Elk-if ‘ 2th C:V;+ ---A+C2Lz\/L(:— O (Uggnnt )5“ L if k 513 c, 5calcnr5 'tn-r \f; span E2122, dug / there arr-5' Leb WQV be. (:2 vector ,, 5?an [32—4) mum; ‘06- {.21} "V U kIVHrH- + $5“qu 51W Bl)? “5m“ LU :2Orw 3 (.k:+c\) V‘ +“ ”‘ " ‘4‘ LkQ4CQ)\/¢r afld. Wt. fifirrfl ’1- é, g“; 7&3 1‘1;+c~,¢ L51 - 50K we get Cc fi‘Hlerc-znt Wear espreaman #30” w mfikwxlfih entrre: ‘3”"7 I?” ’ produce Ll Tn V such thee-l: lull-331%.. 0'3 K: L94: {BL—WM)”, bnfi be albafiT'5 {or a vecwr Space \f‘ The coordinate V“) 1’12“ .‘5 62!. \mear tranfiformatfofl (sec—:1 T‘heor‘emg P 1.50) ma 3353703, § \1 t X- ~43 LX1® p??? {-11 ! '0: “73"” (3 Note. 'thad‘: Vr—fipcm &: -S’Pan g3" 7 W3; g H lgfi—w—chgnH; PM”; ling ’RS’ w" ._ . | I' ' '- "n'fi - t «y n (’i) “$813,: ‘ (210“ (it; n M affirm u“ ‘3‘? ' g \f d {Try «5%: - 5;. CLO ul“ «(VJ I“ of. span 3“ ‘jvfi +>tnLj_n Qspom §‘g-nvr%0§ H1 pf)" {TM —-=,¢ “M u. : *-\ “(I .— 2fl'V' _ '-C¢:ordan¢@ Mapping, .3 traffic {Rn 2&)Gruan vecwr: uLHNLAP and UU ?n\/ (show that u.) ‘a ka'F u.,.,_, L’(1‘3 ‘4; and on)? 1",;- iLultg 1:» cc \:l\V&c%ar5 {L139}, -k , Luplg n 3%, Theorem 8' 1Q (2.3)2 (944) , that. accordi'na‘ce mapping, 0 i'svmorpm-sm 0+ vii 112 . c,,-,cp€—R/ é-hen O‘Ppt‘j"h (Q) PCA {at (1)) Mn 00 z: C\Ll,k—*CPUp 54W" acme mquTnfi' we %Qt Ew303 : C, Lu.3&+—"‘”+“ (—9 iuplfi “‘ Asher) shag-2 W T‘nuerje Lwlg z; muggy.“ -m- k9 $1,913 L451) Camera-2%! q“ TbomofPthm , ”‘ n we have IL .9 ) E301 fl {: LU~ k u.+~- -+\r_p 59?- 30) U33 coorchnate ueoeors {:9 479.51: «:“ne ”new!" 7ndepencbeflce 0,?— the -‘\0“Sca-{::> «2;. ”p0 55.nonmh L3 U”? (“{th3, C2m3t)'2, mama-t3 e 1??) Pr boa-33': "F5“ F3 :5 $:§4,~b,t2,~:3j ,cmd Umtf; #311: +3t9w-t3 (2.3132: a, _ my +36 36"“th SO, the. coardi'natfi vac—tmfaa urea U,-3, 32 “U a» [4;"‘2'/3'O-) I (O’O’ 3’41“)! K .‘ _ U) , F” ”J r35pecaueiné, , Udmtmcar, the MOW!“ gjr‘ (3:;th cars; rnfli‘ncém Ufii‘éfifiW ‘ Q 0 \ £4: 0 . ~ , , _ _ , t m. M “WW“ 33 522 g N (0 ~21. 1 creahjmwm mm: WW” 5‘" A», E ‘ . A_ I: . '- m; o 1, c9 (3 L LU arm” rmi‘m-‘flw‘ ““4“" A (13' (9 Q So, aha 90ignom7a}s are knead? Pryclependen-b (‘H «10" (”M/“lugs.“ a5 EXERCISE-.5 \) Far +139 SUbSPC’Ce QT b C (y (C!) {Lillfld Ct b03535 ‘52:» :55 : Q'b 55R w 173 Lb) 3:01:61 1539 cfiimeznsi'on ”b . Lea: mam a? .4. i W , i ' g a 2. H: 0 9- spam 2 , 3::b 3 5 ’ D J 1 ,5 2c,:.O (2MB row) :3 97'ch . , «-~:-?‘:‘7:aiv‘5‘3'3°""' j ~C3 $0 LL bihraw) ca) &=§[‘?’[é’]‘ :5 a has” new“ “‘9 SUbSP‘m W 'r" ”w '5 M) 343K d'irmefvsacrm I2) find the dimenfi?on ‘0'? the? $0b5?¢¢ce fipanneci b'aL the vac-tar.) F531 [W is] [a ~3 ,2 , (r ) é : 3 1. 5] [a] L ..~,-.. (-2») ,HS!’ r’L‘itg 3'9“"{L’LULM N (I ‘7'} hr ' He Ce (,5, 6, spam g Ci, c2,c3g JR. C{:C\l, (:3 are \mea 3F agape gems; n ‘- 1“ P " ‘I/'C {9‘25 4 x _ r “A a x Ly". é-fi‘u' fhfld‘iflffi J .a’ a ( {} #1:?! {j ! 1_‘,1B‘)_Jl‘nn ”D 65 »§::4 CACS} anrJ J7men5mfi 7?: 3 A i 3 "if 2 w: 5 “-f) Determme h‘u! A and Cot A for the matrix A; O O i #5 q 0 I'LL-k O O O ( Lt -—3 W T" 6* refluxed maerrfi. “.1 —, gym 53¢ /—. 3 "- “ I FF is The—re are" 3 was; dur?ab\e:$ XL, K’s/’99 Hence clumenS-awn 0.; Nu ”‘ MOT: Alfie chm Cbl A gr. 3 , su‘nce A has thread pwa Tnciét; ( I!“ CM A and 21-) The firm: 6‘49“ Laguerr-e pohafiomml‘s are 1/4115, 2.—g,.e+t2’ Li. _ “f1 6,1321: +3tzpt3' Show "that" thm Pdfinomhls ¥Orm a. boars 0;- W5 A Emcee “3.355;?020 gt, Ape-2,1333 , chm P3:— 4 3%, Thwart—2m ‘9» LP 2S3), 7—5- T5 L Ff, Lam—t1 and é-le'++-E§t2d€'.3' enough to :how tho-1': the 90lgnochxl-fi, ! n i\( unfit? " [1:1 ‘( 1'6”? K.- ‘ ts. \‘maar’g tndepencfianfi (.9) r43; 13mm) (.3...) 1“"! \rwr-wr‘ Let a, i- 4—ch ht) +c3 (l—ZrePtl) Arch [bpifi'wgtawt3) :0 C\ + C14- 2C3+6C4 : O «ngbcs #fYC—qz—O 5;) Ch: / C3; / Czar-O; C150 flab; 32) 1.9.4:: H' be a h0n~&er0 5013590263 0,}; V, and suppose; T 3'5 (.1 {at (Ii-near) Mapping, a“: V 7nto W. ’Proue tho-é: chm "TLHJM-zwm H2. 1;, quprOS to be {Ouch mnewto—one mappm? 0+. \I ante W; than chm V=chm W‘ '{?\Isomorpk1'c. Hm‘te cfi?menaionai space-E’s have». the scum char-ensmn ' [“1 L24: 1103.}! H S; V M T \/ r-mrgw (6% ohm TLHJ;{) and B:§e,,., Eng be a barf-3:3: ,fer H Them 3’: ETEU_..,TQ03 39am TfH) :smcfi for any, XGTEH) 3?..€:H~ 1}:ng "1 I «tcch-i, .lcnjgf1ESfDafigTC—‘JII ,icznj t “"' a, 1% (E “-5 hflECtHEfiT i'ndepancfiamt. 1H$€€ri¢cfif, "554-1 $61159“? -« ~ ’4‘“ é’mT-en :— O 3:) T(.k!e! 4" ‘ 4'i‘1-(1Efi); 0 Wu -. — "it“ e? 3':- 9 7x: 7(6),):0 1i 1 “1:: 1,1, 553 m muxa‘t: baud? KEEN“ h n G 3 ...
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