W08_M136_Assn6_sols - MMH IBb 3355:6313 MEN“ 6 1 $32...

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Unformatted text preview: MMH IBb 3355:6313 MEN“? 6 1) $32.). mas-42.3 #10,|2,Ié,3h ‘O.a. Aprofiuce o4; 7nuerthle nxn mafir?¢es is T'WEV'tszlca’ and the inverse 0+ the product: :3 the product 9’? their rfluerfieg rr) m “the name archer (K) (Paige) L33: Phi?) be. invert-rTHe _ r-nwtwr-T-ces , wanker; AB :5 ”we M5131 Q h ‘ ' —: M1 LUF'th (A8) I z 8 ‘A' Lub‘ud’x T5 not admit)? equal “(:0 fl' )3 5“” ”31:16: 3 H531» <33] 3 {as} .33”‘=££>3'J CAB)"; [10*] am A" [Kbfifllj and A”‘B“Cfl8): [—2 31,31. r .h‘ _ w x. t“ ‘ ’ '5“ TN" r..'r):v\_:t;“t" L" 'D +L_\ MA p1 rfi‘l‘fltl‘? t: 300 " ‘ use Pr“: :5 5 fl: A T5 'Inuer‘tib‘e, "then the mace L0,}. Pg We}; H) (True) I; A 73 Tnuezrt?b§6§‘, “(rhea we and: m"..1“‘ KL ‘ .. a Stage mveraes are amt; ‘mucs Mime—:3. ‘ C- Lg. Anziitdbl and 0d:b¢;, than A 7‘5 (10+: yfi' 7]“ CU" U) (True) 9— r". A 7: A v '- ‘ ‘ fl— ‘5 ("OW 5 K ‘I ' .bie ff- ‘ ‘ n ('1 matrix 1.: muer ihecrem (.0 @123) 3 1" -L- F €Ciu7ucdéinb to .lna b at“ n 32—13403) ab 1”S,OS a: Ca " a A M i -19;- 3 0 "F pals-31 and a r3030 0d a _ in CUOHO‘E‘. be rlgw mutua\€nt‘ 0+ 37066.) Gd SbC 35> d;% 33‘.) I} . 7 new": Tnuerfib‘e— Theré€+0re by, Theorem 2}; A 5 ._.p *4— a.=:.© , f‘nc-zfi “(1&st 3) 33:0 or (”5.0 ;> A has at Grow n _ O ‘ n” {Or C.)3 column Mao A 75 met 'nuarbbie .313 fii'tm cl 1; A can has row erUCfi-TPL‘J to £21362 fdent‘ltg_ "Hui“; then A must bg Muertible [A .1 ) (True) T1115 T52: Theorem 3} 211;. A— 13 ‘muert‘s'bm, «than flamefltamé row operafi'tons tho—b redme A" 4:0 the Meow-beg, "Ln misc: recfime A”, to in fimflgar 1:1) (False) ”E w m we ,1 =12)“ I 'erR9. O ’9‘“ @1421 1 ‘2 I r”; I p: a @1333; but > [O 1.1% .1. fi-Rflnidr 12” Let Pr be can Tover‘thlea nxn ma—tr?x., and lea—1:.— B be. cm nxp matr‘rx‘ fixp‘amn “113% P143 can be compatrécl Irma. row reduct-Fon. (514511;, m a"; m ~11; x1,then muffle at. we know 1;. LA’TJN ,m Humilnlx] , ‘t’hefl Xsz (11 Ram restaurant) 1:: ‘nmcfi: mu!-¢1p‘%tfi€fi w1-thelemen-tand» mortflcgas 50, wh‘fla raw rerJufiflcg. A +0 In , we are? mulfipijfinfi, Fr hurt?“ 1014: $0 In .—_ Pr’l.‘ 1.1.) Now, 74, we ”put LA | El] and row reduce. Hr +0 5,1“ 1X3 , we 03o?!) “LBW “7 Nth A“, 50 £31,1th ; Wm 153 ..—: £H“A~1 N183 1460118, Y; PEI-B. l‘f) L73 lb. Sappose Prune! B are run, B :5 Show that: A 75 ?nUert‘\bte. -.‘ "‘ I (B; ‘Inver‘mb‘e :2) 3: exists 3.9.5) aims invert-7H3- a) CAB)":_C”‘ exifa'ts Nob”; A43 x: C x) A 1 CB“! and :nuert?bie, and RB 7‘5 inver-ifibla. [OO-—*O Pr" {[email protected]_. O Proue 1:“th wour gags; r5, Correswfi. " (zs‘n—O 12.3" _n (i) ”‘93 ”90 1:31 {00 L90 RE~R2 (OO {00 kg 100 {[90 {£253 (3:9? R3»: 8:: —HO IM> 0'10 ””0 ”‘31 0‘0 "3&0 ‘ L 003 ~24“! @123 0t?! 4,3111. 333 \‘- O _- Ln) HOOD {003 gig: {000 4600 R343; HDOO 1.000 ”“90 0t M} (92.00 «1100 Rang; 02,00 1100 ERMBOiOOEO RL—Ri 0230 4010 FAA—11303030 $410 .zgtfioom mat. —:0{91 {mag $92—11. :92 A? 1000 LOGO 3,19 @100 45,500 .1 (gait) -gqxlo (42" OEQO‘ 5,111 a 3:411 {g_ m. eueas 4 j». 9 PV :2. 2 2'3 0 #2: —.L “ g 3 0053123 P\?>lw\3>?b #b,%',.20,2t,29_rbo 03g. \ 1 «S -» . x [0‘ Determme A: [ A I 75 ‘muer’tlblefi’. "3 b “O. Q“ :63 *1 i 0 O R3+3R1 i. _5. ~(, 1 O 0 R3622 1, “53L! i o 0 F$é40:0 f5) (03 q QIOM‘B oaqwo o 00} 0-3 42 30’ 00033: 50, A cannow he rainwecpiuuleht tag :13 5) A15 one Wwarti'biéa <5. Defiermme SJ. 3 '9“ 4‘ $5 :nuer‘thlc—a Br— ;OS‘ 8 Q £0 a 2. ya LQ LO {9 0 ID”. £333»L, m L310 RL,%R3 L300 cat—gm L953?) 053 A; ,3; 0-530 w) @300 fl» £010 (90 2 ‘3 Rial—11m, c9 (9 20 {Lilia}, E? O .9— O 0 000 to ~ ELEM, O 0 (9:0 '2' \o 0 OH) 90 it) 10 gm Loom I __ A a .r. Q3 > (9 i (9 O f 3 J41, mt) B mi,“ 3) B 1‘55 W‘Nertlble if (DO 101 “#139" (9 oo 1. 3 20. H, mm mat-Haas E5. and F have the garopemrfi, that; EFLIN than £1 and {-1 commmfl E—Wp’fii'n wing” WA EF‘ 2:3: :9 EFLx) 310(k) _-.~. x :a EF x..:O has :4 uvfique sciation x475 =9) 3% :0 75 the unique fiflhrfion 0+. ELFX) :9 :3 E :5 Knuert‘lble , T-e. E" exTfifiSA Hence E'F‘Lin a» E”'EP s: E‘ .2) F-L‘Ffl gilt“; :, Pa :1“; Es:— E and F- ccommutfl» 2L. Lg. the equal-£91.00 Gamma, has more than one 50(96th .F-or some firefg” ( Can the columns «34-» 6 59cm El”? LUhtd, or whgm? m each beta“ 4:5) The columns 0+ A .gorm u “Decry. (-3) Tndepancfien-t 59+, 30, ”5: 6x:\j' has; more "than ”“3 50‘01‘3‘00 ,por somé ‘férfilfl, ‘muer-th‘e— and coluvmns 0,9 6 mum; be; \Tneurbé, cannot (3 We 1:,an 6 T5: Ynuerflble 4.2”) Gxaqéf has a unklue SOlU‘H'OO for Hugh 6 canneafi be fiepencfiem, so ”:le co|umn A Ah so Column $313055: 0,?» A” be ill”. roacnsTsten-t ,gcgr some. 5:619“, whcrt: $11 [,9 the gafua-t-‘Ion ngc rs ("41.5.0 9 M)h6-o Can L630 salaL about "the aqucrHcan m 14%;“: T5 70C905T5temt- 31:). H T5 not “invertYflC-z card a ha nap-t: Ct athsm (9+ columns 0,}. H 0, ant) l-lr V5 “at h'n ear (:69me {*1 Since A30 is dlu)a%5 a solLrtTon 4.0:" szc— Ewe-“awe, when H‘Xzao has nonm-tr'TUECJI mlafions ((Ofl fioppofie that T and $ 5a-t?5+%f(i)5(Ti.K,J)-=X ’éxefpn}/ where {27) T TE) 0 hnear tran5formaflon Shot“ cfi‘ractl‘jr that 5 1:“: a “near I tranfifor man-HOG “ due) “50» Lee.» up} 9113 and tea—G; x... z ‘5»— (9..) «3-) TL5CU))::U. :2») TLX):LL! 11303)) ::.\I T'Lug) ml - .— * ) TL ). T \‘ ear we have TLX‘HfiJ :TLX)+T(%) 3—) 5(TL“+%))*5LT£X *‘ 3‘) Mass 7:: m L 50 (,4) 1-,) m—‘j, :2. 5mm +1133) m3, S(_u)+5[v) .1: smw) La Cbzdr{3~)) Let uéflln and gem , and iet >1: 30.1) ,:> TV):— thx‘) 2:. c. TLx) :3 5m" Lam) ; 5( Cu) Since 'T 71-. “near ,. ' 5 is hneczr. u) g) ax; ECCUL) a) c.5lu) : .Sflcu.) —~ x5] 6] i P? 3' A; ]3~LA Iva: 2+} 2+? '1“ -_ (E5fiw’3‘3’ Cl. Fine) a bash; 1 1-; «M 3-1:. {~23 4546. 72.“, 2+3 —D.~"I C1 C2 C3: ~27 +61 ~24 +cr cm] A 4 4 N ‘5 Ac‘hca mcrtflx @+ a l‘meaar $rans+ormcrtion i {'1 4w: . fl) ]O 12+ 5; 2+3; M: o 25‘. 2+ 5"; 0 4+2; 4+2: 9 o 0 Hence, C3 :1 C2" 26L 5;) A— ba’j‘s WV We; 4E9Hi1€<] 3 b. Qur basis has demne 72 ; is” "“5 CL= ]3i~ui] Q Vectors, 97.2: Q. 6:2 -»-—~> col A .Qa—i my: <2:]f:1] 2+1 h‘ x x \ Then \9_ T5 an unjec—L—ron, smcca Tndapc-Emflefit cc!) Iumns , f“ '9. E5 {£90150 (0! A Since CL and c. Find '1‘; ( ]“5*;_]) W5}. I ”2»? wS+b3 ~12— —¥ : l \-'i Firm: observe that ]:'”‘”“' ] 2.: Pg 3+5 -+ L] {4}] 2+? 1H c0] A 7—5 Shae. (£1 has: a bash §£é3,193] 2 0.069 (ex-bench if" hear]? "£0 E Jrhen 750+: 50/ {WT : c. +bwb1 a: {—i a l‘mecer comancmt‘iOfl 0+ Cpl}, C2 2. H bail. £- 0-3.0 .53“. ¢ 0(3-.L,1).+ {(4.43) 4'27 4-3 . - - . [143,511] a 1m T1 :9 T; 'L( [‘;:;7]) 080615 mm exxfst- {~21 ...
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