AK-MATH225F09-WS7

# AK-MATH225F09-WS7 - l'IATHEQS Fall EUUQ Name “...

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Unformatted text preview: l'IATHEQS, Fall EUUQ Name: “_ ‘Workshcnt ’F (3.4, 3.5) Section: éﬂlutimﬁ For full cred-LIL! you must. show all work and box answers. 1. 3-1 eat-2h mull-m" Lhe l'ulle-illg matrims with its possible phas-r portrait. Hint: Find 111-3 eigenvalue-s. if“? :L;.L_(_g Li“) (a) Adm-mks Act ('1: :{w-JLB:O [ I TA.) [-- I ~a)—L—3)(5)= :rr’ﬁ. H (LL) Acﬁ(a 3—2050 LL — UL— :H) {Way‘s ,iiL iiLiﬁiiL ,L5:51:23.ii-”\$?’\$°;§:.L 1‘ ”LL L LEVE L , ﬁﬁ’ﬁ7ﬁ“ ‘ " ’::--"¥°:-°:--' HM “mi-ova.»-<-+L>->->-+->L>L L.-L.-l LLLLLLLLLLLLLLLLLLLLLLLLLLLL +.LV.L>.L>.L.--<.-L.- ‘ m ”MW 2. Given L113 system [3,) Find the general solutinn. ... AI: ‘ '1 _ __= ALF-t 4% .jrA)'—'O 1LT '1 KIA} (Lg-1:)Vr C) m)(~¢)a(3)(ﬂs)rcn (- ILL-‘3': ET; BK X' )1/3 1 h ”Lag": mmsk W .- 2"2 “Z", I . PM I. ‘ . :. FELT L k} X __ firi- Ina—Ii 7* T .2 a 9'4 Elf-Lt 1F? [I :2 I -. W r at a. .4. amt (:1) .,- W (magma? a VI - 71—14: KCGEKE‘t) +1941??th Ki >ixiﬂm E a: , ‘6' @565?) I :gyﬂfgjfy) J- __.___ Q'L_T%'§fjf“: 1 l_'-t' :nrff‘t {T1 5"?) C95 l‘tf. lib} Slim-tlhthﬂ phfa=})1ri:alL)JCI1-aallw the Zorfgﬁf r/ Vghé): KI ( Flu. K‘ﬁ'K‘E-‘Pﬁ + £1 (35Tﬁ(ﬁi} a“ = :r. F. E E? @5531) 63-”? \m IT‘S (A CEr-Hccrl f QEJ‘EJ Lat Elm/a) LI) . £3: K 5 K3: 5 d’ ‘12:: :33 :23 (LL43 {'33 Find the hartimllar salutitz-n LhaL satisfies Lhe iniLlul ut-ndiLi-nn 5E3“ _y|:l]:'3 " '16: [53. Rﬁport 15er Eulution 3.3 one real ‘-'!.E'IZLCIl' {:3} __ {a T: ij— ' /< K3) MK ) — K a /'==g;’é'_ :/: 31-90» JEH x5555: :' 6-: --. i .. < ‘3“ £1 3r 3—- L: — c: IT 4331 €?4(Eﬁ‘£) K 17(1) : 3 (‘SCefafW'ﬁj u: (émsKWt)>:/cc¢s(af€t) 3. Given the system by _ '3 ﬂ - A“ K H =5 ) car ' ' " "DH-ML F 6 {all Find the general mlutinn. [Gr .. A: P i H 31¢) .r '7_ A _. S ‘— _ s. -—._-=. ‘3’! 91:34 H Mer Abram 1 (A—mr)%=g Lia—magma ‘5 .>z**>=z:) —-_L_ fem/LJHHFG . 2 h 75 . plum iZ“Hr)>*I‘5>4=~’—'> 1r»: 1 K71: (‘2'..L1H')Kf X1129: "V' - :Dtm_ :o:‘3\$_g+ ~ 5‘ / ' 2. * l ‘ ~53 7r=da—HE.M 5 a; .4. a; (FEL:EJF( x MIL—S; V’ L 34'” at ( scangangE-gmw amsfht) 411's Tami) “Ln—ﬁcﬁﬂ-rf) +Ljs?e(tytb * 5'1 miﬁiﬂﬁw} ‘ 5: < ssﬁthtj > lb: Skﬁ-Cl‘. the phase purbz'ait. (Ilaisiﬁ’ thll origin. : 1— L {'1' ET LIT. ELIMM _ ‘ _:= 5f: Scaaﬂ‘f‘f.) 7 _ J: 1-1 h A. k‘SK :1 . K16. LEDEEH1J+'L1 SFF‘JI‘ELTO) QT”. I11 '5 '9‘ St EEP'TIKL‘IFC) II “ . 1.:3P‘F“_1__‘Ewr“ “(LC 2qu M) 43mm 9* A? a *7 - s 4 - ------- 23? , Li a )kﬁ / [ﬁt-945,0) :f“? “5 1): 8*?) .ﬁi'ptgfbr Fray-r *Cm) , . .. _ ﬂ L1 35 >Z ﬂ L'l Vac fur“ Filled F2) 13:} J- Ind the pﬂrmculm wELtLl-jll that. satisﬁes: the inlL-ial condition YQEJZ: — I5, 1]. anorl; your mlution 3;. lane r'nnl warm: __.3=~ S C} 7-"? E 'LﬂG): KIZL)+‘K3[“L~1) (I) (6% )_(5> 39195 will’tiiz ._- ‘__ L— lift-11L; J Lid—r _H£1:_r//ZL:~L—-1L ! s t | h: _ SEEtCD-gﬁwt) + {5; c: 5hﬁflﬁ)\ _ 5‘4:- Sﬁnsi‘it} + *3 quth) Ll/ng)” 5‘5 .E‘L. 51— x . — C: a L; Ca5£Htj 4- L Ci arnLL-it} Cari. (Ht) + Egynggg 4. Given the wwnd-or-im dilihrential equation ﬂ-Ey' J_ oily cat? at: [it] Find the corresponding ﬁrst-order EysL-E'TI'I by letting {1.1:} Find the cigem-itiuns. Du rlnt ﬂit-:1 the general ambition. | oict (:2: ﬂit) :O drMH—A) — (13 ('335'0 AE' +A+ZPC> "L: “'II‘ t i’rg (a) SlcctL-h the. phase [JCJFT.1'FI..1L. Class”? 12-h 423-441 / '7 =“Z}"‘>v at; r: _ aft [d] What 1:; the natural pericld 01' the say-'stem? A : £24.. 1' i: t . k ‘i .1 2n"- ._ 2—H" 1—. partisan»: E: F n———-E h 1 (a) Sketch the yttfl— and 4.:{tj—gruplis for the particular an] ‘7’ 10:1 L at. Ha ' . 1:: 1.. _‘ {3 I K J '— —2_ =4 :3 __ C3 # (—2, ‘if ‘5 CUE} a - .1 r 51' -' 1 _/ E £12 iEE the initiat Condition fylﬁfl}. {71:0}: —_ [1, {1-}. V it 1: 3. lSix-e11 the e__1'r'::1.1111'1 .- . 1 3:11 1" I] - 2 '\:1Y _ 2.. —. 15.: Y_L_1 W1} PT '-"I H) AA'L [ALP-111::J 1:111 Fin-:1 11111.1 11111111111131 111111111011 1.11111 the 1111111111 1'111111i111.11 Y1 U'I — I, l 11:1.Hepor1 your solution as (I111: real 1111111111. 11.111111 0 7511) WK... 1 1:11."; (1"411‘111‘UY'DZD .— 51") \$111) 1:11 .___ ._ :1 ,. .111 JC' .1151 1’13 V: .y'" :7 11—1111'311'0 17". = (.4 ~11I>1EQ “—3 3 t 1 311 —1 _- Lr'K—tjf'ﬂ ¢)+1':C {-1) I:I':1I [1111,1111 the 111111111.- 111-1111121111 11.111111, ill-“(1311' 5.1.- 1111501'1'e1' .11'1- -111 the 11111111111111: assaeialed 11i1h 110 1111111 51111111111111. 11.11.11 1111111123 in 12-111 pheajm'tr'ain. P1ir11 211111jm-iude 1.1111: results. 561:”- 9. 11121111171: Er. 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