AK-MATH225F10-WS10

# AK-MATH225F10-WS10 - MATH225 Fall 2010 Name Worksheet...

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Unformatted text preview: MATH225, Fall 2010 Name: _\ Worksheet 10 (Appendix II, 8.1, 8.2) Section: so! a {(Oq\$ For full credit, you must show all work and box answers. 1. I_fA= ( _; ‘3 > andB= :13),ﬁnd 2A+B (a) x—2 (4,3 V62'H eécs) ZA+€D:2’(~Z,3 + z! ’ “we 1' v are ~H+3 ? [‘5 wi ~H+z (,+~»I v-2 '5 b AB U ; —2 Q 3 _ (0(a) ream) L nun-r6303 ’43 t ("'3— 3 Z ’ > L~a)éé)+(s>(z) (1)0) HEM) S (b) Write the given system Without the use of matrices. O J 54% 513 )Z =x_y 25m 9/ 2: X: X ) 3. Given (a) Verify that )3; (t) = 65t ( Z: > and X2 (t) = e‘ < 1 1 > are solutions to the given system;a t S _ ~ . '7)? : C St) X z, I ( I 3 c, . ( 3 L4 5 z 2 ej: _¢‘E V 1491‘ +3515 5 ‘3 \ 2" / 361:- Lid: ' aft—Ha“ I559 >9 7.. at n Y / I \ A 50.14). ( “at W a Is ' (b) Verify that X1(t) and X2(t) form a fuélémgnéal set on thte interval C C i 51> {: ’ Lo (Salt) , 75415))‘ =- %o on babe) jrét‘l/VL L’tl AFQ “ﬂc‘Ayﬂl’li’L‘Pm'E Solutfroos cm (“Pgbob‘ (c) Write the general solution to the given system. X I / XL ‘9 off") A {dole/Hﬁfﬁl st“, ; C1 ><I ’kC-LXZ, / (d) Verify that Xp= ( _ ailme ) is a solution to (e) Find the general solution to the nonhomogeneous system from part I _; C/Y/+C;7<: + T 4. Given the system dx , E = —5:1: — 2y A : — S 2 > @ = _;,; _4y 'l ’L’ dt -. g —& - (a) Find the general solution. 4 ‘A I '1 .5 ) vl—{vaB -5- — ' _ A i _‘ g M J wilt-o detain—«7:», =0 «2. - 3 1/1121?an (vs—«>14;va “6%)” :0 K v); 3/97: (fl :’ > ‘3' = ‘3 v, '"vao '1” ‘3 V50 (A+G)(/L+3):’O v2} % v “7': “i’ ,l - \ i \/ “" __ Z l = : A|--G/ ’(Z.¥ 3 (E‘I‘)/\/’:Z/ "/I) (‘V, /VI \I/ (b) Find the solution that satisﬁes the initial condition (93(0), = (1, —1). Re ort your solution as one real Vin _» a) ——-'> _ “(i-st? ‘ XZO): +CL(\‘,>W(I‘J ,C’B‘t ZC, +Ca:' C) 127:.w/ “WM‘ 6;: )~2c, c.~t+2§, =4 C2, '1 l C" —O 5. Given the system X =(_g ﬁx 4%,; 3,) 4—41: \$351) (a) Find the general solution. >N q l >__.. Q _, _ :«j ' ,Iv:~o 4‘47]: VL-Tl/ Act/é i: 53% '0 A. a (A A , VI 1, (steels/Wm :: 31:91:) (swat/w A1+L~Ixx+ur :0 EV; + Eva-=0 1” *1”; CK +L)z‘-O vz='\/, V V2,: D A; (‘54,) / V/ :l/ V/ :L /J’ (‘é'l’lj/ VIZO/ V2,: / 72145) :1: X": J) +¢LEethK~l> +5663] ; (b) Find the solution that satisﬁes the initial condition X(0) = (1,0). Report your 3 ion as at J -— l O _ l ) .._> :— wzl c4, X (0)“ Lb.) +CLCO+Z~ZQJ "/0 xlt) C 2 - ~21: C1 :l v C’! + CL: “1:8, 6. Given the system 2'2 22 2%,: %=( )X 91(4le /A”A:;Z’L“*E —46 (a) Find the general solution. a 16(ka 2 8:0 A2=H+22 : (warm—35 a ~L\ é-rt, ' \ CD '2 24 Z V _—_ L2~m)éé~«l‘(2>["">‘¢> *H 2,22)th (a) 7—-<z/\+zo=~o, ' § ; A/g ilm‘ 31):; [272\$ VI +ZVz/‘O “: Z “ Z VL=LI+L>V, A = LL? : H :2} . . -—*_ {\ (Z)+Z)VI\/VI:I/\/Ir (H‘LJ I .3 l l—f ‘ l \ 0 6A itv’ : é LN: (74%» >C ﬁght Z )H) I 6L1 ibéCos(Zt>+tslo[Zt)%+1/ Ht Coslzé) +L‘5/‘n (at) , =a (ma) modal ﬁddle) ~04“)3 Lit COSLZ’t) . Ht( 3“?) (at) \ )5 v (c195 (it) “574 (21) + t C Ccdg—t) +sm ("2t \ '7, V ‘ <— 95 L2 0 +-*<,;! a (2,1)) (b) Find the solution that satisﬁes the initial condition X(0) = (2A, 4). Report your solution as one real vector. v — i 0> ~z Z XZO> 'Cx ( 1>+CCZ’ Lt (4:2. Cl'l’CZ/iH 3, —1). Report your solution as one real vector. Yakcl U “a! ll‘ﬁsl L, : 3 C, +CZ>"/ S: : BCHfCDS[Zt> ‘LlCLItS"‘ﬁ{..Z‘—'i) “If '6, CcSLa-é) ~Wéqtsl‘ql2ﬁ) ...
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