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M235A3Soln - WW ALL X“ MED/HAM Wag WWW/«MM M cfl—®...

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Unformatted text preview: WW ALL X“ MED/HAM, Wag) WWW/«MM M cfl—® MMCC—AI cub WW :1 O o o .- ~— - o o 61.0 NOEL)“ XEC: .4 )\ 00 --- o 0 0., O ”-l /\ O " 7“ 0 O 0‘2. (9 O ~l >\ “' O O 0‘2 ‘ I t O O 0 ~—-* -‘ A dM’Z. o . ,‘ j / G >3 " Uffi ”mud; V >5ch ML91 NW J M, o o o - , :wgwflo xii-am: >\ + -~+Ck0 ~l X 0 - r —— o O Q“ ’ O. 0 ~\ % ~ , 0 $3 2 1 \ \ ‘ ‘ _ / I o 0 ~— :, “‘ A (MA—o. O o o o , , - O “\ X+qu W35” 7:95 elm-W W LA, W x/ ‘ ' Wm M MC?!) . ., \\ mwm/ We ww MW) Mme <sw M M-l aéfii)fl I 7— ) +Ow-'>‘ + ' "+0‘O. CM 4W 5 W (AA/0'06] WM flail/Waxy 75%? M10 Wm M 0&6” " W 1 .4.— C(30) ‘3: Lao) / 0L \X ‘ ”'MW/I M / W C (Q‘3q1)‘ ‘/ (kit-y ) 0*“ LM'}[email protected]—|)HJ W ' K/ W L*)\:.A~A (96%) j “a“ = >\ (X10 w.) + +azk+ab+6>mboer>w O ’ —2 +204) x552;— »v ' ,A—g» O Q—XCA’D 3~>\ , Z ~>x2 +,\+2 g-) 2,\~+ A~3 z ’[Q">V7‘—+?\+Z)Q\-3‘)-Q,\~4><2~,\fl :: /\~-— ‘ Z ' 1 Q 24> D at; +41%] 2 (3—3) (A —3x+2) =(E29—2 cw) // Sir M (ADE) ==_ M 0") TM 8 WMWMLMW , \/ mm“ (iii) High M “few. 'W. ‘ WWWQ§XBAWF4 @«A M plate/we MQML%(Me-W Matte/4 o.—-/\ 9:— *6”..me QQ wmé AMA M x~TA<A>\'/”+wgé\)\ W M::)’@+d) : :)[email protected]"A 52%)(0 l)\/ :: .QZ’HQV’C’ albi-Qmi)“ Haida abide)” 4, acihlm. 0 MW £9er Qua/c QM? " <0 041,) Cat—firm, «okaai Moi «fir/c: a 9% 91A. «1 Qroi 9r >2 6 C3 I Am» +ci,<:-arc»o{/c ,cQ»+<i hmA’Ci‘fdA “£316 0 0/ , (Z marks) W W‘Qfid’ “M‘th/S—Fggzzo ,Q MW®WWWWIM Mm \/\/ G ZAC/KXA +5Ag+3fltv§>= 4/\A+g’/\ZM+§P2&:’ wwwwmw < zQxA 4&pr +Q3LA ~gA/u)” . } EJmfigAd/f gigwfiwwfifiewww j M «A «)3; ,1— O 2%A"@>‘f’ j ¢/: c327. 4c/\(/\ 31) =0 gg/WXVJ) 7 HM WWW WM) ww‘fw / 30“ 11A - O = 43A ' W- KWWW©~>+0 [email protected] 32A (9 W @Wefi 4414+1<~3U“-00‘ MW — (-77“ mark») If“. M13 3‘; m MA3 Quest1on 12) So1ut1on: Beg1n by enter1ng the 1n1t1a1 vector x, and matr1x A: X = [1; 1; 1] X: 1 1 1 n = 25 n: 25 format 1ong = [3.72 3.19 0.93; 0.97 —3.04 2.11; 3.45 0.17 2.32] A: 3.72000000000000 0.97000000000000 3.45000000000000 Enter the 100p: fo r j=1: n y = A x [t_]=m y/yCr ) end 3.19000000000000 0.93000000000000 —3.04000OOOOOOOOO 2.11000000000000 0.17000000000000 2.32000000000000 axCabsCyD; mu — —y(r) \/ (gr efl1'Cv‘1A3 Loop) The output 15 11sted be1ow: (To save paper on1y the f1rst and 1ast resu1ts W111 be 11sted here) for j=1 we get: y: 7.84000000000000 0.04000000000000 5.94000000000000 mu: 7.84000000000000 X: 1.00000000000000 0.00510204081633 0.75765306122449 for j=25 we get: y: 5.71147483920800 2.01093424107969 the number of t1mes to execute the 100p n, MA3 5.78515363295003 mu= 5.78515363295003 \/ (—flm imi' (“Mi M 50(9) X: 0.98726415953374 0.34760256488716 1.00000000000000 Examining the output, the dominant eigenva1ue of matrix A to 3 decima] \/// p1aces is 5.785 and 1tS corresponding eigenvector is [0.987, 0.348, 1.000] Now, using the command [P, D] = eigCA), we obtain: [P, D] = eigCA) P: —0.68200516215198 —0.5174869003256l 0.44945221619252 —O.2401249517ll82 0.36160084743634 —O.85144881235287 —0.690803l3l40825 0.77553345197014 —O.27023623980236 D = 5.78515373538554 0 0 0 0.09719754360055 0 0 0 —2.88235127898609 The dominant eigenva1ue is in fu11 agreement with that found above; however, the corresponding eigenvector is different. The reason for this is that MATLAB norma1izes the eigenvectors. If we 1et v = [0.987, 0.348, 1.000] V// and norma1ize using vn = v/norva) we get to 3 decima] p]aces: vn = [0.682, 0.240, 0.691] which apart from a negative sign is in agreement with that found ear1ier. 5 x a + ”QM/‘3 C “W Q 2. $1.0M [mini o—i: LPG MarkS] Page 10 ...
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