M235A8Soln

M235A8Soln - ‘A 1.0“ v 8‘ 1 (NAT; :ATTCA“3T :Aofif...

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Unformatted text preview: ‘A 1.0“ v 8‘ 1 (NAT; :ATTCA“3T :Aofif / Siam g \5 gjmme‘Xfl‘sg BT=3- _ -\ A ‘AT =- A LATE mdflx'plos \ost swes b3 ' . 1‘ _ A O‘f\ W V. | La. lefl' ‘/ AT: A (“3‘ (“meta xmw mu 5% AT 1 ‘ n +4”. A 14+. / em =A‘ O a T 1. 1. .. , :15 CAL} 2A “:9 A x; ,synmeMCJ. W.“ Ca marh8> *' T j’ v ‘30 :I‘ZC .SWLC . \/ 15 jAmHLV‘ £95.ch ‘X’Lq‘r y‘HX' 15 cu \x\ mdle —‘-<-J H—‘IA 0\ 0.:me ade- M For oaM‘oVL‘é anq‘aa/S‘ CH, \xk mdvkce;\ OJ 0+2?) ML? 4‘ —>> ‘6 .759 ‘L ‘39 KHW”) (x M) =7< HS? \// mnéflre) a; 719%? Is ecuzd‘ +e 1—K cm camp\t% dim/{33331 J TV Mid— Rox er\ Adv/dear. C3> = {ASE/5&7 5% CW4" nj’i’k A?qu Mmrproddd‘em (En. \/ AP?“ G‘qm ’ Schm‘wfi': xx “@232 (3 ‘\"Z O c‘ if 3- 3 “‘5 3 [3: Q fig"; 3 O r31——>r ~(o Q 3 O ‘ 3 -~—-> H4“ 0 ll~1 b ‘b’!b O"0\ 0‘ O ~_-\7'Q\~-\ O ‘>O\~\0 OQ‘D‘ O 000:) @004) v “K 00 002 w x3: §> ~\3©o 0430 (302.3 \A ) QM X 1: “VJ—2 V17— "‘/Jro VJ} O ’Z/Jg, ‘f3 7 ~i.4_+} .l-i* z e 3 Z L .\ —-.\. +1: ’5. —-.\_ + 2 b 3 2. a, b4’E-vt’lri O «at: .3, X '3 C \ \ 1 O l l \ O (Q erhi) 13> 0x~b1 7‘ ’q-b{ O‘FfionQ L—3> ’ 0x = O. Nous) wH’k Mm¥® 4m. dz‘indwd Mne/ Pmcifi m Q“) a Math 2 0:le 2 >433? —.— 2\ m0: M an 'Hrfi, 5% hand) “34‘ @zmfifnz “Q’Cmm —.= (arm? firm 3:? v = (Hifibji‘? R . :(*\'\s’\fl i? 5?an 9.3:" A. =ZQ3J-\\§$§ B3 cm or 57 // cgfij~>fi> Em} ; MAM-351:) ‘0 ~13 ~\ ~ 3 \ 0 0 \_‘J3 7,2 0 r.\——>1~Er3+v \ “x5? \ 0 \$ 0 4—H“: H53 0 “+59% ‘ ‘W “I53 6 \ -\ o ’2. O b... O > 8 PM? _.~ 0 ‘ ‘50“‘(33 0 w \__‘J— ._..._ O ~fluid}: O O .?3:(1+\J§\ b \ ~\ -mg C 1 ~\ ~44?) 0 \Kb 0 Oi 2) K; : ~i(l-‘I\E>Kz C ‘ LU'HE) C % \l O iCx-fifi 0 $2 : ”i(\+l\):?>7<3 _~ v V ‘ ~ SM} fetcg a» ~3 2 {UMWK 5E5; «ALCWN‘QKS 2 X3 “’31; H43) 2K3 \ \J. (145:0 Z. -LCHKJE) zg «(Mm W E \/ z, u& l “fie «H4 ‘ l9“; fiflts W A iO-ta) +Z—t-(u—33-H :fi‘ _,..L. 50 “was +75: \/ —~.\.. ...; 7 SS? “5 a MW MWWW 67' A I C) O C O \53 Q 0 Q 453 _. 3. wk. _\ 2%34/2 233 “Z _,\ _ —J. {33 >7; 153;”2 A ,— f3 f3 _\__ J 15 “FWQAU/kx) kmce MM- Question 11: So1ution MA8 Begin by defining vectors X & y containing the X, y va1ues, respective1y: X = [8.025; 10.170; 11.202; 10.736; 9.092] X: 8.0250 10.1700 11.2020 10.7360 9.0920 y = [8.310; 6.355; 3.212; 0.375; -2.267] K< ll 8.3100 6.3550 3.2120 0.3750 -2.2670 Next, define vectors v1 ~> v6 corresponding to the co1umns of the 6X6 matrix (see equation (*)): v1 = X.*X v1 = 64.4006 103.4289 125.4848 115.2617 82.6645 v2 = X.*y v2 = 66.6878 64.6304 35.9808 4.0260 —20.6116 v3 = y.*y v3 = 69.0561 40.3860 10.3169 0.1406 5.1393 8.0250 10.1700 Page 1:3 11.2020 10.7360 9.0920 II v5 y II v5 8.3100 6.3550 3.2120 0.3750 ~2.2670 v6 [1; 1; 1; l; 1] v6 II II HHHHH a1ong row 1 of equation (*). This wi11 require the eva1uation of determinants A1 ~> A6 defined be10w: MA8 H To determine the equation ofthe orbit, perform a cofactor expansion¥§ b//’ A1 = [v2, v3, v4, v5, A1 = 66.6878 69.0561 64.6304 40.3860 35.9808 10.3169 4.0260 0.1406 —20.6116 5.1393 A2 = [v1, v3, v4, v5, A2 = 64.4006 69.0561 103.4289 40.3860 125.4848 10.3169 115.2617 0.1406 82.6645 5.1393 A3 = [V1, v2, v4, v5, A3 = 64.4006 66.6878 103.4289 64.6304 125.4848 35.9808 115.2617 4.0260 82.6645 —20.6116 A4 = [V1, V2, v3, v5, A4 = 64.4006 66.6878 v6] 8 11 10 v6] 8. 10. 11 v6] 8. 10. 11 10. 9 v6] 69 .0250 10. .2020 .7360 9. 1700 0920 0250 1700 .2020 10. 9. 7360 0920 0250 1700 .2020 7360 .0920 .0561 NOUJONOO NOWONOO NOWGOO .3100 .3550 .2120 .3750 .2670 .3100 .3550 .2120 .3750 .2670 .3100 .3550 .2120 .3750 .2670 .3100 .0000 .0000 .0000 .0000 .0000 HHHHH .0000 .0000 .0000 .0000 .0000 HHHHH .0000 .0000 .0000 .0000 .0000 HHHHH 1.0000 Page fL% ,2 MOU‘kS «LP dxhrmininféj mothfcw/Jrl «M46 MA8' 103.4289 64.6304 40.3860 6.3550 1.0000 125.4848 35.9808 10.3169 3.2120 1.0000 115.2617 4.0260 0.1406 0.3750 1.0000 82.6645 —20.6116 5.1393 —2.2670 1.0000 A5 = [V1, v2, v3, v4, v6] A5 = 64.4006 66.6878 69.0561 8.0250 1.0000 103.4289 64.6304 40.3860 10.1700 1.0000 125.4848 35.9808 10.3169 11.2020 1.0000 115.2617 4.0260 0.1406 10.7360 1.0000 82.6645 —20.6116 5.1393 9.0920 1.0000 A6 = [V1, v2, v3, v4, v5] A6 = 64.4006 66.6878 69.0561 8.0250 8.3100 103.4289 64.6304 40.3860 10.1700 6.3550 125.4848 35.9808 10.3169 11.2020 3.2120 115.2617 4.0260 0.1406 10.7360 0.3750 82.6645 —20.6116 5.1393 9.0920 —2.2670 The coefficients c1 —> c6 of the orbit equation c1*xA2 + c2*xy + c3*yA2 + c4*x + C5*y + c6 = 0 are then: c1 = detCAl) c1 = 386.8024 \///’ c2 = ~detCA2) C2 = (\O mark/5} —102.8954 v/// c3 = det(A3) c3 = 446.0293 v/// c4=—mHM) [’E%x\o¥55'ma&5] c4 = —2.4764e+003V/// c5 = det(A5) c5 = —1.4280e+003 \// c6 = -det(A6) c6 = -1.71096+004 V// Page 3:: ...
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This note was uploaded on 01/05/2012 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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M235A8Soln - ‘A 1.0“ v 8‘ 1 (NAT; :ATTCA“3T :Aofif...

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