M235A8Solnpgs

M235A8Solnpgs - l3 MA8 Question 1;: So1ution Begin by...

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Unformatted text preview: l3 MA8 Question 1;: So1ution Begin by defining vectors x & y containing the x, y vaiues, respective1y: X = [8.025; 10.170; 11.202; 10.736; 9.092] X: 8.0250 £3338 ' 1816398 {at enkrma . Yflj VQLMJLO [8.310; 6.355; 3.212; 0.375; —2.267] ‘< ‘< II II 8.3100 6.3550 3.2120 0.3750 -2.2670 Next, define vectors yl ~> v6 corresponding to the co1umns of the 6x6 matrix (see equation (*3): 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 v4 x v4 8.0250 10.1700 Page 1:3 11.2020 10.7360 9.0920 v5 y v5 II II 8.3100 6.3550 3.2120 0.3750 —2.2670 v6 v6 HHHHH a1ong row 1 of equation (*). This wi11 require the eva1uation of [1; 1; l; 1; 1] MA8 H To determine the equation ofthe orbit, perform a cofactor expansionjg b//’ determinants A1 ~> A6 defined be1ow: A1 = [v2, v3, v4, v5, v6] A1 = 66.6878 64.6304 35.9808 4.0260 —20.6116 69.0561 40.3860 10.3169 0.1406 5.1393 8 10 A2 = [v1, v3, v4, v5, v6] A2 = 64.4006 103.4289 125.4848 115.2617 82.6645 69.0561 40.3860 10.3169 0.1406 5.1393 8 9 A3 = [V1, v2, v4, v5, v6] A3 = 64.4006 103.4289 125.4848 115.2617 82.6645 66.6878 64.6304 35.9808 4.0260 ~20.6116 8. 10. 11. 10. 9. A4 = [V1, v2, v3, v5, v6] A4= 64.4006 66.6878 69. .0250 10. 11. 1700 2020 .7360 9. 0920 .0250 10. 11. 10. 1700 2020 7360 .0920 0250 1700 2020 7360 0920 0561 Newman NOWCDOO Newman 8. .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 1L+ ;Z_r7\cxr*§5 4gr~ dflerLn0334LL Moxiv‘fous/Ar] ——>Aé 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 V///’ c2 = ~det(A2) C2 _ (\0 math) —102 8954 V/// c3 = detCA3) c3 = 446.0293 V/// c4 = —det(A4) c4 = —2.4764e+003\/ c5 = detCAS) c5 = —1.4280e+003 V// c6 = -det(A6) c6 = —1.7109e+004 V// Page 15 ...
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This note was uploaded on 04/27/2010 for the course MATH 235 taught by Professor Celmin during the Winter '08 term at Waterloo.

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M235A8Solnpgs - l3 MA8 Question 1;: So1ution Begin by...

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