University:
Swansea University
Course:
MA-252 | Probability Theory
Academic year:

2023
Views:

68

Pages:

8
Author:

Amal J.

83.Gavis Seidal lteration MethodQ.Solve 6x+15y+23=7227x + 6y-3= 85Ans.Consider the system, 27x+6y-3=856x tisy +23=72x+y+ 543=110The as: above system can be rearranged80Px85 6y+3](1)17%27y= =I1572 1-6x - - 23] -(2) Iz==54[ 110 P-px-y: upa (3)First IterationAS BASput y=0, z=0 in eq(1):1x27[ 55]x853.1481R27Put x 3.14.81 3=0 in eq (2)Probise countyY=1/72 15L sf - 6x85 2A. 9/162/OIIy= 15/92 - 1701/1 9 rft55x170=3.5408 returnedput x 3.1481 , y=3-5408 ineq 39we get2103 =I054110 2 3-1481 - 3.5408FC-8.8 D.9132I Seand literationPut y= 3.5408, 3=1.9132 in eq 1)xI(85 6(3.5408) +1-9132)27= 2.432put n 2.4481 z=x = 2-432, 3= 1.9132. in eq(2)y= 1572- - 6 x 2.432 - 2(1-9132)]= 3.572.put x = 2.432, y= 3.572 in eq (33=1110 - 2-432 - 36572]54E= 1.9258Third iterationIy= 3.572, z = 1.9258 in eq (1)x85- 6x3.572 +1-9258]27= 2.425 put x= 2.425 1 31091-9258 ineg 2 .y=isI72- 6 X2.425 -2 (1.99.5)= 3.573put x 2.425 , y = 3.573 inea (3)3= = 1110 - 2.425 -30573754= 1.925613191Fourth IterationOHput y=20425 STAP 3.573, 3. = 1.925nIin eq 12785- 6x3.573 + 1.925]P.I.T 6,627 2.425 put X= 2.425, y=in eq2).y= 3.573put n= 2.425, Y=3.5733=110 - 2.425-3.57354=1-925The values of nyy in the thirdand 4th iteration are almost equal;the root of the S System are :x = 20425yf 3.57 Bf=1.925Q.Solvelox - 5y-az=304x-loy+33=-3x+by+103 = 3 Correct to4 decimalEHF=C614.0 2 $&5510x-by- - 23=3rx 3 + 5y + 2 310x103t5y+28](i)4x loy +3z = -3 OH12y=-10-337-(2) -brottcloupstaams 910 tip#1-3 3 Yord3 =10-3-by -(3)First lteration2800Put y=0, z=0 in eq (13"x = 3 310 . 1Put x=0.3 3=0 in eq(a)y= 10 -3-4x0.37 -= 0.42 put x-0.3 y= 0.42.3=- 0.5822nd lierationPut y= 0.42, 3=-0.582 in eq(i)X z= 0.3936Put x= 0.3936 Z=-0.582 cq(2)y=- I -3-4(0-3936) 43 (0.582)10ox 0.282.8put x 0.3936 / g=0.28283z to - - 6x0.2828 - 0.3936= - 0.5090[ 3rd iterationput y 0 . 2828, 3= -0.5090x to (3 + +2 (-0.5090)= 0.3396put x 0.3396 2,32-005090.y==(=3= - 4 (0.3396) +3(0.509))0.2831put y=0.28313=110- 0.3396)f= -0.5037Oxd6-76P0Z4O