Question

Question 7 Solve the following system of equations using the Gauss-Seidel iterative method 10.61 - 72 +263 6 -21 + 11.72 -13 +3.04 25 2.11 - 12 + 10.03-24 -11 3x2 - 33 + 844 = 15 starting with x(0) = [0,0,0,0)", and iterating until e = 10-3, where || x() – x(4+1) || ||x(4+1)||

Answer 1

solve the following system of Eruations using the Gauss seidel iterative method 10X,-X2 + 2xy = 6 -X, +11x2-x3+34y=25 2X | - x2 + 6x - x = - 4 3x2 -*3.+8x4 = 15 starting with x10!= (0,0,0,075 sel" NOWN The Herie we let x = x, X2=Y, X₂=2, Xo = 0 ow tox-y+ 92 = 6. 3w - x +lly-z=25 -W + 2xy +107 =-11 8W - OX + 3y - 2 - 15 coethicient matrix of the given system is not diagonally dominant rearrange the equatias as follows, such that the elements in the coefficient matrix are digonally dominents. 8W -0x +3y-2.15 ow tox-yta2=6 3W-X+lly -2 -25 -Wtex -y +1025-1 from the above Equections - (15-0xx + 3 Yk-ZK) to (6-0 wktity, - 22x) t (25-3W.K+1+XkH+Zx) ZXH = to (-11+ WK+) -2RkYK+1) Xkti Ykti -

initial gauss Iw, xiy, 2 = 10,0,0,0) salution steps are est approximation X 6 0.6 y = Wii = ţ115 - 0+0+0) = $(15) = 1.875" to 161 = i (25–361.875) + (0.6)+o) = + (14.9758 = 1-81591 to (-1141-875)-2108)+(1.815 41) 5 i 1-8.58909) approximation 212 -0.8509 ind 2 X2 Z2- W2= $(15–361.81541)+(-0.850910] = $18.70136) = 1.08767 to 10 + (1-81591)-21-0.85091))= ito (9.51771] = 8-95177 825 ti (05-311.08767)+10.95177) +(-0-85091)] t[21.98914) - 140l 198524 to L-11 +1108767)-210.95177)+(1.98526)] =to (-9.83062] = -0.48306 approximation wysŚ L15-010-9517) – 311.98526)+(-0.983061] - [ 8.06116) = 100765 to [6+ (1.98520421-0.98306)] (9.95738 )= 0.44519 932 t 125 - 31.000 765) + (0.495148 +4-0-98306] 3rd x3= 1.99901 Ť Ľ21.98914) =

23 - 16L-11 + (100761) - 2 ( 44514) + (1१११० --१. १४ 362) - - 0• ११ । apo roximations 4th tes - 3 - 4 4 0 ) + (-0 1 4 834)3 8310 63 | - 00057 1526 1. ५११/ २(-0.११836] - १.११ 5740 - 099950 %3D zu - y. ४५ : + 25-3 ( 1 •oobs 7) + (0 •१११52)+ (-०.११:30 12) १११५१] - ।.११११७ 1-1 + 1. 0005 1) -२ (०.१११52) + 1.५५११६)) 1-१.११862] - -० १११४६ sth approximation [is- 361 ११११5) + (-0 . • • १११86)] -108-000230 Xy - 1606 - [१११५5-21-0• ५११86)] -+9.१११68] - 0.१११११ 1,223-- 3८1.00003) + (०.१११५7) + (-० ११५४6) =122] ३. +-) + (1.00003-2 10 ११११ 7) +२) 32 1-00003 Jy-- 25 - + (-१.११११) - -0.१११११

Solution By Gauss leidal metho y W = Xų =1.00003 - I x = x1 0:49997=1 yeQ x2 = 2. 2=X3 = 0.99999 = -1 Answer.