Question

Please show all steps clearly. thanks

1. (40 points) Rearrange the equations to form a strictly diagonally dominant system. Apply two steps of the Jacobi and Gauss-Seidal Methods from starting vector(0,0,0". [i -8 -21 1 1 5 (3 -11

Answer 1

5 L 13 1 -1 L & - 2 -822 -20221 14 +X2 +5Xz=-4 34 - Xq +7z = 2 Now reduce the given diagonally dominant. System inte strictly Remarks..

wale... 3x4 - X, + x3 = 2 24 - 8R2 - 2x3 = 1 1 + x2 +5X3 24 Itlethod & Jacobi Method so by given system = 1 (2+X, -2₂) 541-24 +3337- of equations 2 x 3 X -4 - 34 -X2) I ste xz = 16-4-x -x₂) here Initial approximation is given as - fone)? Bu or I approximation Your trouot otthon moyen *foothol ---0.125 X = 1 4 (-4-0-0) = -1/2 = -0.8 2C) - 5 ( 2 +2° -2] =${2+4*7--) 2,177 34 | -*+- 7 = (00-5 +33 ? Isle x H2 28 -98 10. 93 33.. Teacher's Signature..... 4o o

hc e (64-18 + 8-134- =-6(1-27 -6149770-24] = $(-19) and play = 4 (4 - " - ) 91-9b + -109 २५ 190 =${434+3) -0908883 (2) - 0.9333 - x2 2 2.375 regled 2-0-908333 - - so 2 )

- y2010) I Method approximation (8,6 g I apponimenion Gauss seidal Method with Intal by system of equations we have - H&to-o) z ot66- 7 24 taxoy - ay 0044766-- - yetu 11 - 4 2 - 1 - 4) 1-96-16 + I approximation 342+7cm) 2} 2370) = 5(240cm 5+

346 360 2629. goye - 0.967) = 0.96 101 - eyle - 5 11- 60+ 25"] 346 360 - 346 360 CO =*0726-60] =$(662 ] *1*3 = = -0.986377 |- اه UTI 1 251-520-2760 76527 = -13636 = -0.94677 ao (24) = 0.901 | 140 2-0-22 627 E P 2-0-946971 14400 Remarks................