Question

rx2 has 0 coefficient in the first equation

QUESTION 2 Consider the linear system 11 + 0.5X1 T1 12 0.5x2 + 13 0.25x3 X3 0.2 -1.425 2 = whose solution is (0.9, -0.8,0.7). (a) Determine whether the coefficient matrix is strictly diagonally dominant. (b) Approximate the solution of the system by performing two iterations of the Gauss-Seidel algorithm, using x(0) = (0,0,0)t as the initial guess. (c) Approximate the solution of the system using one iteration of the SOR scheme, with w = 0.7 and x(0) = (0,0,0)

Answer 1

Answer Consider the given callabong x,-z = 0.2 0.5u +H ₂ -0.2503 = -1.425 x, -0.5U2tuz = 2 written in Cochcient mabil. 10.5 1 -0.25 a 042 a an a 2 as Az as ازة laila 1921 +19,31 = 120 + 1-11 21 (C2221 zlail tlay1 = 1210.51+0.25. (233l 3 lagel +232 1 - 1112 1-0.5+111 111 * 11.51 Condition is not satisfied 1933) Llazol tlagal coeficient Matril is not strictly dicigonal dominant. (6) from the above equations + (0.2-04 + 2,4) A4LTI f (-1.425-0-52x++ 0.2524) = f (2-44 11 ta symt Yk to ZKT

I 0.2 Initial gauss (14,9, 2) = (0,0,0) st approximation - +(0.2-060) +)) = (0-2] (1425-0.5(0-2) +0-2500)) = 444.525) = (2-(0.2) +0.56-1.525)) = 0.0375) = y, = -1.525 =1.0375 Z, and -1.2375 appropimaton 2 = 0.2-064.525) +(1:0375) -11-2375) = 1425-0.5(4.2375) +0.250.0375)) =144.18438] 42 = y = -1.78438 le Rate = 22 - (2-(1-2375) +0-561.78438)) - 4 [0.12969) –-0.12969 SOR Method with w=0.7 (1-w), 2 tw. f (0.2-oyktz4) +0.2574) Ykt (1-w). Y + wif (-1.425-0.524440 -(1-w). ZL + W. 1 (2-744+1 +0.59K+1) (1-070 +0.7 (0.2-0+) = 0.3+0-14 = 0.44 y =(-0.700 +0.76-1425-0.5(0.44)+0)=-0.8515 = (1-0.7)0 +0.7(2-0,44+0-5(-0.8515)) = 1.093975 ZILH 2,