Question

For the following linear system, Show how to approach the values of xt and X2 that would satisfy this system using the Gauss-Seidel method technique. You should check the Coefficient matrix for the system before you start, if it is not diagonally dominants please state and show how to handle this issue. Show two iterations, and at the end of the second iteration show if you can stop the iterations if the es (Pre-specified error) -0.54 Falling to show the detailed steps for your work may lead to receiving zero in this question. 4x1 - 8x25 -1 6x2 - 25 Attache rome uy computer

Answer 1

linear ear system Solution The given of equation is 4*, 8x2=5 -x + 672 = 25 The given system of equation also can be written as -8 x 5 6 25 -1 x2 .: the co-efficient matrin is A = 4 -1 6. Since, 161 >/11 The given system of equation is not diagonaly dominant

so we do not use Gauss-seidel method to solve this system linear or equation. of we use Cramer's Rule to solve this system of system of equation Νοιώ the determinant of A is A 8 11 6 and -8 5 A. = 2.5 6 5 A2 25 - 1

Now ; U= 5 - 8 25 6 4 -8 - 1 6 230 16 14.375 and A2 X2 = A 니 5 25 4 -8 - 6 105 16 6.5625 x = 14.375 , X2 = 6.5625

Here x. = 14.375 and x2 = 6.5625 be the exact solution of the given linear system of equation Now We find the the computed solution of the given linear system of equation by by using Gauss elimination method. Grive system of equation is 40 - 8x2 = 5 -X, & 642= =25 21 m 6 X2 -8. 5. 0.25 6 - 1 25 23.75 4 The Pivotal equations are 40 - 812 = 5 422 23.75

Solving this equation (1) we have 23.75 22 -5.9375 4 and 4x, - 802 = 5 = 40, = 5 + 802 52.5 = 40, 2 52.5 4 - = ) 811 = 13.125 :: the computed solution of the given linear system of equation is x = 13. 125, 72 = 5.9375 : the percentage of Error for the value x, is 13.1251 x 100% 114.375-13. 14.375 UI 8. 696% correct to three decimal Places

the percentage of error and the for the Value X2 is 16.5625 - 5.9375) y 100% 6.5625 9.524% correct to three decimal Places.