Question

2. Occasionally we use a numeric method to solve a linear system, especially if it is a large system with many zeros in it (a sparse system). For example, to solve the system below, we would first rewrite it as shown 2x+3y 5 6x-2y-7 This can be rewritten in the form below 5-2x Note that the largest coefficient in each row has been used as the divisor. This is desirable, but not essential. Once this has been done, we start with an initial estimate for both x and y, say (0,0) or maybe (1,1, or something similar. Set initial values in MATLAB to this effect. In this assignment, use (0,0,0) Once this has been done, we enter a for loop, and repeatedly use the equations above to calculate new values for x and y. I suggest doing this 10 times. Make sure you use the command format long before entering the for loop, to print out lots of decimal places. After the for loop has ended, substitute the x and y values obtained back into the LHS of each equation, subtract the RHS and square. Add up all these values and display the result. Solve the system below using the Gauss-Seidel method. Submit you MATLAB file to Turnitin BUT make sure you zip it first. Please do not use the RAR format. 2, +7x -11

Answer 1

clc;
close all;
clear all;

%%%we can write given equation in Ax=b form
A=[5 1 -1;2 7 1; 1 -2 -6];%%%%%A matrix
b=[2 -11 -1]';%%b vector
x=[0 0 0]';%%initial guass
N=size(x);%%number of unknowns
sum = 0;
xold = x;
%%%main algorithm
for n_iter=1:10
for i = 1:N
for j = 1:N
if (j ~= i)
sum = sum + (A(i,j)/A(i,i)) * xold(j);
else
continue;
end
end
x(i) = -sum + b(i)/A(i,i);
sum = 0;
end
if(abs(x(i)-xold(j))<0.001)
break;
end
xold = x;
end
%%displaying x vector after 10 interations
disp('x vector');
disp(x);

古古古we can write given equation in Ax=b form b= [2-11-11';%8b vector x= [ 0 0 0]';%%initial guass N=size (x) ;%%number of unknowns sum = 0; 10 12 %%&main algorithm for n iter=1:10 13 for 1 1:N 15 16 17 18 for j = 1:N if (j ~= 1) (A(ǐ,j)/A ( i , i)) surn= sum + * xold ( j ) ; else continue 20 21 end -um =0; b(i)/A(i,i); 23 sum - Command Window x vector 0.9997 -1.9996 0.9996