Question

The pscudocode shown below solves a system of n linear algebraic equations using Gauss-Jordan 125] elimination. DOFOR -1,n DOPOR 1 = k + 1,n + 1 END DO ae 1 DOFOR 1 = 1, n k THEN IF i DOFOR j- k+1,n+ 1 ENDDO END IF END DO END DO DOFOR m-1,n END DO Write a Matlab function program GaussJordan(A,n) which implements this algorithm and a) returns the solution. Here A is the augmented matrix consisting of the coefficient matrix and the right hand side vector and n is the number of equations. b) Write a Matilab main program which calls the function program developed in part (a) to solve the system of equations 2x-3x24 4x1 + 2x2 =-1 and prints the result. pcrations of the algorithm to obtain the solution of the problem ented in part (b). Show the augmemted matrix A after every change in any of its elements

Answer 1

%% function

function x = Gaussjordan( a, n )
% This function solves linear algebric equations using Gauss-Gordan method
% Inputs are a and n
% a is augmented matrix consiting of the coefficent matrix and the right
% hand side vector
% n is number of equations

for k = 1:n
for i = k+1:n+1
a(k,i) = a(k,i)/a(k,k);
end
a(k,k) = 1;
for i = 1:n
if(i~=k)
for j = k+1:n+1
a(i,j) = a(i,j) - a(k,j)*a(i,k);
end
end
end
end
for m =1:n
x(m) = a(m, n+1);
end
end

%% main code

clc
clear all
A = [ 2 -3 4; 4 2 -1 ];
n = 2;
x = Gaussjordan(A,n);
fprintf('Reqired solutions\n');
for i = 1:n
fprintf('x(%d) = %0.4f\n',i,x(i));
end