set of n-linear equations in matlab [closed] - matlab

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I have some trouble on setting of n-linear equations in matlab.I don't know how can I declare in matlab.I need matlab code for setting of n-linear equations..

Answer 1

You can write n-linear equations as one matrix equation to solve it. Here you can find great example:
http://blogs.mathworks.com/pick/2007/09/13/matlab-basics-video-solving-linear-equations/ (video!)
See also these pages:
http://en.wikipedia.org/wiki/System_of_linear_equations
http://en.wikipedia.org/wiki/Matrix_equation

Answer 2

You can solve a linear system in various ways, depending on whether there exists a unique solution or not.
A simple way is by reducing it to reduced-echelon form (rref).
Consider the system:
x + 5y = 4
2x - y = 1
You can write the coefficient matrix A, and the RHS, B as follows: (' is the transpose operator)
>> A = [1 5; 2 -1]
A =
1 5
2 -1
>> B = [4 1]'
B =
4
1
You can write it as an augmented matrix (A|B):
>> horzcat(A,B)
ans =
1 5 4
2 -1 1
And then find the REF(A|B)
>> rref(ans)
ans =
1.0000 0 0.8182
0 1.0000 0.6364
And hence x ~ .8182, y ~ .6364.

Answer 3

The absolutely fastest way to solve linear equations in MATLAB is simply to setup your equation on the form
AX = B
and then solve by
X = A\B
You can issue
help mldivide
to find more information on matrix division and what limitations it has.

Answer 4

A Code for iterative method Guase Seidel
tol is error tolerance
x0 is first guess for solution
function seidel(A,b,x0,tol,itmax)
%Solve the system Ax=b using the Gauss-Seidel iteration method.
clc
% =======================================================
% Programmer : A. Ziaee mehr
%
help seidel
n=length(b);
x=zeros(n,1);
%fprintf('\n')
disp('The augumented matrix is = ')
Augm=[A b]
Y=zeros(n,1);
Y=x0;
for k=1:itmax +1
for ii=1:n
S=0;
for jj=1:ii-1
S=S+A(ii,jj)*x(jj);
end
for jj=ii+1:n
S=S+A(ii,jj)*x0(jj);
end
if (A(ii,ii)==0)
break
end
x(ii)=(-S+b(ii))/A(ii,ii);
end
err=abs(norm(x-x0));
rerr=err/(norm(x)+eps);
x0=x;
Y=[Y x];
if(rerr<tol)
break;
end
end
% Print the results
if (A(ii,ii)==0)
disp('division by zero')
elseif (k==itmax+1)
disp('No convergence')
else
%fprintf('\n')
disp('The solution vector are : ')
fprintf('\n')
disp('iter 0 1 2 3 4 ... ');
fprintf('\n')
for ii=1:n
fprintf('%1.0f= ',ii);
fprintf('%10.6f ',Y(ii,1:k+1));
fprintf('\n')
end
fprintf('\n')
disp(['The method converges after ',num2str(k),' iterations to'])
x
end