# Performing Gauss Elimination with MatLab

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Lukumon Kazeem on 11 Jul 2012
Commented: Ilyas Nhasse on 26 Oct 2021
K =
-0.2106 0.4656 -0.4531 0.7106
-0.6018 0.2421 -0.8383 1.3634
0.0773 -0.5600 0.4168 -0.2733
0.7945 1.0603 1.5393 0.0098
I have the above matrix and I'd like to perform Gauss elimination on it with MatLab such that I am left with an upper triangular matrix. Please how can I proceed?
Raphael Chinchilla on 8 Oct 2017
use the function rref(K)

József Szabó on 29 Jan 2020
function x = solveGauss(A,b)
s = length(A);
for j = 1:(s-1)
for i = s:-1:j+1
m = A(i,j)/A(j,j);
A(i,:) = A(i,:) - m*A(j,:);
b(i) = b(i) - m*b(j);
end
end
x = zeros(s,1);
x(s) = b(s)/A(s,s);
for i = s-1:-1:1
sum = 0;
for j = s:-1:i+1
sum = sum + A(i,j)*x(j);
end
x(i) = (b(i)- sum)/A(i,i);
end
##### 2 CommentsShowHide 1 older comment
Ilyas Nhasse on 26 Oct 2021
what if we got an A(i,i)=0

Richard Brown on 12 Jul 2012
The function you want is LU
[L, U] = lu(K);
The upper triangular matrix resulting from Gaussian elimination with partial pivoting is U. L is a permuted lower triangular matrix. If you're using it to solve equations K*x = b, then you can do
x = U \ (L \ b);
or if you only have one right hand side, you can save a bit of effort and let MATLAB do it:
x = K \ b;
##### 2 CommentsShowHide 1 older comment
Richard Brown on 13 Jul 2012
I wouldn't expect it would necessarily compare with published literature - what you get depends on the pivoting strategy (as you point out).
Complete pivoting is rarely used - it is pretty universally recognised that there is no practical advantage to using it over partial pivoting, and there is significantly more implementation overhead. So I would question whether results you've found in the literature use complete pivoting, unless it was a paper studying pivoting strategies.
What you might want is the LU factorisation with no pivoting. You can trick lu into providing this by using the sparse version of the algorithm with a pivoting threshold of zero:
[L, U] = lu(sparse(K),0);
% L = full(L); U = full(U); %optionally

James Tursa on 11 Jul 2012
##### 2 CommentsShowHide 1 older comment
James Tursa on 13 Jul 2012
You need to download the gecp function from the FEX link I posted above, and then put the file gecp.m somewhere on the MATLAB path.

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