I was trying to modify the matlab built-in lutx function, by using for loops, but when I tested the results with my new function it didn't give the same results.
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function [L,U,p] = lutx(A)
%LU Triangular factorization
% [L,U,p] = lutx(A) produces a unit lower triangular
% matrix L, an upper triangular matrix U, and a
% permutation vector p, so that L*U = A(p,:).
[n,n] = size(A);
p = (1:n)'
for k = 1:n-1
% Find largest element below diagonal in k-th column
[r,m] = max(abs(A(k:n,k)));
m = m+k-1;
% Skip elimination if column is zero
if (A(m,k) ~= 0)
% Swap pivot row
if (m ~= k)
A([k m],:) = A([m k],:);
p([k m]) = p([m k]);
% Compute multipliers
i = k+1:n;
A(i,k) = A(i,k)/A(k,k);
This solution provides a detailed step by step explanation of the given discrete math problem.