matlab. i recognize the answer will differ by hardware, but please give a solid answer for the part about the order of the matrix.

provided lutx code

function [L,U,p] = lutx(A)

%LUTX Triangular factorization, textbook version

% [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,:)

% Copyright 2014 Cleve Moler

% Copyright 2014 The MathWorks, Inc.

[n,n] = size(A);

p = (1:n)';

for k = 1:n-1

% Find index of 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]);

end

% Compute multipliers

i = k+1:n;

A(i,k) = A(i,k)/A(k,k);

% Update the remainder of the matrix

j = k+1:n;

A(i,j) = A(i,j) - A(i,k)*A(k,j);

end

end

% Separate result

L = tril(A,-1) + eye(n,n);

U = triu(A);

2.8. Modify the lutx function so that it uses explicit for loops instead of MATLAB vector notation. For example, one section of your modified program will read % Compute the multipliers for i = k+1:n A(i,k) = A(i,k)/A(k,k); end Compare the execution time of your modified lutx program with the origi- nal lutx program and with the built-in lu function by finding the order of the matrix for which each of the three programs takes about 10 s on your computer