How to eliminate combinations while looping?

I am given a 39x6 matrix (lets call it A) and I have to make a 6x6 matrix (B) . The last row of the 6x6 matrix is fixed and for the remaining 5 rows, all possible combinations of the initial A matrix's rows are taken 5 at a time to create B. Then the determinant of the B matrix is determined and the output are the cases when the determinant of B matrix is non zero.

The code I was able to do so far is given.

The issues are:

1) I am not able to come up with a system to eliminate the combinations that occur so that I can reduce the number of iterations.

2) I also couldn't figure out a way to store the matrices that have non zero determinant values.

also is there any possible way to make the code such that the it could have less loops?

[Atsushi Ueno]

1) I am not able to come up with a system to eliminate the combinations that occur so that I can reduce the number of iterations.

The code below uses nchoosek function to eliminate the combinations to be nCr = n!/(r!(n-r)!) = 575757 (n=39,r=5).

Binomial coefficient or all combinations - MATLAB nchoosek - MathWorks

Also, perms function is used for making permutation nPr = n!/(n-r)! = 69090840 (n=39,r=5).

All possible permutations - MATLAB perms - MathWorks

2) I also couldn't figure out a way to store the matrices that have non zero determinant values.

You can write it to console (or file) by disp function (or writematrix function or any other built-in functions).

Write a matrix to a file - MATLAB writematrix - MathWorks

also is there any possible way to make the code such that the it could have less loops?

The loops are reduced by using nchoosek function and perms function.

clear; close all;
Pos_E_Op = [0,0,0,0,-1,-1;-1,0,-1,0,0,-1;0,1,-1,0,0,-1;-1,1,0,0,0,-1;0,0,-1,1,0,-1;-1,0,0,1,0,-1;0,1,0,1,0,-1;0,-1,0,-1,-1,0;1,0,0,-1,-1,0;0,0,1,-1,-1,0;1,-1,0,0,-1,0;0,-1,1,0,-1,0;1,0,1,0,-1,0;0,0,-1,-1,0,0;-1,0,0,-1,0,0;0,1,0,-1,0,0;0,-1,-1,0,0,0;1,0,-1,0,0,0;-1,-1,0,0,0,0;0,0,0,0,0,0;1,1,0,0,0,0;-1,0,1,0,0,0;0,1,1,0,0,0;0,-1,0,1,0,0;1,0,0,1,0,0;0,0,1,1,0,0;-1,0,-1,0,1,0;0,1,-1,0,1,0;-1,1,0,0,1,0;0,0,-1,1,1,0;-1,0,0,1,1,0;0,1,0,1,1,0;0,-1,0,-1,0,1;1,0,0,-1,0,1;0,0,1,-1,0,1;1,-1,0,0,0,1;0,-1,1,0,0,1;1,0,1,0,0,1;0,0,0,0,1,1];
 [M,N] = size(Pos_E_Op);
 total_ite = factorial(M)/factorial(M-5); % nPr = n!/(n-r)! = 69090840 (n=39,r=5)
 j = 1; i = 1;
 text1 = "Running iteration : %d of %d";
 text2 = "Possible combination %d";
 clist = nchoosek(1:M, 5);
 for m = 1:size(clist,1)  % nCr = n!/(r!(n-r)!) = 575757 (n=39,r=5)
     plist = perms(clist(m,:));
     for n = 1:size(plist,1) % nPr / nCr = r! = 120 (r=5)
         status = sprintf(text1,i,total_ite)
         A = [Pos_E_Op(plist(n,:),:); [1, -1, 1, -1, 2, -2]];
         i = i+1;
         if det(A) ~= 0
             sprintf(text2,j)
             disp(A);
             j = j+1;
         end
     end
 end

[Walter Roberson]

2) I also couldn't figure out a way to store the matrices that have non zero determinant values.

Create a cell array that is the size of the maximum number of combinations. Initialize a counter to 0. Each time you find a suitable matrix, increment the counter and use the new counter as the index into the cell array to store the matrix.

At the end, cat(3, TheCell{:}) to get a 6 x 6 x something array of all of the matrices.