generating matrices of the possible combinations

How do I find all the possible matricies (not their number but the matricies themselves) that are formed as a result of taking a combination of a certain number of columns y from a matrix with a total number of columns x ?

example

X = 1 7 9 10 15

4 8 5 9 21

2 14 3 6 16

here X is 3 by 5 ( 5 columns), now suppose I want to obtain the MATRICIES THEMSELVES that are the result of mixing any of the 3 columns of matrix X

In this case 5c3 , i should obtain 10 matricies, how do I get them ?

[Luna]

Do you want to get 3x3 matrices?

Answer 1

[Stephen23]

X = [1,7,9,10,15;4,8,5,9,21;2,14,3,6,16]
P = nchoosek(1:5,3)
N = size(P,1);
C = cell(1,N);
for k = 1:N
    C{k} = X(:,P(k,:));
end

And checking the output:

>> numel(C)
ans = 10
>> C{:}
ans =
    1    7    9
    4    8    5
    2   14    3
ans =
    1    7   10
    4    8    9
    2   14    6
ans =
    1    7   15
    4    8   21
    2   14   16
ans =
    1    9   10
    4    5    9
    2    3    6
ans =
    1    9   15
    4    5   21
    2    3   16
ans =
    1   10   15
    4    9   21
    2    6   16
ans =
    7    9   10
    8    5    9
   14    3    6
ans =
    7    9   15
    8    5   21
   14    3   16
ans =
    7   10   15
    8    9   21
   14    6   16
ans =
    9   10   15
    5    9   21
    3    6   16

[Abeer Abdelhadi]

Thanks works perfectly

Answer 2

[Luna]

Try this;

M is a 1x10 cell array which contains 3x3 matrices chosen from the X.

X =  [1 7 9 10 15     
        4 8 5 9 21            
        2 14 3 6 16]   
 
   A = nchoosek(X(1,:),3)
   B = nchoosek(X(2,:),3)
   C = nchoosek(X(3,:),3)
   
   for i = 1:nchoosek(5,3)
       
       M{i} = [A(i,:);B(i,:);C(i,:)];
       
   end

[Abeer Abdelhadi]

thanks