Solving 3 x 9 matrix all posible combinations

How can i find every posible combination of 3 x 9 difrent matix [mn] from 3 row matrix [a1,a2,a3]?

for example:

a1=[1,0,0];

a2=[0,1,0];

a3=[0,0,1];

>> m1=[a1;a1;a1;a1;a1;a1;a1;a1;a1]

m1 =

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

>> m2=[a2;a1;a1;a1;a1;a1;a1;a1;a1]

m2 =

0 1 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

>> m3=[a1;a2;a1;a1;a1;a1;a1;a1;a1]

m3 =

1 0 0

0 1 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

>> m4=[a1;a1;a2;a1;a1;a1;a1;a1;a1]

m4 =

1 0 0

1 0 0

0 1 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

>> m5=[a1;a1;a1;a2;a1;a1;a1;a1;a1]

m5 =

1 0 0

1 0 0

1 0 0

0 1 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

>> m6=[a1;a1;a1;a1;a2;a1;a1;a1;a1]

m6 =

1 0 0

1 0 0

1 0 0

1 0 0

0 1 0

1 0 0

1 0 0

1 0 0

1 0 0

>> m7=[a1;a1;a1;a1;a1;a2;a1;a1;a1]

m7 =

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

0 1 0

1 0 0

1 0 0

1 0 0

>> m8=[a1;a1;a1;a1;a1;a1;a2;a1;a1]

m8 =

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

0 1 0

1 0 0

1 0 0

>> m9=[a1;a1;a1;a1;a1;a1;a1;a2;a1]

m9 =

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

0 1 0

1 0 0

>> m10=[a1;a1;a1;a1;a1;a1;a1;a1;a2]

m10 =

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

0 1 0

>>m11=[a2;a2;a1;a1;a1;a1;a1;a1;a1]

m11 =

0 1 0

0 1 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

0 0 0

>>m12=[a2;a1;a2;a1;a1;a1;a1;a1;a1]

m11 =

0 1 0

0 0 0

0 1 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

0 0 0

Answer 1

[Rik]

There are 4686825 possible combinations, so I would recommend not storing all of them, especially not in numbered variables, which are a bad idea.

idx=nchoosek(repmat(1:3,1,9),9);

a=cell(1,3);
a{1}=[1,0,0];
a{2}=[0,1,0];
a{3}=[0,0,1];

n=1;
current_combination=cell2mat(a(idx(n,:))');

But if you insist, you can use the code below. Note that it takes a lot of memory and a lot of time (about a 4GB increase in RAM usage and 3-4 minutes on my machine (W10x64,R2019a)).

idx=nchoosek(repmat(1:3,1,9),9);

a=cell(1,3);
a{1}=[1,0,0];
a{2}=[0,1,0];
a{3}=[0,0,1];

total=cellfun(@(n) {cell2mat(a(idx(n,:))')},num2cell(1:size(idx,1)));
total=reshape(total,1,1,[]);
total=cell2mat(total);