MATLAB: Combination of vectors to build a matrix

combinations

I have 10 column vectors with 4 elements each. I need do build a 4×4 matrix with different combinations of 4 of those vectors.
Example:
V1 = [2;4;2;1];
V2 = [3;3;5;1];
V3 = [4;1;2;1];
V4 = [7;8;1;1];
V5 = [5;4;2;1];
V6 = [1;8;7;1];
V7 = [3;2;0;1];
V8 = [9;8;1;1];
V9 = [1;4;7;1];
V10 = [2;1;5;1];
First 4X4 matrix combination should look like this:
M1 = [V1 V2 V3 V4];
Second 4X4 matrix combination should look like this:
M2 = [V1 V2 V3 V5];
I need a code to give me all the possible matrix with 4 different vectors.
Thank you!

Best Answer

As per Stephen's answer do not use numbered variables. As all your vectors are the same size, you could all store them as rows of a single matrix. If you don't like that, you could store the vectors as elements of a cell array.
%direct conversion of your code. Not the most elegant way of generating the cell array
V{1} = [2;4;2;1];
V{2} = [3;3;5;1];
V{3} = [4;1;2;1];
V{4} = [7;8;1;1];
V{5} = [5;4;2;1];
V{6} = [1;8;7;1];
V{7} = [3;2;0;1];
V{8} = [9;8;1;1];
V{9} = [1;4;7;1];
V{10} = [2;1;5;1];
Once you've got your vectors in a cell or matrix, it's easy to generate all possible combinations of rows/vectors: use nchoosek.
vectorcombinations = nchoosek(1:numel(V), 4); %all combinations of 4 vector indices out of however many there are
You can then use the indices to create your matrices. You can use a loop iterating over the rows of vectorcombinations, or more advanced techniques such as cellfun:
allmatrices = cellfun(@(c) [V{c}], num2cell(vectorcombinations, 2), 'UniformOutput', false);
The important bit in the line above is just [V{c}], where c is the content of just one row of vectorcombinations. This just concatenates the 4 vectors referred by the indices of that row.
Related Question