MATLAB: Select mxm matrix from mxn matrix and solve systems of linear equations

linear equationsmatrix

Hi everyone, 
I has started using Matlab recently. There are two problems in my following code:
+ Firstly, I would like to choose different sets of m columns from n columns matrix. e.g,5 columns from 10 columns. 
There must be 252 sets, however, my code randomly select so there are some sets are the same (only the position of the columns are changed).
+ Secondly, when solving the systems of linear equations with matrix: a=xb then x=a\b, there appears error "Warning: Matrix is close to singular 
or badly scaled.Results may be inaccurate" since the det(a)~0. I have set "if (det(a)<=-1e-12) | (det(a)>=1e-12)" but it seems not so good.
Hope to receive your help. Thank you so much in advance.
A =[ 0     0     2     2     6     3     4     5     2     1
     2     2     0     0     0     1     0     0     0     1
     0     2     0     1     2     0     1     0     0     1
     0     0     0     0     0     0     0     1     1     0
     3     7     1     3     7     3     4     4     3     4 ];
 %choose different sets of 5 columns from 10 columns: 10!/(5!5!)=252 sets
for i=1:252
    c=randperm(length(A),5); 
    a=A(:,c);
b=[5.8; 2.4; 1.6; 0.2; 10];
%Error "Warning: Matrix is close to singular or badly scaled" 
%if det(a)~=0
if (det(a)<=-1e-12) | (det(a)>=1e-12)
   x=a\b;
%Find non-negative and non-Infinities x values
    if (x(:,:)>=0) & (x(:,:)~=Inf) 
        disp(x)
        disp(a)
    end
end
end

Best Answer

Does this help with first problem: https://www.mathworks.com/help/matlab/ref/nchoosek.html
Second problem, maybe make tolerance more stringent?
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