Delete rows of a matrix

This is a portion of the matrix :

   8   9   10   12

   5   4    3    2
  10   8    6    4

As you can see that row number three : [10 8 6 4] is row numbre two *2, I want their to be only one row. general, if a row1 in matix have a relation with other row2 : row1=row2*k then delete just one row of them: row1 or row2.

So I want the output to be like:

   8   9   10   12
   5   4    3    2

[dpb]

Basically have to compute the pairwise logical of

all(fix(x(i,:)./x(j,:))==x(i,:)./x(j,:))

over unique combinations of i and j then remove those for which result is true.

Answer 1

[Azzi Abdelmalek]

Try this

A=[8   9   10   12
  5   4    3    2
  10   8    6    4]
m=rank(A);
n=size(A,1);
k=0;
idx=[];
while k<n-1 & numel(idx)<n-m
  k=k+1
  if isempty(intersect(k,idx))
      ii=bsxfun(@ldivide,A(k+1:n,:),A(k,:));
      idx=[idx ;find(all(bsxfun(@eq,ii,ii(:,1)),2))+k];
  end
end
A(idx,:)=[]

Answer 2

[Amit]

Lets say you matrix is something named A.

Tol = 1e-6;
count = 1;
flag = 1;
while (flag == 1)
temp1 = A(count+1:end,1)/A(count,1);
temp2 = (bsxfun(@minus,bsxfun(@rdivide,A(count+1:end,:),temp1),A(count,:))).^2;
temp3 = [zeros(count,1); sum(temp2,2)<Tol];
A(find(temp3),:) = [];
[m,~] = size(A);
if (m == count)
flag = 0;
end
count = count + 1;
end