How to vectorice a set of linear system of equations over 4D and 3D matrices

Dear

I have a 4D and a 3D matrix, and over them we have to perform the following operations:

   for i=1 to n
       for j=1 to m
           v(i,j,:)=Jac(:,:,i,j)\F(:,i,j);
       end
   end

Is there any way to vectorize this operation in order to improve the efficiency?

Many thanks,