Gauss-Jordan linearization by blocks using symbolic variable

Supouse there is a linear system with the form: Ax=B. A partition by segments in the vector "x" is performed so the resulting system has the form:

[A11, A12, ... ,A1n][x1]=[B1]
[A21, A22, ... ,A2n][x2]=[B2]
  .         .
  .          .
  .           . 
[An1, An2, ... ,Ann][xn]=[Bn]

So... Does anyone knows an strategy for solving symbolically the Gauss-Jordan elimitation of this equation...

Some code lines like:

As=sym('A',[num,num]); Bs=sym('B',[num,1]);
As_gauss=[As,Bs];
for k=1:num
    As_gauss(k,:)=As_gauss(k,k)\As_gauss(k,:);
    for j=k+1:num
    As_gauss(j,:)=As_gauss(j,:)-As_gauss(j,k)*As_gauss(k,:);
    end
end 
for k=num:-1:2
    for j=k-1:-1:1
    As_gauss(j,:)=As_gauss(j,:)-As_gauss(k,:)*As_gauss(j,k);
    end
end

Are helpfull when the cluster of the variable x is no longer than length 1... otherwise the matrix algebra rules are not taken into acount since the elements of A and B are scalars for matlab...

I guess my real question is: Is it possible to build symbolical matrixes in which each element is also a matrix of some determinated dimension but with solutions in function of the submatrixes instead of its smallest elements ???

eventhoug my problem intrigues me.. I've reach the point where I need anotherone's opinion... If some of you think about a better framework to attack my problem I would be grateful... thank you. Saludos!