Solving a large system takes too much memory?

Suppose i have a sparse matrix M with the following properties:

   size(M) -> 100000 100000
   sprank(M) -> 99236
   nnz(M) -> 499987
   numel(M) -> 1.0000e+10
   who's('M') -> 8.4mb

How come solving the system takes way more than 8GB of RAM?

I'm using the following code (provided at http://www.mathworks.com/moler/exm/chapters/pagerank.pdf

   function x = pagerank(G,p)

   G = G - diag(diag(G));

   [n,n] = size(G);
   c = full(sum(G,1));
   r = full(sum(G,2)); 

   % Scale column sums to be 1 (or 0 where there are no out links).

   k = find(c~=0);
   D = sparse(k,k,1./c(k),n,n);

   % Solve (I - p*G*D)*x = e

   e = ones(n,1);
   I = speye(n,n);
   x = (I - p*G*D)\e;

   % Normalize so that sum(x) == 1.

   x = x/sum(x);`