Thank you very much for your help; however, it appears that this is not the method used to obtain the solution. This paper (www2.bc.edu/james-anderson/IncidenceGeog.pdf, p. 5. Different notation is used here.) mentions a normalization, and then if I'm not mistaken some iterative process. In any case, I think the process requires an additional assumption, so I'm not sure if your method is "valid". But thanks again!

Sorry, I'm new to this place! I encountered this system in my research in economics. I found several papers claiming that this system is solvable, but none of them state how they are solved. I have very little knowledge of linear algebra, so my own attempts at solving this have failed. Any help at all would be greatly appreciated!