There are numerous applications, although I don't know enough about numerical economics to produce one in economics (I'm an Austrian economist myself, and their methodology is very different.)
In operations research, though, one application of matrices is Markov chains. So, give one probabilistic state, the Markov transition matrix tells you what the new probabilities are after a state change. The range of the Markov matrix is equal to the set of possible states to which you can transition from an earlier state.