So the point of all this really now,

is that we'd like to very much find if we could, or solve for that vector 'x', that steady-state vector 'x'.

If we can do that, we've basically cracked the case, we've solved the problem of what is the long-term behavior of the Markov Chain.

If you think about it then, we're really getting our "biggest bang for our buck", in that case, because I can maximize the predictive power of my Markov Chain model by finding the steady-state vector 'x'.