Why are cities and capitals located where they are?

They are located where they are because of the government. The government tells the states where they should have there capitals and there cities.

Below Is What google Says I have cited where I got it from. I did this so if you needed more of an explanation

(A capital city (or capital town or just capital) is a city or town, specified by law or constitution, by the government of a country, or part of a country, such as a state, province or county. It usually serves as the location of the government's central meeting place and offices.) (https://simple.wikipedia.org/wiki/Capital_city)

Hope This Helps!!!

are you referring to matrix mathematics!