Exploring Linear Algebra - Part 1: Estimating Route Costs

This is my first entry in a series of articles with creative applications of linear algebra to problems. This one was inspired by an Uber ride. So, imagine you are Google Maps, and your client wants to know the best path to take from point A to point B. If you have the city's map, it's easy, right? Just wearily apply Dijikstra's algorithm to find the shortest path, and that's your answer. If you've taken enough Uber rides, you know that sometimes the shortest path also happens to be the one under worst maintenance, or maybe it's the most jammed up.