I'm currently trying to solve this exercise (sorry for link to image, but there's a bit text):
https://i.stack.imgur.com/XNcz6.png
But there's a few things in the exercise I don't understand. For example, F^n, why would'nt it just be F^0 all the time? Said in other words, why would a password be hashed and tried unhashed more than one time? As I understand the exercise, the number n can be very big. Also, why is there a table AND a matrix? Why not just one of them?
This exercise is an attempt at walking you through Hellman's Time Memory Tradeoff, for a specific case. The matrix is conceptual, the end points are stored (first and last column) to save space.
Look up TMTO related questions in crypto.stackexchange for more detail.