I am reading this text book about discrete math, and it says that space solution to this example: $ a_n = 5a_{n-1} - 6a_{n-2} ,a_0 = 2 ,a_1=5$
$ a_n = 2^n + 3^n$
$ x^2 = 5x -6$
and solution space is this: https://i.stack.imgur.com/opFt6.jpg
I don't know how to get vector bases and would really like to understand how we got them.
Thank you!