Hi. I’m currently a senior in high school and I also attended a private school and I’m going to Yale (Comp sci) in the fall. Hopefully… however, one word of advice is, don’t skip any math levels. Each math level is there for a purpose and to skip by taking a summer course is not the best decision imo. Like you, I really enjoyed math classes and wanted to pursue higher math but I saw others who did that and struggled miserably bc their motivations got ahead of their proficiency which is what I witnessed.( they were literally math wizzes who are currently attending Harvard and Stanford).
I took geo In 9th
Alg 2/trig in 10
Pre Calc in 11
And ap calc bc in 12.
To skip by taking summer courses is simply not good enough compared to a full year normal course. You need to build proper foundations by taking school courses so you don’t struggle in college, SAT/ACT and etc. by doing this, I was able to get a 1590 sat it he writing got me), accepted to Harvard, Yale, mit, northwestern, and Uofchicago and I was able to have a good social life. So I recommend sticking with geo which is such an Uberly important Course like any other math class.
Best thing is to just do well on what u have rn and ull succeed!
So good luck and lmk what u decide to do!
On a side note, unless ur school is rlly known for its academics, idk how much a hs Linear Alg course will help in college.