Hi, I am a senior in high school and have completed my school's math curriculum, including AP Stats (5 on exam) and Multivariable Calculus (Calc III). This year, in my independent study class, I am looking to study linear algebra. Are there any online college courses in linear algebra where I could get transferrable college credits? I know there is one from LSU and another from BYU but I am looking, in addition to those two, for some other options out there that I can take without being enrolled/having to apply for the university itself and that I can receive college credit for completing the course. Thanks.
The University of Illinois - Springfield has a Mathematics degree completion program that might offer such a course. Also, there are several Mathematics threads in the archives that might proves useful.
For college credit, take a look at the NetMath program offered by UIUC (https://netmath.illinois.edu/highschool), in particular the linear algebra course at https://netmath.illinois.edu/node/23?stu=hs. You might also consider the EPGY program at Stanford (EPGY University-level Mathematics Courses), though that may only be available for high school credit.
The UIS degree completion program does, indeed, offer Linear Algebra -- I took it last Spring. However, it requires "Departmental Approval" before registration and I suspect that may in practice mean that only enrolled math majors are allowed to take it. But it doesn't hurt to ask. The UIUC Netmath course is probably a better option for your situation, though.