I'm teaching mathematics at my former high school and the next topic will be vector geometry. When I attended high school, I was only taught vector geometry and never learnt anything about matrices until university. I feel like my pupils would be missing out on something if I didn't teach them very basic linear algebra and I also have the permission to teach linear algebra.
There are two possibilites: Treat vector geometry and linear algebra as two "different" topics (i.e. with other topics in between, such as integration, probability, etc.) or merge the two.
I experienced the "merged" variant in university, but obviously following that course wouldn't make any sense for high schoolers. However, as I didn't learn linear algebra in high school, I don't really know how I should merge the material I already have from my time in school with new linear algebra. Whenever I try to come up with a plan, I end up putting all of vector geometry (scalar product, vector product, intersection problems) before and linear algebra (matrices, Gauss elimination, determinants, eigenvalues) after.
Do you have a suggestion, how I could teach the two topics in a comprehensive "linear algebra" course for high schoolers?