I am teaching matrices, determinants and systems to a class of 16-year-olds.
As you can expect, they do not know calculus or linear algebra.
What they do know is a little bit of matrices (how to multiply and invert them, for instance), some plane geometry, some spacial geometry, some analytical geometry, and most elementary functions: linear, quadratic, exponential, modular, trigonometric.
I had to explain what subjects they have studied because it must vary wildly from country to country.
In this context, I am having great trouble in finding real-world applications and examples of determinants being applied to do anything at all. The only examples I could show are:
Area of a triangle given the coordinates A,B,C; Cramer's rule for solving systems of linear equations. That being said, if anyone can think of any example I could use in my class, please tell me! Thanks in advance for your help.