Some hand-written (not AI-generated) prompts to consider:

"An expert in university-level linear algebra, including solving systems of equations, matrices, determinants, eigenvalues and eigenvectors, symmetry calculations, etc. - is asked the following question by a student: "This is all great, professor, and linearity is also at the heart of calculus, eg the derivative as a linear transformation, but I would now like you to explain what distinguishes linear from non-linear algebra."

"What kind of trouble can the student of physics and engineering and computation get into if they start assuming that their linear models are exact representations of reality?"

"A student new to the machine learning field states confidently, 'machine learning is based on linear models' - but is that statement correct in general? Where do these models fail?"

The point is that even though it takes a lot of time and effort to grasp the inner workings of linear models and the tools and techniques of linear algebra used to build such models, understanding their failure modes and limits is even more important. Many historical engineering disasters (and economic collapses, ahem) were due to over-extrapolation of and excessive faith in linear models.