I am currently teaching a university-level linear algebra course and recently encountered an issue that made me question the assumed foundational math skills for students in this course. The issue arose during a quiz where students were required to find eigenvalues of a 3x3 matrix, necessitating the factorization of a cubic polynomial:
$$ −λ^3 + λ^2 + λ − 1 $$
One student challenged this, pointing out that extensive polynomial manipulation was not covered in our syllabus, which led me to reflect on what foundational math skills should reasonably be expected of students entering this course.
What basic math skills (e.g., polynomial manipulation, trigonometry, complex numbers) is reasonable for us to expect students to have when they enroll in a linear algebra course at the university level?
And when student challenges our assumptions by saying "it's not what the course is about" when they fail to carry out basic mathematics task, what should our response be?
Update: The same student took another course I am teaching. This time I only give the students problems that requires factorization of polynomials of degree $2$. The student still does not know how to do it because there is a $9$ in $9 x^2$. 😃
