I think they should clarify whether they want somebody that has passed a linear algebra class with high marks based on something like strangs' entry level book before...or are on the cutting edge of graduate level linear algebra research. It's not clear from the post and I suspect that might be an issue.
Give me a couple months and I could recite strangs entry level textbook. I passed that class with an A+. But I could not become a PhD level maths student with a linear algebra research focus in that amount of time.
There are multiple very different ways to interpret a requirement for being competent in linear algebra.
Knowing everything covered in strangs introduction to linear algebra is actually quite low on the potential list of requirements and could be self studied.