Depends on what you mean by "web software engineering." Really it's almost a useless term, since a web-frontend can be the front-end for almost any sort of system. The question really should just be "where does linear algebra have applications to software engineering?" in a general sense.
Pedantry & ranting aside, the obvious place is anything to do with machine learning / text mining. If processing large amounts of text and searching for things within, or based on, that text, you may well wind up using algorithms that involve linear algebra.
One of the Mahout project founders speaks fairly often in the Triangle area, at User Group meetings and such, and he always seems to mention Linear Algebra in his talks. There's a reason for that.