> > Linear algebra is really about linear transformations of vector spaces, which is not captured in this blog post.

> I... disagree.

This is literally the definition of the term "linear algebra".

> really at no point are we viewing what we're doing as transforming a vector space, we're just solving equations with unknowns.

You may not see what you're doing as transforming vector spaces with linear operators, but that is what you're doing. It's worth pointing out that the definition of vector spaces allows any field, including finite ones, though it's true that the intuition won't be exactly the same.

Another way to say this: if you're working on a problem without thinking about the connection to linear transformations, then it's not correct to say it's a linear algebra problem without obvious connection to linear transformations; instead, it's not a linear algebra problem at all, by definition.