I have yet to encounter an approach that is not boring. You just have to power through it. This approach seems as good as any.

Once you get to eigenvalues (in my opinion) things start to pick up in terms of seeing that linear spaces are actually interesting.

This approach sort of betrays itself when the very first section about scalars has this line:

> Vectors are often written vertically in column form, which emphasizes their role in matrix multiplication:

This is a big "what?" moment because we don't know why we should care about anything in that sentence. Just call it a convention and later on we can see its utility.

Maybe we can petition Paul Lockhart to do a book on Linear Algebra, I would definitely buy it.