In my world (I'm not a mathematician) vector geometry is a subset of linear algebra. Consulting Wikipedia doesn't tell me otherwise:
Linear algebra has a concrete representation in analytic geometry ...
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.
Regarding another comment of yours it also said:
Thus matrix theory is often considered as a part of linear algebra.
I guess the point is that these are parts of a field that is significantly larger and deeper than just these parts.
Vector Geometry is a part of Linear Algebra, it's just not a very big part, just as arithmetic is not a very big part of calculus.
Matrix theory is a much bigger chunk, but the article submitted doesn't go into matrix theory, it just uses a piddling bit of a small amount of using matrices.
And these are valid questions - I don't know why someone down-voted you, and I've upvoted you for asking.
Linear algebra has a concrete representation in analytic geometry ...
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.
Regarding another comment of yours it also said:
Thus matrix theory is often considered as a part of linear algebra.