I am new to linear algebra and am trying to find the motivation behind defining it in such a way and need for defining it. To study $2$-D,$3$-D space we have geometry, so why do we need linear algebra then?
Why did they choose the exact properties which a vector space should have? I haven't found any satisfactory answer. The text books directly starts with the theory.
Can anyone explain please?
Edit: "Why we study linear algebra?" is different from my question. That question need the applications of linear algebra, I already know that and there are many source to answer that question. What I need is background of introduction to linear algebra, not only the history, also the motivation behind choosing the properties that need to be satisfied to be a vector space - why not extra why not less? Will taking extra or less condition give something which is not very useful? Please explain it.