In Linear Algebra, what is a vector? I understand that a vector space is a collection of vectors that can be added and scalar multiplied and satisfies the 8 axioms, however, I do not know what a vector is. 
I know in physics a vector is a geometric object that has a magnitude and a direction and it computer science a vector is a container that holds elements, expand, or shrink, but in linear algebra the definition of a vector isn't too clear. 
As a result, what is a vector in Linear Algebra?

Just to help and understand the change of concept from physics to linear algebra about vectors, without pretending to be rigorous.
Consider that in physics (Newtonian) you consider an euclidean space, so you can speak in terms of magnitude. In linear algebra we want to be able and define a vector in broader terms, in a reference system that is not necessarily orthogonal, what is called an affine space/subspace.
Infact in affine geometry (which help to visualize)  an oriented segment  $\mathop {AB}\limits^ \to$ is an ordered couple of points, and a vector corresponds to the ordered $n$-uple of the difference of their coordinates (the translation vector). A vector therefore is a representative of all the segments, oriented in the same direction, which are parallel and have the same "translation" (and not modulus, which is not defined, or better it is not preserved under an affine change of coordinates). 
