If we have strings of length n, we know we are in an n dimensional vector space. A few more words on each of the above topics Vector space R n is just lists of n numbers, which can represent all kinds of things, eg, R 2 can be points on a graph, or on a map. The span of these two vectors is the set of all vectors you can get to from them. A line is a solution of a linear system that has infinitely many solutions. If c is zero, then the line goes through the origin.
Any line is a line through the origin that has been shifted.
A line through the origin is the span of a single vector. A homogenous system is one that corresponds to lines or planes, or higher dimensional things, that are through the origin. These three vectors correspond to an overdetermined system. On the other hand, if we have a set of vectors, and none can be expressed in terms of the others, then they are independent. Vector Spaces You can add vectors to each other, and multiply by a scalar.