I've got a good grasp on the definition and meaning of linear dependence and independence. If you have a set of vectors, and one of those vectors can be replicated via a linear combination of the other vectors in the set, you would call the call the vector set linearly dependent.
However, I'm somewhat curious on why it is called "dependent". What exactly is dependent? When I think of the word dependence, it makes me think that something is affected by the actions of something else (e.g. if y = f(x), y is dependent on x). However, I don't see what the dependency is in linear dependency. What exactly is the dependency?
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$\begingroup$I'd think about it in terms of a dependence relation you can get. That is, let $\{v_1, v_2, \ldots, v_n\}$ be linearly dependent. Then there exist scalars $a_1, a_2, \ldots, a_n$, not all zero, so that
$$a_1v_1 + a_2v_2 + \ldots + a_nv_n = 0.$$
The above equation is a linear dependence relation, or a linear dependency. There are infinitely many choices for scalars $a_1, \dots, a_n$ satisfying this equation, but at the same time, not every set of $n$ numbers will work. You could say that the values for some subset of your $a_i$'s depend on your choices for the others.
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