What does Linear Dependence (or independence) even mean

• In spanning sets, we could exclude certain elements and the span of the set would still be the same.
• Here, the element that was excluded could be expressed as a linear combination of the other elements.
• This means that the element is linearly dependent on the other elements.

$$\begin{array}{r}A=B+C\\ ⟹B=A-C\end{array}$$

• This means that we could exclude some other element by expressing it as a linear combination of the remaining elements.
• So linear dependence basically ties in all the elements of the set.