In simple terms, if you choose absolutely any vector, anywhere in , you can get to that vector using a linear combination of and . And because of that, you can say specifically that and span. If a set of vectors spans a space, it means you can use a linear combination of those vectors to reach any vector in the space.
In the same way, we can get to any vector, anywhere in , using a linear combination of the basis vectors , and span, the entirety of three-dimensional space.
These facts are denoted by:
We cannot span with fewer than vectors.
Given any two linearly independent vectors, we can use them to define the entire real plane ()!