So if you were given two distinct arbitrary vectors in 2 dimensional space does the vector space created by is possible for these two vectors cover the entire 2 dimension?
So in otherwords, can you create any given vector in that 2 dimensional space using combinations of the two arbitrary vectors.
Take the standard basis of $\mathbb{F^2}$ $$I_2 = B = \begin{pmatrix}1&0 \\ 0&1 \end{pmatrix} \in \mathbb{F^2}$$
Then define the span of $B$ as : $$Span(B) = \{ a_1 \begin{pmatrix}1 \\ 0 \end{pmatrix} + a_2 \begin{pmatrix} 0 \\ 1 \end{pmatrix}, \forall a_1,a_2 \in \mathbb{F} \}$$
These are all the vectors on $\mathbb{F^2}$ spanned by basis $B$ (the set of all linear combinations).
Further reading: Vector Spaces and Linear Independence