1. The problem asks to define the span of a vector space. 2. The span of a set of vectors is the collection of all possible linear combinations of those vectors. 3. Formally, if we have vectors $\mathbf{v}_1, \mathbf{v}_2, \ldots, \mathbf{v}_n$ in a vector space, the span is defined as: $$\text{span}\{\mathbf{v}_1, \mathbf{v}_2, \ldots, \mathbf{v}_n\} = \{a_1\mathbf{v}_1 + a_2\mathbf{v}_2 + \cdots + a_n\mathbf{v}_n \mid a_i \in \mathbb{R}\}$$ 4. This means any vector in the span can be written as a sum of the given vectors multiplied by scalars. 5. The span is itself a subspace of the vector space, containing all vectors that can be formed this way. 6. In simple terms, the span is all the vectors you can reach by stretching and adding the original vectors together.