Span of 3 linearly dependent vectors The vectors are $(1,1,1)$,$(1,2,0)$, and $(2,3,1)$. I have shown that they are linearly dependent but don't really know how to find their span. (Note: my lecturer just literally defined what a span is and didn't get to the part where we actually calculate spans, so I'm completely lost!). Any help will be appreciated.

Since the third vector is a linear combination of the first two, and the first two are not scalar multiples of each other (that is, they are linearly independent), we have that the span is all linear combinations of the first two vectors. So,
$$
\mathrm{span}\left\{ \begin{pmatrix} 1\\ 1\\ 1 \end{pmatrix}, \begin{pmatrix} 1\\ 2\\ 0 \end{pmatrix} \right\} = \left\{ a\begin{pmatrix} 1\\ 1\\ 1 \end{pmatrix} + b\begin{pmatrix} 1\\ 2\\ 0 \end{pmatrix} : a, b \in \mathbb{R}\right\}.
$$
This is some plane in $\mathbb{R}^{3}$.
