With the real numbers as scalars,
is \(\begin{bmatrix} 1\\1\end{bmatrix}\)
in the span of \(\left\{\begin{bmatrix} 1\\2\end{bmatrix},
\begin{bmatrix} 2\\1\end{bmatrix}\right\}\)?
The answer is “Yes”.
Note that
\[\begin{bmatrix} 1\\1\end{bmatrix} =
\frac{1}{3}\begin{bmatrix} 1\\2\end{bmatrix}+
\frac{1}{3}\begin{bmatrix} 2\\1\end{bmatrix}.\]
This linear combination can be found, for example,
by solving for \(\alpha\) and \(\beta\) in
\[\begin{bmatrix} 1\\1\end{bmatrix} =
\alpha\begin{bmatrix} 1\\2\end{bmatrix}+
\beta\begin{bmatrix} 2\\1\end{bmatrix}.\]