###### Exercise1

In this exercise, we will consider the span of some sets of two- and three-dimensional vectors.

1. Consider the vectors

\begin{equation*} \vvec_1 = \twovec{1}{-2}, \vvec_2 = \twovec{4}{3}\text{.} \end{equation*}
1. Is $$\bvec = \twovec{2}{1}$$ in $$\span{\vvec_1,\vvec_2}\text{?}$$

2. Give a written description of $$\span{\vvec_1,\vvec_2}\text{.}$$

2. Consider the vectors

\begin{equation*} \vvec_1=\threevec{2}{1}{3}, \vvec_2=\threevec{-2}{0}{2}, \vvec_3=\threevec{6}{1}{-1}\text{.} \end{equation*}
1. Is the vector $$\bvec=\threevec{-10}{-1}{5}$$ in $$\span{\vvec_1,\vvec_2,\vvec_3}\text{?}$$

2. Is the vector $$\vvec_3$$ in $$\span{\vvec_1,\vvec_2,\vvec_3}\text{?}$$

3. Is the vector $$\bvec=\threevec{3}{3}{-1}$$ in $$\span{\vvec_1,\vvec_2,\vvec_3}\text{?}$$

4. Give a written description of $$\span{\vvec_1,\vvec_2,\vvec_3}\text{.}$$

in-context