##### Exercise2

Consider the vectors

\begin{equation*} \vvec_1 = \threevec{2}{-1}{0}, \vvec_2 = \threevec{1}{2}{1}, \vvec_3 = \threevec{2}{-2}{3} \text{.} \end{equation*}
1. Are these vectors linearly independent or linearly dependent?

2. Describe the $$\span{\vvec_1,\vvec_2,\vvec_3}\text{.}$$

3. Suppose that $$\bvec$$ is a vector in $$\real^3\text{.}$$ Explain why we can guarantee that $$\bvec$$ may be written as a linear combination of $$\vvec_1\text{,}$$ $$\vvec_2\text{,}$$ and $$\vvec_3\text{.}$$

4. Suppose that $$\bvec$$ is a vector in $$\real^3\text{.}$$ In how many ways can $$\bvec$$ be written as a linear combination of $$\vvec_1\text{,}$$ $$\vvec_2\text{,}$$ and $$\vvec_3\text{?}$$

in-context