##### Preview Activity3.2.1

Consider the vectors

\begin{equation*} \vvec_1 = \twovec{2}{1}, \vvec_2 = \twovec{1}{2} \end{equation*}

in $$\real^2\text{.}$$

1. Indicate the linear combination $$\vvec_1 - 2\vvec_2$$ on Figure 2.

2. Express the vector $$\twovec{-3}{0}$$ as a linear combination of $$\vvec_1$$ and $$\vvec_2\text{.}$$

3. Find the linear combination $$10\vvec_1 - 13\vvec_2\text{.}$$

4. Express the vector $$\twovec{16}{-4}$$ as a linear combination of $$\vvec_1$$ and $$\vvec_2\text{.}$$

5. Explain why every vector in $$\real^2$$ can be written as a linear combination of $$\vvec_1$$ and $$\vvec_2$$ in exactly one way.

in-context