##### Preview Activity3.2.1

Consider the vectors

\begin{equation*} \vvec_1 = \twovec{2}{1}, \vvec_2 = \twovec{1}{2} \end{equation*}in \(\real^2\text{.}\)

Indicate the linear combination \(\vvec_1 - 2\vvec_2\) on FigureĀ 2.

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

Find the linear combination \(10\vvec_1 - 13\vvec_2\text{.}\)

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

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