##### Exercise1

Consider the vectors

\begin{equation*} \vvec = \left[\begin{array}{r} 1 \\ -1 \end{array}\right], \wvec = \left[\begin{array}{r} 3 \\ 1 \end{array}\right] \end{equation*}
1. Sketch these vectors below.

2. Compute the vectors $$-3\vvec\text{,}$$ $$2\wvec\text{,}$$ $$\vvec + \wvec\text{,}$$ and $$\vvec - \wvec$$ and add them into the sketch above.

3. Sketch below the set of vectors having the form $$2\vvec + t\wvec$$ where $$t$$ is any scalar.

4. Sketch below the line $$y=3x - 2\text{.}$$ Then identify two vectors $$\vvec$$ and $$\wvec$$ so that this line is described by $$\vvec + t\wvec\text{.}$$ Are there other choices for the vectors $$\vvec$$ and $$\wvec\text{?}$$

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