Exercise 1

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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