Exercise1

In this exercise, we will consider the span of some sets of two- and three-dimensional vectors.

  1. Consider the vectors

    \begin{equation*} \vvec_1 = \twovec{1}{-2}, \vvec_2 = \twovec{4}{3} \text{.} \end{equation*}
    1. Is \(\bvec = \twovec{2}{1}\) in \(\span{\vvec_1,\vvec_2}\text{?}\)

    2. Give a written description of \(\span{\vvec_1,\vvec_2}\text{.}\)

  2. Consider the vectors

    \begin{equation*} \vvec_1=\threevec{2}{1}{3}, \vvec_2=\threevec{-2}{0}{2}, \vvec_3=\threevec{6}{1}{-1} \text{.} \end{equation*}
    1. Is the vector \(\bvec=\threevec{-10}{-1}{5}\) in \(\span{\vvec_1,\vvec_2,\vvec_3}\text{?}\)

    2. Is the vector \(\vvec_3\) in \(\span{\vvec_1,\vvec_2,\vvec_3}\text{?}\)

    3. Is the vector \(\bvec=\threevec{3}{3}{-1}\) in \(\span{\vvec_1,\vvec_2,\vvec_3}\text{?}\)

    4. Give a written description of \(\span{\vvec_1,\vvec_2,\vvec_3}\text{.}\)

in-context