Exercise4

Consider the matrix

\begin{equation*} A = \left[\begin{array}{rrr} -2 \amp 1 \amp k \\ 2 \amp 3 \amp 0 \\ 1 \amp 2 \amp 2 \\ \end{array}\right] \end{equation*}

where \(k\) is a parameter.

  1. Find an expression for \(\det A\) in terms of the parameter \(k\text{.}\)

  2. Use your expression for \(\det A\) to determine the values of \(k\) for which the vectors

    \begin{equation*} \threevec{-2}{2}{1}, \threevec{1}{3}{2}, \threevec{k}{0}{2} \end{equation*}

    are linearly independent?

in-context