###### 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