Exercise 4

Consider the matrix $$A = \left[\begin{array}{rrr} -2 & 1 & k \\ 2 & 3 & 0 \\ 1 & 2 & 2 \\ \end{array}\right]$$ where $k$ is a parameter.

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

2. Use your expression for $\det(A)$ to determine the values of $k$ for which the vectors $$\threevec{-2}{2}{1}, \threevec{1}{3}{2}, \threevec{k}{0}{2}$$ are linearly independent.