###### Exercise 9

Consider the matrix

\begin{equation*}
A = \left[\begin{array}{rrr}
0 \amp 1 \amp x \\
2 \amp 2 \amp y \\
-1 \amp 0 \amp z \\
\end{array}\right]\text{.}
\end{equation*}

Write the equation \(\det A = 0\) in terms of \(x\text{,}\) \(y\text{,}\) and \(z\text{.}\)

Explain why \(\vvec_1\) and \(\vvec_2\text{,}\) the first two columns of \(A\text{,}\) satisfy the equation you found in the previous part.