Exercise 9

Consider the matrix $$A = \left[\begin{array}{rrr} 0 & 1 & x \\ 2 & 2 & y \\ -1 & 0 & z \\ \end{array}\right]$$.

1. Assuming that $\det(A) = 0$, rewrite the equation in terms of $x$, $y$, and $z$.

2. Explain why $\vvec_1$ and $\vvec_2$, the first two columns of $A$, satisfy the equation you found in the previous part.

3. Explain why the solution space of this equation is the plane spanned by $\vvec_1$ and $\vvec_2$.