Suppose $A=\left(\begin{array}{ccc}-4 & a & b \a & -5&cb&c& 8\end{array} ight)$ where $a, b, c \in \mathbb{R}$. Suppose $u, v \in \mathbb{R}^{3}$ are nonzero vectors so that $A u=-2 u$ and $A v=3 v$. a. Give all of the eigenvalues of $A$, along with their algebraic and geometric multiplicities. b. $\operatorname{det} A=$ CS. JG.082