##### Exercise9

Suppose that $$A$$ is a matrix and there is an invertible matrix $$P$$ such that

\begin{equation*} A = P~\left[\begin{array}{rrr} 2 \amp 0 \amp 0 \\ 0 \amp -3 \amp 0 \\ 0 \amp 0 \amp 1 \\ \end{array}\right]~P^{-1} \text{.} \end{equation*}
1. What can you conclude about $$\nul(A)\text{?}$$

2. What can you conclude about $$\col(A)\text{?}$$

in-context