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 \(\col(A)\text{?}\)

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