Section 7.2 Diagonalization
Let \(A\) be a square matrix. If you would like to know the matrix \(P\) and \(D\) such that
\begin{equation*}
P^{-1}AP=D,
\end{equation*}
you can do it in such way.
Let check if the columns of \(P\) are eigenvectors.
Important: Are you able to see that \(AP=PX\text{.}\) Figure out the matrix \(X\)
Exercise: For the matrix
\begin{equation*}
B = \begin{pmatrix}
1 \amp 2 \amp -2 \\
-2 \amp 5 \amp -2 \\
-6 \amp 6 \amp -3
\end{pmatrix}\text{,}
\end{equation*}
find the matrix \(P\) and \(D\) such that
\begin{equation*}
P^{-1}AP=D.
\end{equation*}
