\(A = P D P^{-1}\): \[\begin{bmatrix} -4 & 35 \\ 0 & 3 \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} -4 & 0 \\ 0 & 3 \end{bmatrix} \begin{bmatrix} -1.0 & 5.0 \\ 0.0 & 1.0 \end{bmatrix}\]

Your answer may differ by scaling eigenvectors (columns of \(P\)) or otherwise choosing a different basis for the eigenspace.

Problem:

\[
\begin{bmatrix} 
-4 & 35   \\ 
0 & 3
\end{bmatrix}
\]

Diagonalization:

\begin{solution}
\[
\begin{bmatrix} 
-4 & 35   \\ 
0 & 3
\end{bmatrix} = 
\begin{bmatrix} 
-1 & 5   \\ 
0 & 1
\end{bmatrix} 
\begin{bmatrix} 
-4 & 0   \\ 
0 & 3
\end{bmatrix} 
\begin{bmatrix} 
-1.0 & 5.0   \\ 
0.0 & 1.0
\end{bmatrix}
\]
\end{solution}