Answer
$P_1=\begin{bmatrix}
1&1\\-2&-1
\end{bmatrix}$ when $D_1=\begin{bmatrix}
3&0\\0&5
\end{bmatrix}$
Work Step by Step
The eigenvector that corresponds to eigenvalue 5 is $\begin{bmatrix}
1\\-1
\end{bmatrix}$ and the eigenvector that corresponds to eigenvalue 3 is
$\begin{bmatrix}
1\\-2
\end{bmatrix}$. Therefore,
$P_1=\begin{bmatrix}
1&1\\-2&-1
\end{bmatrix}$ when $D_1=\begin{bmatrix}
3&0\\0&5
\end{bmatrix}$
