Orthogonally Diagonalize the Matrix, Giving an Orthogonal Matrix P and a Diagonal

Multiple Choice

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D.
- $$\left[ \begin{array} { r r r } 13 & 10 & 4 \\10 & 12 & 6 \\4 & 6 & 5\end{array} \right]$$

A)
$\mathrm { P } = \left[ \begin{array} { r r r } 2 & - 2 & 1 \\ 2 & 1 & - 2 \\ 1 & 2 & 2 \end{array} \right] , \mathrm { D } = \left[ \begin{array} { r r r } 25 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{array} \right]$
B)
$$P = \left[ \begin{array} { r r r } 2 / 3 & - 2 / 3 & 1 / 3 \\2 / 3 & 1 / 3 & - 2 / 3 \\1 / 3 & 2 / 3 & 2 / 3\end{array} \right] , D = \left[ \begin{array} { c c c } 1 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 25\end{array} \right]$$
C)
$$P = \left[ \begin{array} { r r r } 2 / 3 & - 2 / 3 & 1 / 3 \\2 / 3 & 1 / 3 & - 2 / 3 \\1 / 3 & 2 / 3 & 2 / 3\end{array} \right] , D = \left[ \begin{array} { r r r } 25 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 1\end{array} \right]$$
D)
$$P = \left[ \begin{array} { r r r } 2 & - 2 & 1 \\2 & 1 & - 2 \\1 & 2 & 2\end{array} \right] , D = \left[ \begin{array} { c c c } 1 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 25\end{array} \right]$$