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

question 1

Multiple Choice

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D.
- $$\left[ \begin{array} { c r } 12 & - 6 \\- 6 & 7\end{array} \right]$$

• A)
• \[P = \left[ \begin{array} { r r }
• 3 & 2 \\
• - 2 & 3
• \end{array} \right] , D = \left[ \begin{array} { r r }
• 16 & 0 \\
• 0 & 3
• \end{array} \right]\]
• B)
• \[P = \left[ \begin{array} { r r }
• 3 / \sqrt { 13 } & - 2 / \sqrt { 13 } \\
• - 2 / \sqrt { 13 } & 3 / \sqrt { 13 }
• \end{array} \right] , D = \left[ \begin{array} { r r }
• 3 & 0 \\
• 0 & 16
• \end{array} \right]\]
• C)
• \[P = \left[ \begin{array} { r r }
• 3 / \sqrt { 13 } & 2 / \sqrt { 13 } \\
• - 2 / \sqrt { 13 } & 3 / \sqrt { 13 }
• \end{array} \right] , D = \left[ \begin{array} { r r }
• 16 & 0 \\
• 0 & 3
• \end{array} \right]\]
• D)
• \[P = \left[ \begin{array} { r r }
• 3 & - 2 \\
• - 2 & 3
• \end{array} \right] , D = \left[ \begin{array} { r r }
• 16 & 0 \\
• 0 & 3
• \end{array} \right]\]