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

question 22

Multiple Choice

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D.
- $\left[ \begin{array} { l l } 3 & 2 \\ 2 & 6 \end{array} \right]$

• A)
• \[P = \left[ \begin{array} { r r }
• 1 & - 2 \\
• 2 & 1
• \end{array} \right] , D = \left[ \begin{array} { l l }
• 8 & 0 \\
• 0 & 3
• \end{array} \right]\]
• B)
• \[P = \left[ \begin{array} { r r }
• 1 / \sqrt { 5 } & - 2 / \sqrt { 5 } \\
• - 2 / \sqrt { 5 } & 1 / \sqrt { 5 }
• \end{array} \right] , D = \left[ \begin{array} { l l }
• 2 & 0 \\
• 0 & 7
• \end{array} \right]\]
• C)
• \[P = \left[ \begin{array} { r r }
• 1 & - 2 \\
• 2 & 1
• \end{array} \right] , D = \left[ \begin{array} { l l }
• 7 & 0 \\
• 0 & 2
• \end{array} \right]\]
• D)
• \[\mathrm { P } = \left[ \begin{array} { c c }
• 1 / \sqrt { 5 } & - 2 / \sqrt { 5 } \\
• 2 / \sqrt { 5 } & 1 / \sqrt { 5 }
• \end{array} \right] , \mathrm { D } = \left[ \begin{array} { l l }
• 7 & 0 \\
• 0 & 2
• \end{array} \right]\]

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