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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.
- [3226]\left[ \begin{array} { l l } 3 & 2 \\ 2 & 6 \end{array} \right]


A)
P=[1221],D=[8003]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=[1/52/52/51/5],D=[2007]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=[1221],D=[7002]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)
P=[1/52/52/51/5],D=[7002]\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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