Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D.
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\left[ \begin{array} { r r r } 11 & 7 & 7 \\7 & 11 & 7 \\7 & 7 & 11\end{array} \right]

P = \left[ \begin{array} { c c c } 1 / \sqrt { 3 } & - 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 0 & 2 / \sqrt { 6 }\end{array} \right] , D = \left[ \begin{array} { r r r } 4 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 25\end{array} \right]

P = \left[ \begin{array} { r r r } 1 & - 1 & - 1 \\1 & 1 & - 1 \\1 & 0 & 2\end{array} \right] , D = \left[ \begin{array} { r r r } 25 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 4\end{array} \right]

P = \left[ \begin{array} { r c c } 1 / \sqrt { 3 } & 1 / \sqrt { 2 } & 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & - 1 / \sqrt { 2 } & 1 / \sqrt { 6 } \\- 1 / \sqrt { 3 } & 0 & 2 / \sqrt { 6 }\end{array} \right] , D = \left[ \begin{array} { r r r } 25 & 0 & 0 \\0 & 25 & 0 \\0 & 0 & 4\end{array} \right]

P = \left[ \begin{array} { c c c } 1 / \sqrt { 3 } & - 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 1 / \sqrt { 2 } & - 1 / \sqrt { 6 } \\1 / \sqrt { 3 } & 0 & 2 / \sqrt { 6 }\end{array} \right] , D = \left[ \begin{array} { r r r } 25 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 4\end{array} \right]

Find the maximum value of Q(x) subject to the constraint xTx=1. \text { Find the maximum value of } Q ( x ) \text { subject to the constraint } _x T _ { x = 1 } \text {. } Find the maximum value of Q(x) subject to the constraint x​Tx=1​.

Multiple Choice