Find the Maximum Value Of $Q ( x )$ Subject to the Constraints

question 3

Multiple Choice

Find the maximum value of $Q ( x )$ subject to the constraints $_x T _ { x } = 1$ and $_x { T } \mathbf { _u } = 0$ , where $u$ is a unit eigenvector corresponding to the greatest eigenvalue of the matrix of the quadratic form.
- $$Q ( x ) = 14 x _ { 1 } ^ { 2 } + 14 x _ { 2 } ^ { 2 } + 18 x _ { 3 } ^ { 2 } + 26 x _ { 1 } x _ { 2 } + 18 x _ { 1 } x _ { 3 } + 18 x _ { 2 } x _ { 3 }$$

• A) 36
• B) 9
• C) 1
• D) 16

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Definitions:

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