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.
-$$Q ( x ) = 3 x { } _ { 1 } ^ { 2 } + 8 x { } _ { 2 } ^ { 2 } + 4x \frac { 2 } { 3 }$$
A) 0
B) 3
C) 4
D) 8

Question

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.
-$$Q ( x ) = 3 x { } _ { 1 } ^ { 2 } + 8 x { } _ { 2 } ^ { 2 } + 4x \frac { 2 } { 3 }$$
A) 0
B) 3
C) 4
D) 8

Quizplus · Accepted Answer

The maximum value of $Q ( x )$ subject to the constraints is the greatest eigenvalue of the matrix of the quadratic form, which is 4.

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