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Find the maximum value of $Q(\mathbf{x})=7 x_{1}^{2}+3 x_{2}^{2}-2 x_{1} x_{2}$ subject to the constraint $x_{1}^{2}+x_{2}^{2}=1 .$ (Do not go on to find a vector where the maximum is attained.)

$5+\sqrt{5}$

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 3

Constrained Optimization

Introduction to Matrices

Oregon State University

Harvey Mudd College

Idaho State University

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she's so, uh, given this quadratic form the next video off Q x ah subject two X transpose times X equals to one is, um the maximal I am value off the metrics A. So, in this case, a close to seven minus one minus 13 So the agon value off a is the solution to this characteristic equation that would be seven minus lambda times three minus lambda minus one equals zero. So Lamda one equals 25 plus Ruutel five and the Lambda Chewy, close to five minus root. If I so sees Lambda Wise Greater Lambda to sell a maximum value equals 25 plus Ruto five.

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