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

question 12

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

• A) 0
• B) 3
• C) 4
• D) 8

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Definitions:

National Industrial Recovery Act

A legislation passed in 1933 as part of President Franklin D. Roosevelt's New Deal, aimed at stimulating economic recovery during the Great Depression by regulating industry standards and workers' rights.

Economic Recovery

The process of recovery in an economy that leads to increased business activity, employment, and production after a period of recession or downturn.

Workers' Wages

The compensation or earnings paid to employees or laborers for their work or services, usually expressed in terms of hourly, daily, or monthly rates.

Reconstruction Finance Corporation

A government corporation in the United States created by Congress in 1932 to provide financial support to state and local governments and make loans to banks, railroads, mortgage associations, and other businesses.