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Lecture Eight

Explore methods for maximizing (or minimizing) functions subject to constraints, including the use of Lagrange Multipliers. Learn how characteristic roots of the associated vector impact maximum/minimum determination in quadratic forms.

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Lecture Eight

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  1. Lecture Eight Determination of Maxima and Minima Maximization (Q.F.)

  2. Quadratic form can be represented as : To maximizing / (minimizing) some function f(x) subjected a constrain: g(x) = c on values of x and for more general method is that of "Lagrange Multiplier".

  3. From a new function:

  4. Note • If the Q.F. is to be maximum then λ must be the greater characteristic root of A and x is associated vector. Similarly , if the Q.F. is to be minimum then λ must be the minimum characteristic root of A. • As a special case :

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