Finding the Maximum Value of a Quadratic Form Using Lagrange Multipliers | Optimization Problem

In this video, we find the maximum value of the quadratic form

Q(x)=9x_1^2+6x_2^2-2x_1x_2 ​

subject to the constraint

x_1^2+x_2^2=1.

This is a classic constrained optimization problem commonly encountered in linear algebra, calculus, and quadratic forms.

🔍 What you’ll learn in this video:

How to apply Lagrange multipliers step by step

How to handle quadratic forms with constraints

How to identify maximum values under a unit-circle constraint

📌 Topics Covered:

Quadratic forms

Constrained optimization

Lagrange multipliers

Maximum and minimum value problems

🎯 Perfect for:

Undergraduate math students

Linear Algebra & Multivariable Calculus learners

Exam preparation and concept revision

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Видео Finding the Maximum Value of a Quadratic Form Using Lagrange Multipliers | Optimization Problem канала Turnupmath