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Linear Inequalities in the Plane: Definitions, Examples, and Feasibility Regions, Assignments of Linear Algebra

University of Illinois - Urbana-ChampaignLinear Algebra

This section covers the concepts of linear equations, linear inequalities, half-planes, and systems of linear inequalities in the context of graphing their feasibility regions. Two examples are provided to illustrate the process of graphing the region defined by a system of linear inequalities and finding the corner points.

Typology: Assignments

Pre 2010

Uploaded on 03/11/2009

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Section 1.3: Linear Inequalities in the Plane
Definition: linear equality
Definition: linear inequality
Definition: half-plane
Example 1: Sketch the half-plane defined by 2x+y < 1.
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Section 1.3: Linear Inequalities in the Plane

Definition: linear equality

Definition: linear inequality

Definition: half-plane

Example 1: Sketch the half-plane defined by 2x + y < 1.

Definition: system of linear inequalities

Definition: the feasibility region

Example 2: Graph the region defined by the system of inequalities and find the corner points.

x + 2y ≥ 4 − 2 x + 3y ≥ − 6