Let P := {x € R" : Ax < b} be a nonempty polyhedron, where A E RmXn and b E R™. Note that P is not in standard form. Prove that the following result: P does not contain a vertex if and only if rank(A) < n. (Hint: Think about the implications of the assumption rank(A) < n.)
Let P := {x € R" : Ax < b} be a nonempty polyhedron, where A E RmXn and b E R™. Note that P is not in standard form. Prove that the following result: P does not contain a vertex if and only if rank(A) < n. (Hint: Think about the implications of the assumption rank(A) < n.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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