Let AE Rmxn and suppose that the rank of A is m where m is less than or equal to n and be Rm. Suppose further that K is the convex set consisting of all n-vectors x satisfying: JAx = b x≥0. Show that K possesses at most a finite number of extreme points.
Let AE Rmxn and suppose that the rank of A is m where m is less than or equal to n and be Rm. Suppose further that K is the convex set consisting of all n-vectors x satisfying: JAx = b x≥0. Show that K possesses at most a finite number of extreme points.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:6. Let A € Rmxn and suppose that the rank of A is m where m is less than
or equal to n and be Rm. Suppose further that K is the convex set
consisting of all n-vectors x satisfying:
Ax = b
x≥0.
Show that K possesses at most a finite number of extreme points.
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