{x ЄR" | Ax = b,x >0}, where A is an m×n matrix with linearly independent rows. Suppose that two different bases lead to the same basic solution. Show that the basic solution is degenerate.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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Consider the following polyhedron in canonical form 

{x ЄR" | Ax = b,x >0},
where A is an m×n matrix with linearly independent rows. Suppose that two
different bases lead to the same basic solution. Show that the basic solution
is degenerate.
Transcribed Image Text:{x ЄR" | Ax = b,x >0}, where A is an m×n matrix with linearly independent rows. Suppose that two different bases lead to the same basic solution. Show that the basic solution is degenerate.
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