Let A € RPXm have rank r. Show that there are matrices C and B such that A = CB, where C e RPxr and B e Rxm are both full rank (r). Hint. Form C from r linearly independent columns of A.
Let A € RPXm have rank r. Show that there are matrices C and B such that A = CB, where C e RPxr and B e Rxm are both full rank (r). Hint. Form C from r linearly independent columns of A.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 42EQ
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Transcribed Image Text:Let A € RPXm have rank r. Show that there are matrices C and B such that A =
св,
where C E RPXT and B E R*m are both full rank (r).
Hint. Form C from r linearly independent columns of A.
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