Show that 1) The columns of a (row-reduced) echelon matrix that contain the non-zero pivots are linearly independent; 2) Any set of k vectors with m components is linearly dependent when- ever k > m. Hint: V1 V2 Vk X = 0 mxk

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 30EQ
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Show that
1) The columns of a (row-reduced)
echelon matrix that contain the
non-zero pivots are linearly independent;
2) Any set of k vectors with m components is linearly dependent when-
ever k > m.
Hint:
|V1 V2
VE X = 0
mxk
Transcribed Image Text:Show that 1) The columns of a (row-reduced) echelon matrix that contain the non-zero pivots are linearly independent; 2) Any set of k vectors with m components is linearly dependent when- ever k > m. Hint: |V1 V2 VE X = 0 mxk
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