Exercise: 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: Vi V2 V X = 0 ... mxk

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Exercise: 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 =
mxk
Transcribed Image Text:Exercise: 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 = mxk
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