Prove that the nonzero row vectors ofa matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in now-echelo form. If the first column of A is not all zero and e,., em en, denote leading ones, then the nonzero row vectors r,, ...r, of A, have the form of Select- -Select- Select-- and so forth. Then, the equation cr1 + Cr2 +cr= 0 ipelies which of the following equations? (Select all that apply.) O ce2m * C,e2m = 0 OGe1 - 0 O czean = 0 D ce, + ce2n Czean = 0 O ce3n + Czezn + C3e 3n O Cem + Cze2m - 0 You can conclude in turn that c, and so the row vectors are linearly independent.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Prove that the nonzero row vectors ofa matrix in row-echelon form are linearly independent.
Let
= A be an m xn matrix in row-echelo form. If the first column of A is not all zero and e,., eam en- denote leading ones, then the nonzero row vectors r,, ..r, of A, have the form of
Select-
-Select-
Select-
and so forth,
Then, the equation cr, + Cr2
+cr= 0 ipplies which of the following equations? (Select all that apply.)
O c,e2m ! Ce,m = 0
O czean = 0
O cen + ce2n+ Czean = 0
O cean + Czezn + Cze 3n
O Cem + Cze2m = 0
You can conclude in turn that c, = C2
and so the row vectors are linearly independent.
Transcribed Image Text:Prove that the nonzero row vectors ofa matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in row-echelo form. If the first column of A is not all zero and e,., eam en- denote leading ones, then the nonzero row vectors r,, ..r, of A, have the form of Select- -Select- Select- and so forth, Then, the equation cr, + Cr2 +cr= 0 ipplies which of the following equations? (Select all that apply.) O c,e2m ! Ce,m = 0 O czean = 0 O cen + ce2n+ Czean = 0 O cean + Czezn + Cze 3n O Cem + Cze2m = 0 You can conclude in turn that c, = C2 and so the row vectors are linearly independent.
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