Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,,, ezm ean denote leading ones, then the nonzero row vectors r,, r, of A, have the form of --Select-- --Select-- r2 ---Select--- 3 and so forth. Then, the equation c,r, + c,r, + .. + c,r, = 0 implies which of the following equations? (Select all that apply.) O ce11 = 0 O cein + cze2n + Cze3n = 0 O c,e3n + cze3n + Cze3n = 0 O c,e2m + Cze2m = 0 Ceim + Cze2m = 0 O cze3n = 0 You can conclude in turn that c, = c, = . = C = , and so the row vectors are linearly independent.
Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,,, ezm ean denote leading ones, then the nonzero row vectors r,, r, of A, have the form of --Select-- --Select-- r2 ---Select--- 3 and so forth. Then, the equation c,r, + c,r, + .. + c,r, = 0 implies which of the following equations? (Select all that apply.) O ce11 = 0 O cein + cze2n + Cze3n = 0 O c,e3n + cze3n + Cze3n = 0 O c,e2m + Cze2m = 0 Ceim + Cze2m = 0 O cze3n = 0 You can conclude in turn that c, = c, = . = 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
Section: Chapter Questions
Problem 1RQ
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Please help me on this one. The choices for r1, r2, and r3 are given in the other picture. Please fill in all the missing information. Thank you very much!
Transcribed Image Text:Select-
(0, 0, 0, 0,
(0, 0, em.
(0,0, eim,
(0,0,0,-
(e1, , ein,
0, ess
en,
0. e3p.
, , ea
(en, ez,
e, ***)
Transcribed Image Text:Prove that the nonzero row vectors of a matrix
row-echelon form are linearly independent.
Let
= A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,,, e,m ea, denote leading ones, then the nonzero row vectors r,,
r, of A, have the form of
r, = ---Select---
r2 =---Select---
r3 = ---Select---
and so forth.
Then, the equation c,r, + C2r2
C,r, = 0 implies which of the following equations? (Select all that apply.)
O c,e1 = 0
C1ein + Cze2n + Cze3n = 0
Ce3n + Cze3n + Cze3n = 0
%3D
C1e2m + Cze2m = 0
O ceim + C2e2m = 0
O cze3n
= 0
You can conclude in turn that c, = c, = * = Ck
and so the row vectors are linearly independent.
O O O O0
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