Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let a = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,, em ea, denote leading ones, then the nonzero row vectors r, r, of A, have the form of ---Select--- 2 =--Select--- ---Select--- and so forth. Then, the equation c,r, + c,r, + ... + c,r, = 0 implies which of the following equations? (Select all that apply.) Ocze3n + Cze3n + Cz@3n = 0 O Cze3n = 0 Oc,e2m + Cze2m = 0 O cge,n + cze2n + Cze3n = 0 O c,e11 = 0 O c;e,m + cze2m = 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 = A be an m xn matrix in row-echelon form. If the first column of A is not all zero and e,, em ea, denote leading ones, then the nonzero row vectors r, r, of A, have the form of ---Select--- 2 =--Select--- ---Select--- and so forth. Then, the equation c,r, + c,r, + ... + c,r, = 0 implies which of the following equations? (Select all that apply.) Ocze3n + Cze3n + Cz@3n = 0 O Cze3n = 0 Oc,e2m + Cze2m = 0 O cge,n + cze2n + Cze3n = 0 O c,e11 = 0 O c;e,m + cze2m = 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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Transcribed Image Text:Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent.
Let
= A be an m x n matrix in row-echelon form. If the first column of A is not all zero and e, 1, e,m, e3n denote leading ones, then the nonzero row vectors r,,
rk of A, have the form of
---Select---
r
---Select---
%|
---Select---
and so forth.
Then, the equation c,r, + c2*2 + *** + Ck*K
= 0 implies which of the following equations? (Select all that apply.)
C1@3n + C2e3n + Cze3n = 0
Cze3n
= 0
Cqe2m + Cze2m
= 0
= 0
C1ºin + C2@2n + Cz€3n
C1e11
= 0
+ Cze2m
= 0
1m
You can conclude in turn that c, = c, :
and so the row vectors are linearly independent.
II
II
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