Register to reply

Matrices in reduced row-echelon form

by Tonyt88
Tags: form, matrices, reduced, rowechelon
Share this thread:
Tonyt88
#1
Feb9-07, 12:26 AM
P: 62
1. The problem statement, all variables and given/known data
Determine which of the matrices below are in reduced row-echelon form:
a)
1_2_0_2_0
0_0_1_3_0
0_0_1_4_0
0_0_0_0_1

b)
0_1_2_0_3
0_0_0_1_4
0_0_0_0_0

c)
1_2_0_3
0_0_0_0
0_0_1_2

d)
0_1_2_3_4



2. Relevant equations



3. The attempt at a solution
Okay, so I know for sure that (a) is not in reduced row-echelon form because the leading one in row 2 had a nonzero value in its column.

(b) is in reduced row-echelon form.

(c) is the one I'm most curious about. I feel that since there is a leading 1 in row 3, but that there is no leading 1 in row two (and to the left at that) that it's not in reduced row-echelon form, is this correct?

(d) I feel confident is in reduced row-echelon form.

Are all my thoughts correct?
Phys.Org News Partner Science news on Phys.org
Suddenly, the sun is eerily quiet: Where did the sunspots go?
'Moral victories' might spare you from losing again
Mammoth and mastodon behavior was less roam, more stay at home
radou
#2
Feb9-07, 02:28 AM
HW Helper
radou's Avatar
P: 3,224
Quote Quote by Tonyt88 View Post
(c) is the one I'm most curious about. I feel that since there is a leading 1 in row 3, but that there is no leading 1 in row two (and to the left at that) that it's not in reduced row-echelon form, is this correct?
If it is so, what do you propose to reduce it?
Tonyt88
#3
Feb9-07, 08:40 AM
P: 62
To reduce it would you switch row 2 and 3?

radou
#4
Feb9-07, 09:10 AM
HW Helper
radou's Avatar
P: 3,224
Matrices in reduced row-echelon form

Quote Quote by Tonyt88 View Post
To reduce it would you switch row 2 and 3?
You do not need to switch row 2 and 3. Only for the sake of aesthetics, perhaps. The system if completely reduced and you can read out all relevant information from the matrix.
jalexanal
#5
Jul23-10, 08:00 PM
P: 1
radou is right: you do not need to swap row 2 and row 3, but "reduced row echelon form" has a formal definition and it is necessary to swap row 2 with row 3 to put c) in that form.
HallsofIvy
#6
Jul24-10, 09:05 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,293
Well, I agree with the last part of what jalexanal said but, as a result, I would have to say "radou is wrong"! Just for solving equations or related problems, the order of rows does not matter but for this problem, to tell whether or not the matrices are in "reduced row echelon" form, it does matter. In reduced row echlon form, there must be no rows below a given row with first non-zero member further to the left.


Register to reply

Related Discussions
Row-Reduced Echelon Forms Linear & Abstract Algebra 7
Row echelon form Precalculus Mathematics Homework 3
Determinant of a matrix using reduced echelon form Precalculus Mathematics Homework 7
Reduced row echelon form of matrix Linear & Abstract Algebra 1
Reduced row echelon form Introductory Physics Homework 1