# Matrices in reduced row-echelon form

## Homework Statement

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

## 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?

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Homework Helper
(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?

To reduce it would you switch row 2 and 3?

Homework Helper
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.

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