# Thread: Matrix is in row echelon form, reduced row echelon form, both, or neither?

1. ## Matrix is in row echelon form, reduced row echelon form, both, or neither?

Is the matrix in row echelon form, reduced row echelon form, both, or neither?

a)

b)

c)

2. ## Re: Matrix is in row echelon form, reduced row echelon form, both, or neither?

https://stattrek.com/statistics/dict...w_echelon_form

Apply definition. I'll do (a) and leave it to you to complete b,c.

(a)
A matrix is in row echelon form (ref) when it satisfies the following conditions.

The first non-zero element in each row, called the leading entry, is 1. (True; row 1 and 3's first non-zero element is 1. Row 2 has no non-zero elements, so vacuously true.)
Each leading entry is in a column to the right of the leading entry in the previous row. (True; the only rows with leading entries are row 1 and 3. row 3's leading entry is to the right of row 1's leading entry)
Rows with all zero elements, if any, are below rows having a non-zero element. (False; row 2 is above row 3)

A matrix is in reduced row echelon form (rref) when it satisfies the following conditions.

The matrix is in row echelon form (i.e., it satisfies the three conditions listed above). (False)
The leading entry in each row is the only non-zero entry in its column. (False; row 3's leading entry is in the same column as another non-zero entry in row 1)

Therefore, the matrix is neither.

Thank you!