Question

Is this matrix in reduced row echelon form?

1	0	0	5
0	1	1	0
0	0	1	1

The number 1 in bold, Row 2 Column 3, makes me not sure.

Answer 1

The given matrix is not in reduced row echelon form.

Explanation:

A matrix is said to be in reduced row echelon if it satisfies followings:

(i) First non zero element(called pivot) in each row should be 1.

(ii) The column of the pivot  element in a row should be right to the pivot element in previous row.

(iii) A column which contains a pivot element, all other elements in that column should be zero.

In given example, condition (i) and (ii) is satisfied, but not (iii) as row -3 pivot element is in column-3 and in same column in row-2 contains a non zero value(1 in bold).