Determine if the given matrix is in echelon form reduced row

Determine if the given matrix is in echelon form, reduced row echelon form or neither. [1 -5 -5 3 0 0 2 -2 0 0 0 5 0 0 0 0] _______ [1 0 -4 -2 0 1 4 5 0 0 0 0 0 0 0 0] _______ [1 0 0 -7 7 1 0 5 0 4 1 7] _________

Solution

Solution:

A matrix is in row echelon form when it satisfies the following conditions.

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

Now in the given problem:

5) Answer: Neither  row echelon form nor reduced row echelon form

Explanation: Second row first non-zero element is 2, which not the leading entry 1.

6) Answer: Row Echelon Form

Explanation: It satisfies all the above conditions of row echelon form.Here the leading entry in first and second row is not the only non-zero entry in its column. So it is not in reduced row echelon form

7) Answer: Neither  row echelon form nor reduced row echelon form

Explanation: It does not satisfy the above conditions of row echelon form and reduced row echelon form.