Determine if the statement is true or false.

Different sequences of row operations can lead to different reduced echelon forms for the same matrix.

True False

Justify your answer.

False

Step-by-step explanation:

There are two concepts:

1. Row Echelon Form: There can be more than two row echelon forms of a single matrix, so different sequences of row operations can lead to different row echelon forms of a single matrix.

2. Reduced Row Echelon Form: It's unique for each matrix, so different sequences of row operations always lead to the same reduced row echelon form for the same matrix.