In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. is this statement true or false?

This is False.

Step-by-step explanation:

To solve matrices, operations such as the Gaussian elimination can be used. After this operation, a matrix with a row echelon form is obtained. The reduced echelon form is particular case of this, in which the matrix:

1. Is in row echelon form.

2. The first number in each non-zero row is 1 (which is called a leading 1).

3. Each column that has a leading 1 has zeros everywhere else

A matrix in a reduced row echelon form is unique and independent on the algorithm used to calculate it.

yes

yes yes yes