Final answer:
Every matrix is equivalent to a unique reduced echelon form, but a single row alone does not determine a unique reduced echelon matrix. The entire matrix must be considered for such a determination, which is different from calculating degrees of freedom in a Test of Independence.
Step-by-step explanation:
The question concerns whether each matrix row is equivalent to one and only one reduced echelon matrix. In linear algebra, it is indeed true that every matrix is equivalent to a unique reduced echelon form (REF) or reduced row echelon form (RREF). However, a single row does not have enough information to determine a unique reduced echelon matrix on its own. Instead, the entire matrix must be considered. Furthermore, the number of degrees of freedom in a statistical Test of Independence is given by the formula (number of columns - 1)(number of rows - 1), which involves both rows and columns rather than individual rows.