In parts a through e below mark the statement True or False

In parts (a) through (e) below, mark the statement True or False. Justify each answer.

(a) 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?

A.

The statement is true. It is possible for there to be several different sequences of row operations that row reduces a matrix.

B.

The statement is false. For each matrix, there is only one sequence of row operations that row reduces it.

C.

The statement is true. The echelon form of a matrix is always unique, but the reduced echelon form of a matrix might not be unique.

D.

The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix.

Solution

Answer :  

D. The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix.