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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 false. Each matrix is row equivalent to one and only one reduced echelon 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. It is possible for there to be several different sequences of row operations that row reduces a matrix.
D. 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.

Respuesta :

Answer:

The correct option is option A

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

Step-by-step explanation:

The matrix in echelon form is not in a unique form, as such row reduction can yield an infinite amount of answers. However a row reduced echelon form is unique and will give the same answer in every order that the row operation is performed

The statement is false. Each matrix has only one unique row echelon form, therefore, the correct option is option A.

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