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Are the following statements true or false? If A and B have the same RREF then N(A) =...

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hockeyfan54 | Student | (Level 1) Salutatorian

Posted April 13, 2013 at 10:33 PM via web

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Are the following statements true or false?

If A and B have the same RREF then N(A) = N(B).

If B is a row-echelon form of a matrix A, then the nonzero rows of B form a basis for the row space of A.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 14, 2013 at 5:34 AM (Answer #1)

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True ,because

If A is row equivalent to B, then the row spaces of A and B are equal.

The nonzero rows of the row echelon form of an matrix A form a basis of the row space of A. This is so since the nonzero rows of the row echelon form are linearly independent.

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