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.
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.