Question: Let "R" be the reduced row echelon form of an m x n matrix "A". Is the span of the columns of "R", (where each column represents a column vector) equal to the span of the columns of "A"? Justify your answer.

Initially I answered yes, since the operations converting a matrix to its reduced row echelon form are reversible, but the answer at the back of the book is "No".

Any ideas?

P.S. This question is taken from the book "Elementary Linear Algebra", (Here's the URL)

http://www.math.ilstu.edu/matrix/default.html

Thanks.