Why elementary row operation do not affect row space of a matrix?

Question

anonymous · Answer

What do you mean by row space? @Erichooi

anonymous · Answer

I also no quite sure, I search Wikipedia and see this .

anonymous · Answer

From reading some Wikipedia, it seems that the row space of a matrix A is is any linear combination of its row vectors but because elementary row operations don't affect the row space, one can use row reduction to get to the row echelon form of the matrix which will give the basis vectors. Any linear combination of these basis vectors will provide us with the row space. Any questions on any aforementioned terms/concepts? @Erichooi

anonymous · Answer

because u apply row operation on both the matrices one on the left of = and one on the right of =