Subspace of A and a matrix formed by row operation

[Ali Asadullah]

The subspace formed by matrix A and A' will be same or different if A' is obtained by applying an elementary row operation on A?
Please prove it.

 

[HallsofIvy]

In what sense does a matrix or two matrices "form" a subspace?

Are you referring to the subspace of $M_{mxn}$ of m by n matrics spanned by two such matrices?

 

[Ali Asadullah]

Sorry sir i used wrong word.
i meant spanned by two matrices A and A'.

 

[Office_Shredder]

Different compared to what? If you apply a different elementary row operation?

 

[Ali Asadullah]

I mean sir Col A = Col A'
Is it true or not.

 

[Office_Shredder]

Hah, now that that's cleared up.

What have you tried so far? It might be a good idea to look at a couple of small examples (2x2 or 2x3 matrices) just to see what's going on (especially because you don't know if the statement is true, so you might find a counterexample)