Subspace of A and a matrix formed by row operation

Ali Asadullah
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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.
 
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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?
 
Sorry sir i used wrong word.
i meant spanned by two matrices A and A'.
 
Different compared to what? If you apply a different elementary row operation?
 
I mean sir Col A = Col A'
Is it true or not.
 
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)
 

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