# Subspace of A and a matrix formed by row operation

1. Jul 5, 2010

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?

2. Jul 5, 2010

### 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?

3. Jul 5, 2010

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

4. Jul 5, 2010

### Office_Shredder

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

5. Jul 5, 2010

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

6. Jul 6, 2010

### Office_Shredder

Staff Emeritus
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)