Thread: column/row space and RREF

The column space and the row space of a matrix is the span of all its columns and the span of all its rows respectively. Is it true that the column
space of a matrix equals the column space of its RREF? Or the the row space of
a matrix equals the row space of its RREF?


Need a few hints to begin please?

Is it true that the column space of a matrix equals the column space of its RREF?

No. Row operations change the column space.

Or the the row space of a matrix equals the row space of its RREF?

Yes. Row space is unaffected by row operations.