$Let \ A = \left[\begin{array}{cccc}1&2&-1&1\\2&4&-3&0\\1&2&1&5\end{array}\right]$
Using Gauss elimination, lead matrix A to row reduced echelon form:
$\left[\begin{array}{cccc}1&2&0&3\\0&0&1&2\\0&0&0&0\end{array}\right]$
And now using that form I am supposed to say what are column and row space basis. I think that Column space basis is: $\left[\begin{array}{cc}1&-1\\2&-3\\1&1\end{array}\right]$ But what is rowspace basis???
I dont know why I am asking all these question, when wikipedia exist but whatever http://en.wikipedia.org/wiki/Row_space says that row space are all non zero row vectors in (reduced row) echelon form. So i Guess its: $\left[\begin{array}{cccc}1&2&0&3\\0&0&1&2\end{array}\right]$ Good?