# Column and row space basis

$Let \ A = \left[\begin{array}{cccc}1&2&-1&1\\2&4&-3&0\\1&2&1&5\end{array}\right]$

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?

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If you know the sifting algorithm you could also just apply that to the rows of the original matrix, to get a basis for the row space whose members are actually rows of $A$.