# [SOLVED] row coloum space

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• Dec 17th 2007, 10:28 AM
mrheyhey07
[SOLVED] row coloum space
Hey guys, just found this nice site and was wondering if someone can help me out? I need this done an there'll be a similar question on my exam tomorrow. I'm stuck on this question,

http://img511.imageshack.us/img511/6218/mathsgy0.jpg
I don;t know the method. I think I gotta break it down a bit first but I'm not sure. Any takers?

Thx in advance.

mrheyhey07
• Dec 17th 2007, 10:51 AM
galactus
Reduce your matrix to row-echelon form. The row vectors with the leading 1's form a basis for the row space of R and the columns with the leading 1's of the row vextors form a basis for the column space of R.

The rank is the dimension of the row and column space. They should be the same.

For ref, I get:

$\begin{bmatrix}1&-1&2\\0&1&2\\0&0&0\\0&0&0\end{bmatrix}$