Gram-Schmidt process Question:Apply the Gram-Schmidt process to find an orthonormal basis for the subspace.
$S= \mathrm{span} [{(1,2,-4,-1),(-3,0,5,-2),(0,7,2,-6)}]$
The span is suppose to look like a matrix but I couldn't get it to look right here so I wrote it that way.
I was able to do the process but I wanted to check something. When I was working on my 3rd vector I didn't get a cancellation. Is it wrong if something doesn't cancel out?
I got my answers to be $u_1= \frac{1}{\sqrt{22}} \left(\begin{smallmatrix}1\\ 2\\-4\\-1\end{smallmatrix}\right)$, $u_2= \sqrt{\frac{22}{395}} \left(\begin{smallmatrix}-45/22\\ 21/11\\13/11\\-65/22\end{smallmatrix}\right)$, and $u_3= \sqrt{\frac{395}{7947}} \left(\begin{smallmatrix}258/79\\ 929/395\\782/395\\ 4/79\end{smallmatrix}\right)$

Wow what a nasty question...well I get exactly those $u_1,u_2,u_3$, and I cross-checked on Mathematica - it is correct. I am not sure exactly what you thought should have cancelled out, but it seems as if it is not "wrong" the fact that it didn't cancel out. 
But I think it might be worthwhile to try and find a simpler basis for that subspace before applying Gram-Schmidt?
