Put an augmented matrix into RREF format

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I am looking to find an easier way (if there is one) to put an augmented matrix into RREF format. Thanks for the help.
 
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What do you mean by "easier"? As compared to which method? You're using Gauss-Jordan elimination are you not?

There's something known as LU decomposition, but I don't know if that helps:
http://en.wikipedia.org/wiki/LU_decomposition
 
Thank you very much for replying to my blog so fast and sorry it was so vague. I am currently a "struggling" Engineering student and I just get overwhelmed and confused sometimes. Thanks bud.
 

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