Having trouble solving the following equation using the Gauss-Jordan method::eek:
2x-5y+z=11
3x+y-6z=1
5x-4y-5z=12

Anyone know an easy way to solve these equations?

Well, the equations are not linearly independent, because the third can be derived as the sum of the first two. So, in essence, there are only two equations and three variables. For the equations to work, there have to be only two variables, so either x, y, or z must be zero. Plugging these respective zeroes into the initial two equations yields nice, easy 2-d systems which have results:

(0,-2.310345,-0.5517241)
(67/15,0,31/15)
(16/17,-31/17,0)

Hope this helped!

Your system is inconsistent.