The test cases that I would like to see are below.
Several people's code failed on the first one (from the wiki page).
I will give full credit to anyone who eventually hands in a code that works
for all of these examples and any other augmented matrix.


Original matrix:
[[ 1.  3.  1.  9.]
 [ 3. 11.  5. 35.]
 [ 1.  1. -1.  1.]]
Reduced:
[[ 1.  0. -2. -3.]
 [ 0.  1.  1.  4.]
 [ 0.  0.  0.  0.]]

Original matrix:
[[  2.   1.  -1.   8.]
 [ -3.  -1.   2. -11.]
 [ -2.   1.   2.  -3.]]
Reduced:
[[ 1.  0.  0.  2.]
 [ 0.  1.  0.  3.]
 [-0. -0.  1. -1.]]

Original matrix:
[[ 1.  1. 27.]
 [ 2. -1.  0.]]
Reduced:
[[ 1.  0.  9.]
 [-0.  1. 18.]]

Original matrix:
[[ 0.  3. 12.]
 [ 2. -1.  3.]]
Reduced:
[[ 1.   0.   3.5]
 [-0.   1.   4. ]]

Original matrix:
[[3. 2. 7.]
 [2. 4. 3.]]
Reduced:
[[ 1.     0.     2.75 ]
 [ 0.     1.    -0.625]]