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]]