How to choose the starting row when computing the reduced row echelon form? I'm having hell of a time going around solving matrices to reduced row echelon form. My main issue is which row to start simplifying values and based on what? I have this example 

so again, the questions are: 
1.Which row to start simplifying values?
2.Based on what criteria?
Our professor solved it in the class with no fractions but I could not do it. Even though  I know the 3 operations performed on matrices 

You can go in whatever order you want - it won't affect the final answer. If you wanted, you could always go about by eliminating the bottom left corner, then the bottom middle, then the middle left, etc. And I really do mean always.
At any point, if you get fractions and you don't want fractions, then you could multiply everything by the denominator of the fraction you're getting - that will remove all fractions and just leave integers.
