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 

The order of steps doesn't matter.  Here are some tips:
1/ If the first row doesn't have 1 as the leading entry, make it be!
2/ Go by columns when you want to make entries becoming 0's.  Usually, start from the first column and make all entries in the first column (except the leading 1 of the first row) be 0's.  
3/ Avoid fractions.  They create a big confusion when you apply elementary row/column operations.  Sometimes you can multiply the fractional entries to become whole numbers, apply ERO's or ECO's, then reduce it back to be fraction.  It's a bit redundant, but it helps you see what you have done.
