Question 1074117
The steps being abbreviated here:


2E2-E1 and E3-E2 to change E2 and E3


E2 divided by 3


E3+3E2 to change E2


-1*E3


E1-E3 and E2+3E3 to change E1 and E2


E1+E2  to change E1


Resulting matrix became
{{{(matrix(3,4,
2,0,0,5,
0,1,0,-1,
0,0,1,1))}}}


This seems that you cannot completely avoid fractions, none of my steps up to this last part used fractions.  You will need a fraction to do the last step to finish.