with(LinearAlgebra): A:=<<-2,-2,1/3>|<-3,-9,1>|<1,1,-1/3>|<12,9,-2>|<0,1,0>|<0,0,1>|<0,0,0>>;

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNXV6YUIiNFQpb1c9

#Pivot in the 3,2 position (This is the (2,2) position in the notes because # we start with Row 0 instead of Row 1 here. A1:=RowOperation(A,[1,3],3): A2:=RowOperation(A1,[2,3],9);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNU0yYkIiNFQpb1c9

#Pivot in the 2,1 position (to be consistent with the notes) A3:=RowOperation(A2,[1,2],1): A4:=RowOperation(A3,[3,2],-1/3);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNU00PFYiNFQpb1c9

#Pivot in the 3,4 position. A5:=RowOperation(A4,[1,3],3): A6:=RowOperation(A5,[2,3],9);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNXlTO1YiNFQpb1c9

#Pivot in the 2,3 position. A7:=RowOperation(A6,[1,2],1): A8:=RowOperation(A7,[3,2],-1/3);

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNVFdO1YiNFQpb1c9

#Etc... TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2ODg0MTA5MTIzNTQ3OTc0WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjNiIkIighIiNGJiMiIiIiIiQhIiQhIipGKEYoRigjISIiRikiIzciIipGJiIiIUYoRjBGMEYwRihGMEYwRjBGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2ODg0MTA5MTIzNTUwNzM0WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjNiIkIighIiIiIiIjRiciIiQiIiFGKkYnRiohIiMjRiZGKSIiJyEiKkYrRipGJ0YqRikiIipGJ0YqRipGKkYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2ODg0MTA5MTQzMTcwOTM0WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjNiIkIigiIiEiIiJGJkYmRiZGJyEiI0YoI0YnIiIkISIkISIqRidGJ0YnIyEiIkYqIiM3IiIqRihGJkYmRiZGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2ODg0MTA5MTQzMTY0MDc4WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjNiIkIigiIiEiIiJGJiIiJCIiKkYnISIiRicjRidGKEYmRiZGJ0YmISIjI0YqRigiIichIipGLEYmRiZGJkYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2ODg0MTA5MTQzMTY1MDM4WCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjNiIkIigiIiJGJiMhIiIiIiQiIzciIiohIiMiIiFGJkYtRi1GLUYmRixGLCNGJkYpISIkISIqRiZGLUYtRi1GJQ==