So what is another way to find the RREF without the gaussian elimination, but a much faster method
So i found a way to find a quick way to find RREF for many matrices. I look at the columns and see if they form an equation or not and if they dont then it must be a pivot column. For example
Lets say this a the matrix
Now instead of doing gaussian elimination and taking forever, look at the matrix carefully. Notice columns 1 does not match with column 2 and column 2 doesnt match with column three. but -6 times column 1 = column 3
so the RREF would be the following
Now notice the first column and third column and look how it is related to the original matrix without the RREF.
You can also add columns with each other with the appropriate scalars to see if they are related with each other, For example look at this RREF
notice that 5 times column 1 + 3 times column 2 = column 3
So as you can tell this is a much faster/easier way to calculate the RREF.