Gauss-Jordan Method

[aminns]

I know I am suppose to be trying to get a leading 1 in each row but not sure where I am to begin with the large numbers at the beginning.
Solve the following system of equations using the Gauss-Jordan method.
-9x – 2y + z = -2
12x + y = 9
-6x – 2y + z = 1

 

[Harry_the_cat]

If you can handle working with fractions, divide the first row by -9.

 

[Steven G]

I would never advise anyone to get leading 1 initially when reducing a matrix.
You can get any non-zero number (all zero rows at the bottom) where you want 1's. Then at the end, you can divide each row to get the 1s. This way you do not have to deal with fractions.
You have:
-9 -2 1 -2
12 1 0 9
-6 -2 1 1

The next matrix can be

-9 -2 1 -2
0 -5 4 19
0 2 -1 -7

Now using the -5 (and not changing it to 1) get the numbers above and below it to be 0.

Eventually you will get something like.
-9 0 0 17
0 -5 0 -13
0 0 6 33

Now you can can those leading entries to be 1. This will introduce fractions but you will be done. That is no adding/subtracting any fractions.