http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
i recommend keeping things simple from step to step to avoid getting messed up because you've got too many things going at the same time.
if there's an error, it's hell trying to figure out where it is if you try to do too many things at the same time in the same step.
there's no one way to solve it.
some ways are better than others, i.e. more efficient leading to a result in less steps, but any way you solve it is good as long as you follow the rules.
here's my worksheet.
here's how i did it.
step 1:
i made row 1 equal to row 1 multiplied by 3
i made row 3 equal to row 3 multiplied by 3
the result is shown in step 2.
step 2:
i made row 1 equal to row 2 minus row 2
i made row 3 equal to row 3 minus row 2
the result is shown in step 3.
step 3:
i made row 2 equal to row 2 multiplied by 5
i made row 3 equal to row 3 multiplied by 4
the result is shown in step 4.
step 4:
i made row 2 equal to row 2 minus row 3
the result is shown in step 5:
step 5:
i made row 3 equal to row 3 minus 20 * row 1
the result is shown in step 6.
step 6:
i made row 2 equal to 4 * row 2 minus row 3
the result is shown in step 7.
step 7:
i made row 2 equal to row 2 divided by 60
i made row 3 equal to row 3 divided by 12
the result is shown below:
step 8:
0 + 0 + 1 + 2
0 + 1 + 0 + 1
1 + 0 + 0 + 3
i flipped rows.
row 3 became row 1
row 1 became row 3
row 2 stayed where it was
the final matrix is shown below with the heading for each column on top
x + y + z + r
1 + 0 + 0 + 3
0 + 1 + 0 + 1
0 + 0 + 1 + 2
r is the result.
you get:
x = 3
y = 1
z = 2
the results correspond to what the gauss jordan tool shows although the intermediate steps are probably different since i didn't follow their script but solved it my own way which may or may not be as good but it worked.
here's a pretty good reference on the method.
http://math.tutorvista.com/algebra/gauss-jordan-method.html
they exchanged rows up front while i exchanged rows more towards the end.
different methods that both work.