I'm currently trying to understand how to solve systems of equations using Gaussian elimination and back-substitution. I'm also trying to implement some computer algorithms that solve systems of equations using this method.

Now I know Wikipedia is not always a reliable source, but I thought it be helpful to get some sample problems from the Wikipedia entry on Guassian elimination. But, no matter how many times I try to solve it, I never get the answer specified on Wikipedia. Also, the computer algorithm I use doesn't get the Wikipedia answer either. So either I'm doing this totally wrong, or Wikipedia is wrong about it.

The wikipedia entry can be found at

Gaussian elimination - Wikipedia, the free encyclopedia
Here is the system of equations:

2x + y - z = 8

-3x - y + 2z = -11

-2x + y + 2z = -3

So we get a matrix like this:

+-----------------------+

| 2 1 -1 8 |

| -3 -1 2 -11 |

| 2 1 2 -3 |

+-----------------------+

Now, the Wikipedia article gives the solution as:

x = 2

y = 3

z = -1

But the computer algorithm I implemented gets the following results:

x = -0.66

y = 5.66

z = -3.66

At first I thought it's more likely that I'm wrong than the Wikipedia article, so I tried solving the same system of equations using a professional computer algorithm, and I got the same solution. Also, when you plug in the above values for 2x + y - z = 8, you get a true statement. So it seems Wikipedia is wrong here, unless I'm totally missing something.

Can anyone confirm this? I would really appreciate it.

Thanks.