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.