Pivoting (Gaussian elimination)

[fonseh]

Homework Statement

x1 + 2x2 = 9 ,
6x1 + 6x2 -8x3 = 1 ,
-3x2 +x3 = 0 [/B]
Here's a question from my book . I'm asked to find the x1 , x2 and x3 by using the gaussian elimination with pivoting .

Homework Equations

The Attempt at a Solution

Pls refer to this thread for the lecturer's method
https://www.physicsforums.com/threads/gaussian-elimination-pivoting.905132/#post-5699372[/B]
By using the lecturer's method ( circle out the max element in each column ) , I found that all the greatest element lies in 6x1+ 6x2 - 8x3 = 1 ...
So , how could all the largest element lies in the same row ?

 

[BvU]

So , how could all the largest element lies in the same row ?

Fate, coincidence, exercise composer's whim, anything. It happens. You just play along and swap rows 1 and 2 -- by the book .

 

[BvU]

And if we are going to do much more of this, you should learn a bit of $\LaTeX$ instead of making photos. It's fun and pretty easy.

$$\begin{pmatrix}
1 & 2& 0 & 9 \\
6 & 6 & -8 & 1 \\
0 & -3 & 1 & 0
\end {pmatrix} $$

gives you
$$\begin{pmatrix}
1 & 2& 0 & 9 \\
6 & 6 & -8 & 1 \\
0 & -3 & 1 & 0
\end {pmatrix} $$

 

[fonseh]

So

Fate, coincidence, exercise composer's whim, anything. It happens. You just play along and swap rows 1 and 2 -- by the book .

So , I can't use the lecturer's method to do this question ?

 

[Ray Vickson]

So

So , I can't use the lecturer's method to do this question ?

In the thread

https://www.physicsforums.com/threads/gaussian-elimination.904589/

I gave you a detailed explanation of Gaussian elimination and pivoting, along with the main reasons that pivoting is performed at all. You should go back and actually READ that explantion.