# LU Decomposition

1. Oct 22, 2007

### jesuslovesu

1. The problem statement, all variables and given/known data
A = $$\left| \begin{array}{ccc} 2 & 0 & 4 \\ 0 & 4 & -8 \\ 3 & -1 & 2 \end{array} \right|.\]$$

Find the LU decomposition.

3. The attempt at a solution
My question is why do you need to interchange rows 3 & 1 at the start of the problem? My initial attempt was to find the upper matrix using the format as given. I got
U = $$\left| \begin{array}{ccc} 2 & 0 & 4 \\ 0 & 4 & -8 \\ 0 & 0 & -6 \end{array} \right|.\]$$

doesn't that satisfy the requirements for an U matrix?

According to the calculator I'm using the U matrix should be
$$\left| \begin{array}{ccc} 3 & -1 & 2 \\ 0 & 4 & -8 \\ 0 & 0 & 4 \end{array} \right|.\]$$