# Homework Help: Linear Algebra question

1. Nov 9, 2005

### stunner5000pt

Use the $LDL^T$ factorization to solve the following linear system
$$\left(\begin{array}{cccc|1}4&1&-1&0&7\\1&3&-1&0&8\\-1&-1&5&2&-4\\0&0&2&4&6\end{array}\right)$$
now i know ihow to get a matrix in the form LDL^T. But i was wondering how one would go about solving from there?

Last edited: Nov 9, 2005
2. Nov 10, 2005

### HallsofIvy

That should be straight forward- the Cholesky decomposition is supposed to be the hard part! L here is a lower triangular matrix, LT is upper triangular, and D is diagonal, so going from LDLTX= A to DLTX= B is just a matter of "back substitution", starting from the value you get immediately in the last row and working up.
Since D is diagonal, going from DLTX= B to LTX= C is just dividing by the diagonal elements. Finally, since LT is upper triangular, going from LTX= C to X= D is again back substitution, this time working from the top row down.