# LU factorisation

Form an LU factorization of the following symmetric matrix to show that it is not positive definite.

4 1 -1 2

1 3 -2 -1

-1 -2 1 6

2 -1 6 1

Using a little ingenuity we can find a non-zero vector such as x^T = ( 0 1 1 0) that does not satisfy the requirement x^T Ax > 0.

© BrainMass Inc. brainmass.com May 20, 2020, 10:38 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/lu-factorization-matrix-positive-definite-523324

#### Solution Summary

This solution explains the steps to LU factorization and how to show that the matrix is not positive definite.

$2.19