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LU factorisation

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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.

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https://brainmass.com/math/linear-transformation/lu-factorization-matrix-positive-definite-523324

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

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