Find the [itex] LDL^T [/itex] factorization of this matrix(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \left(\begin{array}{ccc}{2&-1&0\\-1&2&-1\\0&-1&2\end{array}\right) [/tex]

now i can find the L matrix by gaussian elimination

that yields

[tex]L = \left(\begin{array}{ccc}{1&0&0\\\frac{-2}{3}&1&0\\0&\frac{-1}{2}&1\end{array}\right) [/tex]

[tex] D = \left(\begin{array}{ccc}{\frac{1}{4}&0&0\\0&\frac{1}{3}&0\\0&0&\frac{1}{2}\end{array}\right) [/tex]

i am pretty sure about the ansswer since i checked my working many times.

However this is not the answer at the back of the book! In fact i am not even close!

What am i doing wrong?? Can anyone please help me iwth this?

Thank you for your help!

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# LDL factorization

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