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So this question was asked in an online quiz. The definiteness of the quadratic form

Q(x) = 8$x_1^2$ + 7$x_2^2$ + 3$x_3^2$ - 12$x_1x_2$ - 8$x_2x_3$ + 4$x_3x_2$

I made the following matrix: \begin{bmatrix}8&-6&0\\-6&7&-4\\0&-4&3\end{bmatrix} Any help would be appreciated.

P.S.: I don't need the explanation on how to solve these type of questions, that is already in my notes. Just the solution please.

OnTimer
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  • Just check whether the matrix is positive definite (determinants!), or not. – Dietrich Burde May 20 '20 at 08:52
  • That matrix doesn’t match $Q$. If there’s not a typo in your expression for $Q$, then you’ve computed the entry for $x_2x_3$ incorrectly. On the other hand if (as I suspect) the last term is actually $4x_3x_1$, then you’ve omitted it entirely from your matrix. – amd May 20 '20 at 21:09
  • If you have a solution method in your notes already, then why don’t you apply it yourself? We’re not here to do your work for you. If there’s a specific issue that you’re running into, then explain that in your question. – amd May 20 '20 at 21:15
  • @amd There is no typo in the question. I just wanted to verify my answer as I was not able to reach my teacher. Anyways, thanks for your support DietrichBurde, now I know the answer. Many thanks. – OnTimer May 22 '20 at 12:28

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