(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]

\begin{pmatrix}

-2 & 0 & 0\\

0 & -2 & 0\\

0 & 0 & -2

\end{pmatrix}

[/tex]

If I evaluate with eigenvalues, I get:

[tex]

det\begin{pmatrix}

-2-\lambda & 0 & 0\\

0 & -2-\lambda & 0\\

0 & 0 & -2-\lambda

\end{pmatrix}=0

[/tex]

[tex](-2-\lambda{)}((-2-\lambda{)}(-2-\lambda{)})=0[/tex]

and thus

[tex]\lambda{=}-2[/tex]

So there exists a local maximum according to this. However, when I evaluate with a different method offered in my textbook, I get a different result, which is confusing me as this method has always worked before.

[tex]det(-2)=-2<0, det\begin{pmatrix}

-2 & 0\\

0 & -2

\end{pmatrix}=4>0, det\begin{pmatrix}

-2 & 0 & 0\\

0 & -2 & 0\\

0 & 0 & -2

\end{pmatrix}=-8<0[/tex]

By this method it is a saddle point. Not entirely sure what is going on here.

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# Second derivative test

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