Given the following matrix:(adsbygoogle = window.adsbygoogle || []).push({});

2 3 0

3 2 4

0 4 2

I'm having a difficult time working out the characteristic polynomial. I used the shortcut that I saw on YT, where it is (I am using x instead of lambda) X^3 - (trace) X^2 + (A11+A22+A33) X - DET(A)

I got the following:

trace is just 2+2+2 = 6

A11+A22+A33 = (4-16) + (4-0) + (4-9) = -13

DET(A) = -42

This is giving me a characteristic polynomial of X^3 - 6X^2 - 13X + 42. Using synthetic division with the correct e-vals, it just doesn't come out right.

The correct roots/e-vals are -2, 2 and 4.

Thanks.

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# Having difficulty working out a Char. Pol. for Eigenvalues

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