I have a link here that I\'m looking at as a shortcut to finding the characteris

Question

I have a link here that I'm looking at as a shortcut to finding the characteristic polynomial of a 3x3 matrix.

http://www.utdallas.edu/~cpb021000/The%203rd%20Order%20Algebraic%20Eigenvalue%20Problem%20on%20a%20TI%2083-84%20Calculator.pdf

I get everything but how to solve for the final first degree X. So using the formula on the matrix A below it would yield....

so the formula would be:

what do the symbols mean on the link I provided? It looks like absolute value or determinant of something but determinate of a11 = 1 determinant of a33 is 32 and i'm not sure what a22 even is so I don't know how to find that determinant. Please help!

Explanation / Answer

Aii are the signed diagonal cofactors of A

i.e

A11 = (1*-2 - (-2)*(-2)) =-2-4=-6

A22 = (1*-2 - 2*2) = -6

A33 = (1*1 - (-4)*(-4)) = -15

=>

formula is

x^3 +(-6-6-15)x -54 = 0

=.

x^3 -27x-54 = 0

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