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linear algebra help about characteristic polynomials?

how do i get the characteristic equation of a symmetric matrix?

e.g.( xI-A )is

|x-1| |2| |0|

|2| |x| |-2|

|0| |-2| |x+1|

the answer is x^3 - 9x

to get it, it's det(xI-A). but i dont seem to get the determinant of symmetric matrix. i tried getting the determinant the long way but it doesn't math the answer.

can anyone show me how to do it step-by-step? thanks.

1 Answer

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  • kb
    Lv 7
    1 decade ago
    Favorite Answer

    Expanding on the top row, we get

    (x-1) * [x(x+1) - (4)] - 2 * [2(x+1) - 0] + 0

    = (x - 1) * (x^2 + x - 4) - (4x + 4)

    = x^3 - 9x.

    I hope that helps!

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