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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
- kbLv 71 decade agoFavorite 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!