any good mathematicians here?

I am lost and need guidance :/

To find an eigenvector corresponding to an eigenvalue $\lambda$ you need to find a vector $(x, y, z)^T$ satisfying:

$\begin{pmatrix} {0-\lambda} & {-1} & {1} \\5 & {-2-\lambda} & {-1} \\{-8} & 0 & {5 - \lambda} \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end {pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}$

If you don't know how to do this, multiply out the LHS to get three simultaneous equations and solve them in terms of a parameter.

EDIT: Corrected my matrix.

i got the cubic equation where x = lamnda


x^3 + 2x^2 -18x -1 = 0



doesnt give integers :/ one of the soloution is 1

How did you get that equation?

ok i got x^3 + 3x^2 + 3x -1 = 0 now




still no luck



i just used the determinant method