Finding eigen vectors/eigen values

Question

Finding eigen vectors/eigen values of $$A=\begin{pmatrix} 7 & 0 & -3 \\ -9 & -2 & 3 \\ 18 & 0 & -8 \end{pmatrix}$$

So I understand the eigen values for this matrix are $~1~$&$~2~$, what I don't understand is why should a $~3\times 3~$ matrix have only two eigen values and not $3~$?

Thanks

Answer 1

Eigen values are the root 's of a (characteristic) polynomial and polynomial can have repeted roots, like e.g. $p(x) = x^3-3x+2 = (x-1)^2(x+2)$.