I need some help with the following:

A = the following matrix

(2 -1 0)

(-1 2 0)

(0 0 2)

I need to find the eigenvalues of A

The characteristic equation is det (A-\lambda I) = 0, that is

|2-\lambda -1 0|

|-1 2-\lambda 0| = 0

|0 0 2-\lambda|

We expand this determinant and obtain

(2-\lambda ) |2-\lambda 0| -0 + |-1 2-\lambda|

| 0 2-\lambda| |0 0 |

Is this expansion correct?

Sorry cant get bottonm line to align up. Also how do I get the greek letters and use large brackets?