Eigenvalues, Eigenvectors and Diagonalization

I have the matrix A=|7 2|

|12 -3|

I found the eigenvalues **λ=9 and λ=-5**

Now i have to find the eigenvector, using Gauss.

I set

A-9I = |-2 2 0| R1

|12 -12 0| R2

and used Gauss this way:

R2+5*R1

R1/-2 and R2/2

R2/R1

R2-R1

R2/2

R1+R2

until i got the vector

|1 0 0|

|0 1 0|

I cant really find out what to do now. And then i have to find a matrix, P, that diagonalizes the matrix A.

In the other example i had the vector

A= |-1 -2 -2|

|1 2 1|

|-1 -1 0|

and i solved for the eigenvalues and got

-**λ^3+λ^2-3λ-1**

But if i solve it with my texas instrument, i get **λ=-0,295598 **wich doesn't sound so right. So how do i solve it?

Thank you :)