Finding Quantum Numbers and Eigenvectors from Matrices A & B

[greisen]

Hey,

I have two matrices A and B which commute. For A I have 1,-1,-1 and for B I have 1,2,2.

I am asked to find the quamtum number for the three states. How to find the quantum states from the eigenvalues. It is further said that it is possible to find the eigenvectors from the quantum numbers. How to get the eigenvector from the quantum numbers?

Any help appreciated - thanks in advance

 

[greisen]

I think I have solved it by combining the three pairs into unique pairs
{1,1},{2,1},{2,-1} having these constraints on the eigenvector equation it is possible to determine a eigenvector for the matrix A fulfilling both A and B.