Understanding Degenerate Eigenvalues and Vectors in Math Operations

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Homework Statement

please see attached

Homework Equations

The Attempt at a Solution

Ok so I've done A and have worked out eigenvalues and vectors of H and B

For H I get 4 possible eigenvectors (1,0,0) (0,1,1) (0,0,1) and (0,1,0) . The q is why does neither matrix uniquely specify its eigenvectors? I guess the answer is because the eigenvalues are degenrate (repeated)..but is there a clearer explanation as to why?

Thanks

 

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Also - i can't seem to find three common eigen vectors.. I can only find (1,0,0) and (0.1.1)

 

[bon]

anyoneeee?

 

[bon]

why can't i find three common eigenvectors?