Question: Construct command to find eigenvectors from two equations.....

Hello I need to find the eigen vectors for eight solutions of an eighth order equation in the parameter 'm' .

This is simple, however I have a 'do' command that generates 2 of these equations, with two values of lambda which you can see in the attached file

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I can do this for one equation but I am not sure how to construct the command to do this for more than one equation. I have attached the maple file with explaination. the first half of the file is just preliminary stuff. 

 

Please if you can help I would be very grateful.

 

Thanks, 

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