Eigenvalues of special matrices pt. 1

[Pythagoras_50]

The differential equations text* I’m using states, “The eigenvalues of the [following] coefficient matrices (see pt. 2) can be found by inspection and factoring.” Please explain how one can “read” the eigenvalues. I see that the top four are symmetric matrices, but I don’t see how that helps. I don’t observe anything distinctive about the last five matrices. I am self-taught and would greatly appreciate your help. Thanks.

 

[HallsofIvy]

You don't say what the matrices are or even what the text book is (most people would be unlikely to have but some might) so I don't know how you expect anyone to be able to answer this question.

 

[Pythagoras_50]

You don't say what the matrices are or even what the text book is (most people would be unlikely to have but some might) so I don't know how you expect anyone to be able to answer this question.

I divided my question into two parts because the images exceeded the capacity of this website's upload. As Ishuda suggested, I will try to find a site to upload them, and then post the link. Sorry for the inconvenience.