What is the Eigen values λ in the given system?

Question

As I have just started to revised my maths knowledge after 8 years, I have a question.

What is the Eigen values λ in the below given (attached image) system?

Perhaps you should read what eigenvalues are and how to find them rather than bugging us to do it for you. — Trevor Gunn, Mar 22 '18 at 05:45

score 0 · Accepted Answer · answered Mar 22 '18 at 05:48

there's a trick that doesn't always work.

it's to sum each column and each row and if the sum is the same for every column OR every row, then the value of the sum is an eigenvalue.

here you have $4+1=3+2=5=\lambda_1$

also another property very useful is that the sum of the diagonal elements is equal to the sum of the eigenvalues.

so if you use that here then because we have $\lambda_2 + 5 = 6$

then the eigenvalues are : $\lambda_{1,2} = 5, 1$

but if you'd like to know how to proceed in more general cases I highly recommend to review some linear algebra material.

see here for book references : Very good linear algebra book.

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