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Please help

Answer 1

please note that if you solve the equatio to eigenvectror, you will find a line of eigenvector, namely the subspace associated to the eigenvalue a+b has dimension equalt to 1.
so your eigenvectors are:

Answer 2

\[\left(\begin{matrix} \xi \\ \frac{ b }{ a } \xi \end{matrix}\right) \]
\[\forall \xi \in \mathbb{R} \]
so?

Answer 3

I'm sorry for my typo mistakes!

Answer 4

for example if \[\xi = a\]
what do you get, please?

Answer 5

I don't know :/

Answer 6

please multiply the components of your eigenvectors, namely:
\[\frac{ b }{ a }* \xi =\frac{ b }{ a }*a=b\]
and the first component:
\[\xi =a\]
so?

Answer 7

it becomes

Answer 8

that's right!

Answer 9

ok but when I solved it I thought it would be