Question

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Answer 1

So first you need to find your eigenvalues and eigenvectors right?

Answer 2

https://www.wolframalpha.com/input/?i=eigenvalues+of+%28%283%2C2%29%2C%28-9%2C-6%29%29

This has 0 and -3 D:

Answer 3

Okay, then the vectors (sorry I'm using the wolf to cheat, I would do it on paper myself :P). But once you have the eigenvalues/vectors you just have:
\[y(t) = C_1 e^{- \lambda_1 t} \vec{v}_1 + C_2 e^{- \lambda_2 t} \vec{v}_2\]
If my memory serves me right.

Answer 4

Let me work it out on paper and I'll post a picture :P

Answer 5

Let me know if you can read that :)

Answer 6

No problem!