Well, if you know how to find the characteristic polynomial, then that's all
The roots of the characteristic polynomial are the eigenvalues. So find such that there are indeed positive.
Characteristic polynomial - Wikipedia, the free encyclopedia
Positive-definite matrix - Wikipedia, the free encyclopedia (but I'm afraid this article may not correspond to your level...I can't tell)
That's the part you need.Let M be an n × n [...] matrix. The following properties are equivalent to M being positive definite:
1. All eigenvalues λi of M are positive. [...]
Hmmm
A diagonal 2x2 matrix is in the form
And the equivalent diagonal matrix to a given matrix will be formed by its eigenvalues. That is to say, in our case here, and are the eigenvalues of A.
Did you find them ?
For the eigenvectors, it's better you have a look on the internet...
Try this : Pauls Online Notes : Differential Equations - Review : Eigenvalues & Eigenvectors (it's also explain how to get the eigenvalues)
Take the time to read it please