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## Homework Statement

I need to find the general solution of the system

[3 5]

[-1 -2]

## Homework Equations

so to get the eigenvalues, det(A - λI)

## The Attempt at a Solution

determinant is (3-λ)(-2-λ) + 5

which would be λ

^{2}- λ - 1

so by the quadratic equation the eigenvalues are λ = 1/2 + (√5)/2 and 1/2 - (√5)/2

but now I don't know how to reduce the matrix to get the eigenvectors?

I think the matrix for the first eigenvalue would be

[3-(1/2 + √5)/2) 5]

[-1 -2-1/2+(√5)/2]

What to do now?