Solving First order differential equations using matrix methods

I have been trying to solve this equation using matrix methods to find the general solution for x1(*t*) and x2(*t*)

(There should be a dot above the x1, x2 to show first order)

* x1* = **4***x1*+ **7***x2*

x2 = -**6***x1-***9***x2*

Now i have been shown how to do a second order question so i have used a similar method with this which gets me to this point.

det (a-lambda^2I) = (4-lambda^2)(-9-lambda^2)+42

(lambda^2+2)(lambda^2+3)

lambda^2 = -2 and lambda^2=-3

This is where its different to the question i have been through

As this would mean lambda is j1.414 and j1.732

The second order question i have been through comes out with lambda +or- 2j and +or- j which is then obvious how to continue.

Could somone point me in the right direction or to where ive gone wrong?

I have an exam on wednesday and realy need to be able to work with any combination of question they give me, It could be first or second order.

I didnt think it mattered which kind i was until differentiating the general solution part.

Thank you!