# Thread: General solution for a matrix with 1 real and two complex eigen values.

1. ## {SOLVED}General solution for a matrix with 1 real and two complex eigen values.

Hey guys, I was hoping you could help with a problem I'm having.
I found from my 3x3 matrix 3 eigenvalues where one is real and the other two are complex. I don't know how to express the general solution for this though and it is the first time I've tried to solve for the GS of a 3x3.
the eiegen vectors are
v_1 = (1, 0, 0)
v_2 = (5/26+i/26, -1/2+i/2, 1)
v_3 = (5/26-i/26, -1/2-i/2, 1)
I haven't put the into vector column form yet but that's pretty straight forward.
Any help is appreciated,
Thanks!

2. ## Re: General solution for a matrix with 1 real and two complex eigen values.

What is original matrix?

3. ## Re: General solution for a matrix with 1 real and two complex eigen values.

Originally Posted by MaxJasper
What is original matrix?

[(3,0,-1),(0,-3,-1),(0,2,-1)]

the eigen values were 3, (-2+i), and (-2-i).

I tried using (c_1)*(e^3t)[1,0,0]+(c_2)(e^-2t)[cos(t)(v_2)-sin(t)(v_3)]+(c_3)(e^-2t)[sin(t)(v_2)+cos(t)(v_3)]

which is the GS for a real rood plus the GS for 2 complex roots in a 2x2 matrix.

It is incorrect though.