Use eigenvalues and eigenvectors to find the general solution of the system of ODEs..
x1 = 3x1 - x2
x2 = -x1 + 2x2 - x3
x3 = -x2 + 3x3
The Attempt at a Solution
I converted that into the matrix
(3-λ -1 0)
(-1 2-λ -1) using 0=[itex]|A-λI[/itex][itex]|[/itex]
(0 -1 3-λ)
Sorry, I am new and don't know how else to write out the matrix... but I hope you get the gist..
I then solved through to get (3-λ)(λ-3)(λ-2)
λ=2 got me an eigenvector (5,1,5)T
λ=3 got me an eigenvecotr (6,1,6)T
Not really sure if I have done this correctly, and if it's correct I'm not sure how I would get this into a general solution eλt(eigenvector)T seeing as there is a repeated root.