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**1. Homework Statement**

Use eigenvalues and eigenvectors to find the general solution of the system of ODEs..

x

_{1}= 3x

_{1}- x

_{2}

x

_{2}= -x

_{1}+ 2x

_{2}- x

_{3}

x

_{3}= -x

_{2}+ 3x

_{3}

**2. Homework Equations**

**3. 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 e

^{λt}(eigenvector)

^{T}seeing as there is a repeated root.

Thanks