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# Eigenvector/value problem watch

1. =M
has eigenvalues 2, -2, 1 and respective eigenvectors ,and

Notice that

Prove where c and d are scalar constants.

No idea how to go about doing this. It should be fairly simple, done in 1 or 2 steps so I think I'm missing something obvious/ a piece of knowledge.

M^n[1,2,3] = M^2 u + M^2 v I don't see where you can go from there since M is a vector and we need scalars.
2. To see what's going on, let M = 1.

M(u + v) = Mu + Mv.

u and v are eigenvectors, so by definition, what are Mu and Mv?
3. (Original post by Scipio90)
To see what's going on, let M = 1.

M(u + v) = Mu + Mv.

u and v are eigenvectors, so by definition, what are Mu and Mv?
I don't understand what you are getting at by 'let M=1')

Mu + Mv = (eigenvalue for u)u +(eigenvalue for v)v = 2u -2v

=> M[1,2,3] = 2u + -2v

Mv = lamda v

How do I get it in the form M^n?
4. Sorry, I meant let n = 1.

From there, carry on by induction.

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