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Matrices - eigenvalues and eigenvectors questions. May be hard?

A matrix, M \mathbf{M} , has 3 distinct eigenvalues, α,β \alpha, \beta and γ \gamma with corresponding eigenvectors u,v \mathbf{u}, \mathbf{v} and w \mathbf{w} .

It is given that the vector p=u+2v3w \mathbf{p}= \mathbf{u} + 2\mathbf{v} -3\mathbf{w} .

Find an expression for Mnp \mathbf{M}^n \mathbf{p} in terms of u,v \mathbf{u}, \mathbf{v} and w \mathbf{w} .

[Note. Your answer should not contain any matrices.]

Try this question and rate how hard it is. It might be really easy but I'm not sure.
Reply 1
Original post by Ano123
A matrix, M \mathbf{M} , has 3 distinct eigenvalues, α,β \alpha, \beta and γ \gamma with corresponding eigenvectors u,v \mathbf{u}, \mathbf{v} and w \mathbf{w} .

It is given that the vector p=u+2v3w \mathbf{p}= \mathbf{u} + 2\mathbf{v} -3\mathbf{w} .

Find an expression for Mnp \mathbf{M}^n \mathbf{p} in terms of u,v \mathbf{u}, \mathbf{v} and w \mathbf{w} .

[Note. Your answer should not contain any matrices.]

Try this question and rate how hard it is. It might be really easy but I'm not sure.


Easy, but I am kinda busy with MOTD
Reply 2
Same.
Quickly give an answer if you can.
Reply 3
M^n x p = M^nxu + M^nx2v - M^nx3w

replace with M^nxu=α^nxu and so on
Reply 4
Original post by Ano123
Same.
Quickly give an answer if you can.


Well???

Posted from TSR Mobile
Reply 5


Well what?
Reply 6
Original post by studos
are you blind? or that lazy that you did not bother to look the previous posts?

I posted you the solution


I know you posted the solution. Thank you. What do you want from me now?
(I don't come on here very often).

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