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    hello i have two questions infont of me that i dont no how to start or even do, they are as followed...

    Let A = (4 2)
    (-3 -1)
    (A)Find an invertible matrix P such that P^-1AP is diagonal, compute P^-1.

    (B) Find scalars U1 and U2 such that A^6=U1A^5 + U2A^4


    Thanks for your help!
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    (A)
    Let D be the diagonal matrix such that D=P^{-1}AP.

    Then D contains the eigenvalues of A along its diagonal, and P has the corresponding eigenvectors as its columns.

    (B)
    D=P^{-1}AP <=> A=PDP^{-1}

    Then note that A^n=(PDP^{-1})^n=PD(P^{-1}P)D(P^{-1}P)D....DP^{-1}=PD^nP^{-1}. (as P^{-1}P=I)

    From there it should be inspection.
 
 
 
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