math-matrices

You are given the 2x2 matrix M= (k 3) , where k is not 2.
(0 2)
i)Find the eigenvalues of M, and the corresponding eigenvectos.
ii)Express M in the form UDU^(-1), where D is a diagonal matrix.
iii)Hence find the matrix M^n.

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  1. k 3
    0 2

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  2. thats the 2x2 matrix, i m really stuck

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  3. det [ A - L I] = 0

    det [ k-L , 3 / 0 , 2-L ] = 0

    (k-L)(2-L) - 3*0 = 0
    2k - (2+k) L + L^2= 0
    L = {(2+k) +/- sqrt (k^2-4k+4) } / 2 but sqrt(k^2-4k+4) = (k-2)
    so
    L = {k+2 +k-2}/2 = k
    or
    L = {k+2 -k+2}/2 = 2
    eigenvalues are k and 2

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  4. suggest this:
    https://www.youtube.com/watch?v=IdsV0RaC9jM

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