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Eigenvalues for matrices proof

  1. Apr 8, 2010 #1
    Let C be a 2 × 2 matrix such that x is an eigenvalue of C with multiplicity two
    and dimNul(C − xI) = 1.
    Prove that C = P |x 1|P^−1
    |0 x|
    for some invertible 2 × 2
    matrix P.

    I'm not sure where to start

    |x 1|
    |0 x| is the matrix I don't know why it's not posting the way I want it
  2. jcsd
  3. Apr 9, 2010 #2
    Consider P which makes C upper diagonal & use the nullity condition.
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