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Let A be a 2x2 real matrix which cannot be diagonalized by any matrix P (real or complex). Prove there is an invertible real 2x2 matrix P such that

[tex]

P^{-1}AP = \left( \begin{array}{cc} \lambda & 1 \\ 0 & \lambda \end{array} \right)

[/tex]

I know how to diagonalize a matrix by using eigenvectors but I don't think that really helps here. I tried proving it by letting A be {a, b, c, d} and P be {e, f, g, h} but it gets really messy and I don't think thats the right way to do it. Any help appreciated!

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# Homework Help: Matrix Diagonalization

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