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Math Help - Find A^2 = A * A, A^3 = A * A * A, A^4, and A^100, given

  1. #1
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    Find A^2 = A * A, A^3 = A * A * A, A^4, and A^100, given

    that A equals

    \left[\begin{matrix}0&2&0\\0&0&2\\0&0&0\\0&0&0\end{matri  x}\left|\begin{matrix}-1\\0\\2\\0\end{matrix}\right]
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  2. #2
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    To find A^n you can firstly need to diagonalise A for an example look here.


    Diagonalization
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  3. #3
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    thanks for the link but those symbols aren't in my textbook and therefore i can't understand it.
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  4. #4
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    Ok, you may not need to know the symbols, just the ideas. Do you know how to find eigenvectors?
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  5. #5
    Senior Member roninpro's Avatar
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    Actually, you can't diagonalize the matrix. However, it is upper-triangular. Finding the first few powers of A should give a recognizable pattern.
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  6. #6
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    Blast, roninpro got in ahead of me!

    Yes, it is not necessary to diagonalize this matrix. Direct calculation gives A^2 and A^3 and shows that A^4= 0.
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