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Math Help - Nilpotent Matrix

  1. #1
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    Nilpotent Matrix

    Hi,

    Is my working and answer to the following question correct?

    Question: Show that matrix A is nilpotent and state the index of nilpotency k

    A = \begin {pmatrix}<br />
-2 & 1 \\<br />
-4 & 2 <br />
\end {pmatrix}

    Definition of Nilpotent: A matrix A is said to be nilpotent if A^k=0 for some positive integer k. The smallest k is called the index of nilpotency for A

    A^2 = \begin {pmatrix}<br />
-2 & 1 \\<br />
-4 & 2 <br />
\end {pmatrix} \begin {pmatrix}<br />
-2 & 1 \\<br />
-4 & 2 <br />
\end {pmatrix}

    = \begin {pmatrix}<br />
0 & 0 \\<br />
0 & 0 <br />
\end {pmatrix}

    A is nilpotent, k=2
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  2. #2
    A Plied Mathematician
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    Looks good to me!
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  3. #3
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    Thanks Ackbeet
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  4. #4
    A Plied Mathematician
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    You're welcome.
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