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Math Help - matrix problem

  1. #1
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    matrix problem

    <br />
\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & -1 & 0 \\ -2 & 1 & 0 & -1\end{bmatrix}<br />

    That's A and I have to compute A^2010
    I'm given a hint to first compute A^2
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  2. #2
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    If you calculate A^2 you get the following matrix:
    \begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix}
    As you can see its the I matrix and therefore
    A^3=I*A => A
    So you always get either A matrix or the I matrix depending on your square.
    If its an even square you get the I matrix otherwise A matrix.
    A^2010 you do the math.
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  3. #3
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    Quote Originally Posted by wicked View Post
    If you calculate A^2 you get the following matrix:
    \begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{bmatrix}
    As you can see its the I matrix and therefore
    A^3=I*A => A
    So you always get either A matrix or the I matrix depending on your square.
    If its an even square you get the I matrix otherwise A matrix.
    A^2010 you do the math.
    thank you so much ! You're a life saver
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