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Math Help - Matrices........

  1. #1
    Biz
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    Thumbs up Matrices........

    Hello!

    I have this to "decipher":

    If 1 + ALPHA + ALPHA^2 = 0, show that ALPHA^3 = 1.

    Many thanks!
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  2. #2
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    Re: Matrices........

    I'm not sure why your topic says "matrices", but if \displaystyle \alpha^3 = 1 then

    \displaystyle \begin{align*} \alpha^3 - 1 &= 0 \\ \alpha^3 - 1^3 &= 0 \\ (\alpha - 1)(\alpha^2 + \alpha + 1) &= 0 \\ \alpha^2 + \alpha + 1 &= 0 \textrm{ or }\alpha - 1 &= 0 \end{align*}
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  3. #3
    MHF Contributor chisigma's Avatar
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    Re: Matrices........

    Quote Originally Posted by Biz View Post
    Hello!

    I have this to "decipher":

    If 1 + ALPHA + ALPHA^2 = 0, show that ALPHA^3 = 1.

    Many thanks!
    If '1' means 'unity matrix' and '0' means 'null matrix' then is...

    1 + A + A*A=0 \implies A*A = -1 - A \implies A* A* A = - A - A* A = -A +1 + A = 1

    Kind regards

    \chi \sigma
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  4. #4
    Biz
    Biz is offline
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    Re: Matrices........

    Thank you!

    Just curious but the font used looks very similar to a set of workbooks that we have been advised to study called HELM.

    Might just be a coincidence!
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