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Math Help - An uknown in a matrix

  1. #1
    Junior Member Fnus's Avatar
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    An uknown in a matrix

    'Solve for x, when A^4 = C,

    A:
    ( 1 X )
    ( 0 1 )

    and C:
    ( 1 51 )
    ( 0 1 )'

    At first I took the 4th root of 51, which gave me 2.67,
    but when I plotted that into my calculator, it was wrong,
    and didn't give me 51.
    According to my calculator x = 12.75, but why is that?
    12.75 is 51/4, but isn't that wrong since it's A^4?

    If anyone understood that and can explain it to me, I'd be very grateful (:
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Fnus View Post
    'Solve for x, when A^4 = C,

    A:
    ( 1 X )
    ( 0 1 )

    and C:
    ( 1 51 )
    ( 0 1 )'

    At first I took the 4th root of 51, which gave me 2.67,
    but when I plotted that into my calculator, it was wrong,
    and didn't give me 51.
    According to my calculator x = 12.75, but why is that?
    12.75 is 51/4, but isn't that wrong since it's A^4?

    If anyone understood that and can explain it to me, I'd be very grateful (:
    Do the matrix multiplication:
    A^2 = \left ( \begin{matrix} 1 & 2x \\ 0 & 1 \end{matrix} \right )

    etc.

    -Dan
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  3. #3
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Fnus View Post
    'Solve for x, when A^4 = C,

    A:
    ( 1 X )
    ( 0 1 )

    and C:
    ( 1 51 )
    ( 0 1 )'

    At first I took the 4th root of 51, which gave me 2.67,
    but when I plotted that into my calculator, it was wrong,
    and didn't give me 51.
    According to my calculator x = 12.75, but why is that?
    12.75 is 51/4, but isn't that wrong since it's A^4?

    If anyone understood that and can explain it to me, I'd be very grateful (:
    A^4 =
    ( 1 4X )
    ( 0 1 )

    (Use matrix multiplication to get AA and then (AA)(AA). There's an interesting pattern due to the special property of A. Do you see it?)

    Therefore .......
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  4. #4
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by topsquark View Post
    Do the matrix multiplication:
    A^2 = \left ( \begin{matrix} 1 & 2x \\ 0 & 1 \end{matrix} \right )

    etc.

    -Dan
    I dispensed with the latex pleasantries and you still beat me, dang it!
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  5. #5
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by Fnus View Post
    At first I took the 4th root of 51, which gave me 2.67,
    but when I plotted that into my calculator, it was wrong,
    and didn't give me 51.
    12.75 is 51/4, but isn't that wrong since it's A^4?
    One very important point you are missing is that A^4 does not mean you are raising all the elements of matrix A to the power 4!

    A^4 means A.A.A.A, where . is matrix multiplication. That is you have to multiply A to itself 4 times using matrix multiplication technique.

    Now,do you understand why taking 4th root was wrong?
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mr fantastic View Post
    I dispensed with the latex pleasantries and you still beat me, dang it!
    I'm just that good, what can I say?

    -Dan
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  7. #7
    Junior Member Fnus's Avatar
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    Yosh yosh,
    now I get it.

    Thanks a ton. (:
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