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Math Help - matrix

  1. #1
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    matrix

    M is a matrix

    Let m =
    [
    1 1 2
    0 1 1
    0 0 1
    ]

    Find M^n where n is a positive integer.
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  2. #2
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    How many powers have you tried?
    It very easy to do: try n=2, 3, & 4.
    You should see what the general power n is.
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  3. #3
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    i dont understand what the question is asking. i mean if i do M^2 then isnt n a positive integer?
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  4. #4
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    M^2=M*M
    M^3=M*M^2
    M^4=M*M^3
    .
    .
    .
    M^n=M*M^(n-1)
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  5. #5
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    n=3?
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  6. #6
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    You do know how to do matrix multiplication, donít you?
    Get m^2=m*m, then to get m^3=m*m^2.
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  7. #7
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    Hello, Mr_Green!

    I used a very primitive method . . .


    M is a matrix

    . - . - . . | 1 1 2 |
    . . M .= .| 0 1 1 |
    . - . - . . | 0 0 1 |

    Find M^
    n where n is a positive integer.

    I cranked out the first powers and looked for a pattern.

    . . . . . . . . | 1 2 5 |
    . . M^
    2 .= .| 0 1 2 |
    . . . . . . . . | 0 0 1 |

    . . . . . . . . | 1 3 9 |
    . . M^
    3 .= .| 0 1 3 |
    . . . . . . . . | 0 0 1 |

    . . . . . . . . | 1 4 14 |
    . . M^
    4 .= .| 0 1 -4o|
    . . . . . . . . | 0 0 -1o|

    . . . . . . . . | 1 5 20 |
    . . M^
    5 .= .| 0 1 -5o|
    . . . . . . . . | 0 0 -1o|


    . . . . . . . . . . . . | 1 . n . n(n+3)/2 | .**
    Hence: -M^
    n -= -| 0 . 1 . . . - n - - |
    . . . . . . . . . . . . | 0 . 0 . . . - 1 . . |

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    **

    I worked out the formula for the a
    13 element
    . . by examining the sequence: 2, 5, 9, 14, 20, ...
    . . and constructing a quadratic function for it.

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