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Math Help - finding equation for 4 variable system

  1. #1
    jonod
    Guest

    Unhappy finding equation for 4 variable system

    Hi all,

    I am struggling with a Problem at the momment,

    ax + by + cz = e

    I have a data set of "e" to "x" ,"y","z", and would like to get a possible range of the constants "a","b","c" .

    data set eg.

    e - x - y - z
    6 - 11 - 1713 - 54
    4 - 11 - 1123 - 25
    2 - 9 - 1546 - 64
    1 - 10- 789 - 87

    the idea is to have an equation where x,y,z are entered and e is aquired.

    Any help will be much appriciated.

    Thanks
    jonod
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, jonod!

    Exactly where is your difficulty?


    Determine the equation: . ax + by + cz \:= \:e

    which satisfies these data:

    . . \begin{array}{ccc|c} x & y & z & e \\ \hline<br />
11 & 1713 & 54 & 6 \\ 11 & 1123 & 25 & 4 \\ 9 & 1546 & 64 & 2 \\<br />
10 & 789 & 87 & 1 \end{array}

    We have a system of equations: . \begin{array}{ccc} 11a + 1713b + 54c &=& 6 \\ 11a + 1123b + 25c &=& 4 \\ 9a + 1546b + 64c &=& 2 \\ 10a + 789b + 87c &=& 1 \end{array}

    If we're lucky, it has a solution . . .

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