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Math Help - gauss-jordan elimination

  1. #1
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    Exclamation gauss-jordan elimination

    I have two problems I need help with.

    1.

    [2 1 -1 3 l 0]
    [3 -2 1 -4 l -24]
    [1 1 -1 1 l 2]
    [1 -1 2 -5 l -16]

    2.
    [1 -1 1 -1 l 4]
    [1 2 1 1 l 2]
    [2 3 4 5 l 5]
    [3 4 2 -1 l 8]

    Can you help me with this question. Also, please show the steps to how you got your answer. Thanks!
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  2. #2
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    Quote Originally Posted by starrynight View Post
    [2 1 -1 3 l 0]
    [3 -2 1 -4 l -24]
    Do you realise that the above possibly come from:
    2a + b - c + 3d = 0
    3a - 2b + c - 4d = -24
    ?

    How far can you get on your own?
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  3. #3
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    Hi Wilmer,
    It is supposed to be a 5 by 4 matrix. Then i am supposed to get the matrix to have a diagonal row of ones. The only problem is that i am not sure how many zeros it is supposed to have. (The letters stand for numbers that we do not know yet)

    Is it supposed to look like this:

    [1 0 0 0 l a]
    [0 1 0 0 l b]
    [0 0 1 0 l c]
    [0 0 0 1 l d]

    OR

    Is it supposed to be like this:

    [1 a b c l d]
    [0 1 e f l g]
    [0 0 1 h l i]
    [0 0 0 1 l j]
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  4. #4
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    NO. I think you need help from your math teacher.

    This matrix:
    [2 1 -1 3 l 0]
    [3 -2 1 -4 l -24]
    [1 1 -1 1 l 2]
    [1 -1 2 -5 l -16]
    was obtained from 4 equations, each with 4 variables;
    if we let these variables be a,b,c,d then:

    [2 1 -1 3 l 0] : 2a + b - c + 3d = 0
    [3 -2 1 -4 l -24] : 3a - 2b + c - 4d = -24
    [1 1 -1 1 l 2] : a + b - c + d = 2
    [1 -1 2 -5 l -16] : a - b + 2c - 5d = -16

    There are various ways to solve these;
    the gauss-jordan elimination using a matrix is one of them.

    But that's near impossible to "teach" here...

    Try learning by yourself; go here:
    http://sks99.com/ch9/gauss.htm
    Last edited by Wilmer; April 26th 2010 at 10:44 AM. Reason: add link
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