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Math Help - More Gauss-Jordan help please?

  1. #1
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    More Gauss-Jordan help please?

    Determine a relationship between the constants
    a and b if the system below is to have infinitely many solutions.


    x
    + 2y + z = 1 + b

    x 2y + z = a + 2b 1

    2
    x + 4y + 3z = 2b + 2

    Okay so this is what I have so far:

    [ 1 2 1 | 1+b ]
    [-1 -2 1 | a+2b-1]
    [ 2 4 3 | 2b +2 ]

    .
    .
    .
    .
    After ysing the G-J method, I get all the way to
    [1 0 3/2 | 1/2a + b]
    [0 0 2 | a + 3b ]
    [0 0 0 | -2 ]

    SO its in row-reduced form now...I think. Feeling a bit stuck at this point.



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  2. #2
    MHF Contributor
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    You started with a non-singular matrix. How did it turn singular on you?

    Better try that reduction again.

    Are you sure you reported the problem correctly?
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  3. #3
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    Quote Originally Posted by tuheetuhee View Post
    [ 1 2 1 | 1+b ]
    [-1 -2 1 | a+2b-1]
    [ 2 4 3 | 2b +2 ]
    [1 2 1 | 1+b]
    [0 0 2 | a+3b]
    [2 4 3 | 2b+2]

    [1 2 1 | 1+b]
    [0 0 2 | a+3b]
    [0 0 1 | 0 ]

    [1 2 1 | 1+b]
    [0 0 0 | a+3b]
    [0 0 1 | 0 ]

    [1 2 1 | 1+b]
    [0 0 1 | 0 ]
    [0 0 0 | a+3b]


    [1 2 0 | 1+b]
    [0 0 1 | 0]
    [0 0 0 | a+3b]

    To have solutions we require that a+3b=0.
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