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Math Help - Inconsistency matrix question...

  1. #1
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    Inconsistency matrix question...

    Ok.. Have a look at this problem and then look at the second post:

    Last edited by rodders; May 3rd 2013 at 12:23 AM.
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  2. #2
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    Re: Inconsistency matrix question...

    Can anyone explain the second examiners solution? I understand the first and third approach but what is happening in the second method below, In particular what does trianglex, triangle y , trianglez mean in the second line of the solution i have circled in red?

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  3. #3
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    Re: Inconsistency matrix question...

    The " \Delta" is, of course the determinant. Since that is 0 it follows that there cannot be a unique solution. But I think when they say "Showig \Delta= 0 and thinking this is it" they the mean that alone does NOT show that the system is inconsistent- there might be an infinite number of solutions. I do think that "and \Delta_x, \Delta_y, \Delta_z= 0" is misleading. In order to have the system inconsistent, you must show that \Delta= 0 and that at least one of \Delta_x, \Delta_y, \Delta_z is NOT 0.

    I am rather disappointed that the most direct demonstration is not given:

    If you add the second and third equations, the "y" and "-y" terms cancel leaving 11x+ 11z= 37.

    Multiplying the second equation by 2 gives 6x+ 2y- 8z= 14 and adding the first equation to that gives 7x+ 7z= 14. Do you see why those two equations are impossible?
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  4. #4
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    Re: Inconsistency matrix question...

    Sorry but i still don't know what Det(x), det(y), det(z) actually mean? I know how to work out the det of matrix but never come across det(x) etc?
    How do you actually work that out of a matrix?
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