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Math Help - leontif input output

  1. #1
    Junior Member
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    leontif input output

    Hi, um i just failed my linear exam so but I'm going to take a supplementary exam in a few days so i was wondering if someone could please help me. Because my lecturer is on holiday as its uni holidays now.

    Well this is a leontif input-output question. This question comes from my lecture notes, where the model leads to the linear system,

    <br />
\frac{1}{2}x_1 -  \frac{3}{5}x_2  - \frac{1}{5}x_3 = 50
    <br />
-\frac{1}{5}x_1 +  \frac{4}{5}x_2  - \frac{1}{10}x_3 = 30
    <br />
-\frac{1}{10}x_1 -  \frac{1}{5}x_2  + \frac{7}{10}x_3 = 20

    and it says that the answer is(to the nearest decimal point):
    <br />
x_1 = 226, x_2 = 119, x_3 = 78

    But when i did it i got a totally different answer and then decided to check the online calculator:

    Linear Algebra Toolkit

    yeahhh and it sorta got close to what i got

    it says the answer is(to the nearest decimal point):
    <br />
x_1 = 290, x_2 = 123, x_3 = 105

    I'm just wondering if someone could tell me if my lecture notes are wrong? as i have no idea if they're correct or not. Coz i thought that for leontif input output, all you have to do is get it into reduced row echelon form?

    Thank you
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  2. #2
    MHF Contributor arbolis's Avatar
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    I'd solve the problem exactly as in your link (Linear Algebra Toolkit). The method is good. I won't check all the details to see if the answer is good (afterall you can plug the solution into the first 3 equations to see if they are satisfied).
    So for your exam, if they ask to find the solutions of a system of linear equations, you can form an augmented matrix and row reduce it.
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  3. #3
    Junior Member
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    Apr 2009
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    ohhh i forgot about subbing back the solutions into the equations..
    thanks!!
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