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Math Help - Matrix Problem

  1. #1
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    Cool Matrix Problem

    The question is, Solve the equation!

    Matrix Problem-matris1.gif

    I think I have solved the first part...
    x = 8
    y = -1
    z = 3

    But then they say that the answer has to be written as;

    Matrix Problem-matris2.gif

    Where a,b,c,d,e,f,g,h have to be itegers.

    I have absolutely no idea how to solve this problem. Please help!


    What is...

    a=?
    b=?
    c=?
    d=?
    e=?
    f=?
    g=?
    h=?

    Thanks!
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  2. #2
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    Quote Originally Posted by sf1903 View Post
    The question is, Solve the equation!

    Click image for larger version. 

Name:	matris1.gif 
Views:	7 
Size:	808 Bytes 
ID:	13603

    I think I have solved the first part...
    x = 8
    y = -1
    z = 3

    But then they say that the answer has to be written as;

    Click image for larger version. 

Name:	matris2.gif 
Views:	8 
Size:	513 Bytes 
ID:	13604

    Where a,b,c,d,e,f,g,h have to be itegers.

    I have absolutely no idea how to solve this problem. Please help!


    What is...

    a=?
    b=?
    c=?
    d=?
    e=?
    f=?
    g=?
    h=?

    Thanks!
    You have not correctly solved the system of linear equations. From the first equation:

    x = 4 - y + z.

    The second and third equatins therefore become -3y + z = 6.

    Let z = t where t is a free parameter that can equal any real number. Now solve for x and y in terms of t. The a, b, c etc. is simply telling you that your answer will involve fractions. If you do as I have said your answer will be in the required form.
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  3. #3
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    Quote Originally Posted by sf1903 View Post
    The question is, Solve the equation!

    Click image for larger version. 

Name:	matris1.gif 
Views:	7 
Size:	808 Bytes 
ID:	13603

    I think I have solved the first part...
    x = 8
    y = -1
    z = 3



    This is is only one of the solutions: if you write down your augmented matrix, you get after simplifying it (by Gauss's method, say):

    \left(\begin{array}{cccc}1&1&\!\!\!\!-1&4\\0&\!\!\!\!-3&1&6\\0&\!\!\!\!-9&1&18\end{array}\right)


    As the third row is clearly a scalar multiple of the 2nd one it will vanish in the next step, and the general solution is
    2nd\,\;row\;:\;\;-3y+z=6\Longrightarrow y=-2+\frac{1}{3}z
    1st\,\;row\;:\;\;z-2+\frac{1}{3}z-z=4 \Longrightarrow x=6+\frac{2}{3}z

    As you can see, we wrote x,y as functions of z. Now just write z=t and we're done.
    This solution means: for ANY choice of the parameter t, you plug in this choice above for z and thus for x,y and you'll get a solution.

    Tonio[/color]


    But then they say that the answer has to be written as;

    Click image for larger version. 

Name:	matris2.gif 
Views:	8 
Size:	513 Bytes 
ID:	13604

    Where a,b,c,d,e,f,g,h have to be itegers.

    [color=red]I have absolutely no idea how to solve this problem. Please help!


    What is...

    a=?
    b=?
    c=?
    d=?
    e=?
    f=?
    g=?
    h=?

    Thanks!
    .
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