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Math Help - Please help me to find the general solution of the system of equations in ...

  1. #1
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    Please help me to find the general solution of the system of equations in ...

    Dear Sir / Madam,

    Please help me to find the general solution of the system of equations in x, y, z and w with augmented matrix:-

    1 2 1 -1 3
    0 0 1 -1 2
    2 4 2 -2 6

    Best Regards,

    Tony
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by turboman View Post
    Dear Sir / Madam,

    Please help me to find the general solution of the system of equations in x, y, z and w with augmented matrix:-

    1 2 1 -1 3
    0 0 1 -1 2
    2 4 2 -2 6

    Best Regards,

    Tony
    First observe that you in fact only have two equations as the third is a multiple of the first.

    So we want to find the general solution of the system with augmented matrix:

    1 2 1 -1 3
    0 0 1 -1 2

    Put y=a, w=b, then z=2+b, and x=1-2a. Which you can get by by solving
    the third equation, which in full form is:

    z - w = 2

    and then the first equation which is now:

    x + 2y + z - w = 3.

    RonL
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