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Math Help - Checking a solution to a homogenous system

  1. #1
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    Checking a solution to a homogenous system

    I have the following system:

    2x - y + 7z = 0
    -x + 2y -3z = 0
    x + y + 4z = 0

    I have determined the solution to be:

    x = -y -4t
    y = -1/3t
    z = t

    what I need to know now, is if (0, 7, -1) is a solution to the system?
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  2. #2
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    Quote Originally Posted by blackhug View Post
    I have the following system:

    2x - y + 7z = 0
    -x + 2y -3z = 0
    x + y + 4z = 0

    I have determined the solution to be:

    x = -y -4t
    y = -1/3t
    z = t

    what I need to know now, is if (0, 7, -1) is a solution to the system?
    x = 0 , y = 7 , and z = -1 makes the first equation of the system false ... so I'd say no.
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  3. #3
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    lol yeah, I figured as much. I was just confused about it having infinite solutions.
    Thought it might have been a little more complicated than just putting it into the equation.
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  4. #4
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    Quote Originally Posted by blackhug View Post
    I have the following system:

    2x - y + 7z = 0
    -x + 2y -3z = 0
    x + y + 4z = 0

    I have determined the solution to be:

    x = -y -4t
    y = -1/3t
    z = t

    what I need to know now, is if (0, 7, -1) is a solution to the system?
    Why is the red y part of your solution for x?
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    Why is the red y part of your solution for x?
    Well because I was told to solve this system by reducing it to echelon form.
    So I was left with:

    1 1 4
    0 1 1/3
    0 0 0

    If i had my solution for x as 11/3t wouldn't that be solving by reduced echelon form?
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    Why is the red y part of your solution for x?
    Your solution for x, y and z needs to be in terms of the parameter t only.
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