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Math Help - Sets

  1. #1
    Junior Member
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    Sets

    Hi

    E={(x,y,z) \in \mathbb{R}^3/ x+2y-z=0}
    F={(x,y,z) \in \mathbb{R}^3/x+y+z=0}

    i should calculate E\cap F? How to do it???
    Last edited by lehder; April 24th 2010 at 02:55 PM.
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  2. #2
    Super Member
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    Quote Originally Posted by lehder View Post
    Hi

    E={(x,y,z) \in \mathbb{R}^3/ x+2y-z=0}
    F={(x,y,z) \in \mathbb{R}^3/x+y+z=0}

    i should calculate E\cap F? How to do it???
    (x_1,x_2,x_3) \in E \cap F if:

    1. x_1+2x_2-x_3=0
    2. x_1+x_2+x_3=0

    Now find a new condition based on these two.
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  3. #3
    Super Member
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    Smile

    Quote Originally Posted by Defunkt View Post
    (x_1,x_2,x_3) \in E \cap F if:

    1. x_1+2x_2-x_3=0
    2. x_1+x_2+x_3=0

    Now find a new condition based on these two.
    which means he must solve the system,
    \left\{\begin{matrix}<br />
x_1+2x_2-x_3=0\\ <br />
x_1+x_2+x_3=0<br />
\end{matrix}\right.
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