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Thread: Sets

  1. #1
    Junior Member
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    Sets

    Hi

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

    i should calculate $\displaystyle E\cap F$? How to do it???
    Last edited by lehder; Apr 24th 2010 at 01:55 PM.
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  2. #2
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    Quote Originally Posted by lehder View Post
    Hi

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

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

    1. $\displaystyle x_1+2x_2-x_3=0$
    2. $\displaystyle x_1+x_2+x_3=0$

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

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

    1. $\displaystyle x_1+2x_2-x_3=0$
    2. $\displaystyle x_1+x_2+x_3=0$

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