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Writing a system of conic equations

  1. Apr 3, 2014 #1
    1. The problem statement, all variables and given/known data
    Given a system like: [tex]\\a x^2 + b xy + c y^2 + d x + e y + f = 0 \\g x^2 + h xy + i y^2 + j x + k y + l = 0[/tex] How write it in matrix form?

    2. Relevant equations

    3. The attempt at a solution
    [tex]\begin{matrix} a x^2 + b xy + c y^2\\ g x^2 + h xy + i y^2\\ \end{matrix} + \begin{bmatrix} d & e\\ j & k\\ \end{bmatrix}\begin{bmatrix} x\\ y\\ \end{bmatrix} + \begin{bmatrix} f\\ l\\ \end{bmatrix} = \begin{bmatrix} 0\\ 0\\ \end{bmatrix}[/tex]
    I don't know how!
     
  2. jcsd
  3. Apr 3, 2014 #2

    HallsofIvy

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    A single set of quadratic terms can be written
    [tex]ax^2+ bxy+ cy^2= \begin{bmatrix}x & y \end{bmatrix}a & b/2 \\ b/2 & c \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}[/tex]

    You should be able to tweak that to give two.
     
  4. Apr 3, 2014 #3

    D H

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    This works:

    [tex]
    \begin{bmatrix} x & y & 0 & 0 \\ 0 & 0 & x & y \end{bmatrix}
    \begin{bmatrix} a & b/2 \\ b/2 & c \\ g & h/2 \\ h/2 & i \end{bmatrix}
    \begin{bmatrix} x \\ y \end{bmatrix} +
    \begin{bmatrix} d & e \\ j & k \end{bmatrix}
    \begin{bmatrix} x \\ y \end{bmatrix}+
    \begin{bmatrix} f\\ l \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix}[/tex]

    But why? What are you trying to do, Jhenrique?
     
  5. Apr 4, 2014 #4
    I can't see!

    I'm trying to write a vectorial equation that represents a system not of linear equations but yes of quadratic equations!

    If a linear equation (or a affim equation) can be represent a linear system, so, a quadratic equation can represent a quadratic system.
     
  6. Apr 5, 2014 #5

    LCKurtz

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    I think Halls means this:

     
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