Results 1 to 2 of 2

Math Help - Matrix Conic Equation

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    15

    Matrix Conic Equation

    I need to write this equation here: X1^2+X1X2+X2^2=8

    in the form of X^TAX=8


    Once ive done that i nee to be able to find the matrix Q such that the transformation X=QY diagonalises A and reduces the equation to a standard form in terms of (Y1, Y2)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by sazzy3 View Post
    I need to write this equation here: X1^2+X1X2+X2^2=8

    in the form of X^TAX=8
    You may assume A is symmetric so:

    \left[\begin{array}{cc}x_1&x_2 \end{array} \right] \left[\begin{array}{cc}a_{1,1}&a_{1,2}\\a_{1,2}&a_{2,2}\  end{array}\right] \left[\begin{array}{c}x_1\\x_2\end{array}\right]=8

    Now expand the expression on the left and set the coefficient of x_1^2 to 1, of x_2^2 to 1 and of x_1x_2 also to 1 and solve for a_{1,1}, a_{2,2} and a_{2,2}

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix equation of a conic.
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: September 10th 2010, 03:12 AM
  2. Conic Equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 12th 2010, 07:32 AM
  3. simplify conic equation
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: July 5th 2008, 08:43 PM
  4. General Equation of a Conic
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 18th 2008, 11:37 AM
  5. Equation of a conic
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 13th 2008, 10:58 AM

Search Tags


/mathhelpforum @mathhelpforum