Matrix Conic Equation

**sazzy3** · August 18th 2009, 09:10 PM

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)

**CaptainBlack** · August 18th 2009, 10:23 PM

Originally Posted by sazzy3

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

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