hi all,

i am trying to do an assignment here and i would like to verify my answer to the following question:

Let $\displaystyle Q=x_1^2+2x_2^2-7x_3^2-4x_1x_2+8x_1x_3$

Find a non-singular matrix $\displaystyle P$ and a diagonal matrix $\displaystyle D=diag(d_1,d_2,d_3)$ such that Q is transformed to $\displaystyle Q'=d_1y_1^2+d_2y_2^2+d_3y_3^2$; under the transformation $\displaystyle X=PY$