Chapter 7.3, Problem 1E

In Exercises 1 and 2, find the change of variable x = Py that transforms the quadratic form x^TAx into y^TDy as shown.

1. $5x_1^2+6x_2^2+7x_3^2+4x_1{x}_2-4x_2{x}_3=9y_1^2+6y_2^2+3y_3^2$

Hint: x and y must have the same number of coordinates, so the quadratic form shown here must have a coefficient of zero for $y_3^2$.