Chapter 7.3, Problem 2E

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

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

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