a) Find anorthogonal matrix P and a diagonal matrix D such that P D P^{T}=\left(\begin{array}{rrr} 2 & 2 & -2 \\ 2 & 5 & -4 \\ -2 & -4

& 5 \end{array}\right) b) Use your answer to part (a) to write the quadratic form Q(x,y, z) as a sum of onlysquare terms, where Q(x, y, z)=2 x^{2}+5 y^{2}+5 z^{2}+4 x y-4 x z-8 y z