Observe that if S $=122221212.$ then S $1=1/92/92/92/92/91/92/91/92/9$ and $702052226=1222212123000600091/92/92/92/92/91/92/91/92/9.($a$)$ Use the facts above to diagonalize the quadratic form q h x y z i $=7$x $2+5$y $2+6$z $2+4$xz $+4$yz $($b$)$ Also provide the transition matrix P for the new coordinate system $[$u v w$]$ such that $$ x y z $=$ P $$ u v w $($c$)$ Finally, classify the quadratic form q as positive definite, positive semidefinite, negative definite, negative semidefinite or indefinite.