Calculate the polarization vector P that results in a lithium niobate crystal when a stress state in the tensor below is applied. The piezoelectric matrix and values for this crystal are shown below.

dij=( 0 0 0 0 69.2 -41.6

-20.8 20.8 0 69.2 0 0

-0.85 -0.85 6.0 0 0 0)

The applied stress state is:

= ( 10 0 0

0 5 1

0 1 2) GPa