question is below:

2. Diamond is a crystalline structure with a cubic unit cell. The lattice basis for diamond is given by 0 1 1 a a (1 LB = 1 , E 0 , E 1 , 1 1 0 Where a is a lattice constant. The reciprocal lattice basis for diamond is given by 2 _1 2 1 2 1 R L B = _7r 1 , _7r _1 , _7T 1 a a a 1 1 Using the appropriate 3 by 6 augmented matrices and row reduction techniques, nd the change of coordinates matrices, P , P , and P , and show that one of these matrices may be obtained as a product of the other two. LB