The matrix description for the (2 x 1) structure is

Rationale

Since this structure may be described by the simplest form of Woods notation with no rotation, the adsorbate unit cell vectors are simply related to the substrate vectors by the equations :

b₁ = 2 . a₁ + 0 . a₂

b₂ = 0 . a₁ + 1 . a₂

hence the matrix relating the two is