"rows" don't have a basis, row SPACES do. rows are vectors. vector spaces have bases.

in this case, each row can be regarded as an element of R^4. since 0-elements are always linearly dependent, only non-zero rows are eligible for membership in a basis. you have 2 non-zero row vectors:

(1,1,0,0) and (0,1,1,1).

to prove this is a basis for the row space, you need to show linear independence.

so suppose a(1,1,0,0) + b(0,1,1,1) = (0,0,0,0). this is the same as saying:

(a,a+b,b,b) = (0,0,0,0)

can you prove that we HAVE to have a = 0, and b = 0 (hint: look at the first two coordinates of the vectors on each side of the equality).