Chapter 4 - Vector Spaces - 4.5 Basis and Dimension - 4.5 Exercises - Page 188: 59

$$S_1=S,\quad S_2=\{(1,0),(0,1)\},\quad S_2=\{(1,0),(1,1),\quad S_3=\{(0,1),(1,1)\}\}.$$

The all subsets of the set $S=\{(1,0),(0,1),(1,1)\}$ that form a basis for $R^{2}$ are the following $$S_1=S,\quad S_2=\{(1,0),(0,1)\},\quad S_2=\{(1,0),(1,1),\quad S_3=\{(0,1),(1,1)\}\}.$$