Answer
$$S_1=\{(-4,1,1),(-2,7,-3),(2,1,1)\},\quad S_2=\{(1,3,-2),(-2,7,-3),(2,1,1)\}, \\ S_3=\{(1,3,-2),(-4,1,1),(-2,7,-3)\}.$$
Work Step by Step
The all subsets of the set
$S=\{(1,3,-2),(-4,1,1),(-2,7,-3),(2,1,1)\}$
that form a basis for $R^{3}$ are the following
$$S_1=\{(-4,1,1),(-2,7,-3),(2,1,1)\},\quad S_2=\{(1,3,-2),(-2,7,-3),(2,1,1)\}, \\ S_3=\{(1,3,-2),(-4,1,1),(-2,7,-3)\}.$$