Answer
See answer below
Work Step by Step
We are given:
$\{(7,1,-3); (6,1,0); (-5,-1,-2); (0,-3,8)\}$ in $R^3$
Since $R^3$ is three dimensionial space, but there are 4 vectors in the set which means $dim R^3=4$. Hence, the set of vectors $S$ is not a basis of $R^3$