The set of vectors S = {(1,0,-1), (2,1,1), (-3,0,2), (1,0,5)} is not a basis of R³ because it is not linearly independent.
To determine if a set of vectors is a basis of a vector space, we must check whether it has the following properties:
1. The set of vectors is not empty.
2. The set of vectors spans the entire space.
3. The set of vectors is linearly independent.
Since the set of vectors S does not meet the 3rd requirement, it