Final answer:
The set of vectors a₁, a₂, a₃ will span R³ unless h is zero, which would prevent the third vector from contributing an additional dimension to the spanned space.
Step-by-step explanation:
The question is concerned with the conditions under which the set of vectors a₁ a₂ a₃ will span R³, which is a concept in linear algebra related to the ability of a set of vectors to cover the entire three-dimensional space through linear combinations. For a set of vectors to span R³, they must be linearly independent and there must be three of them, as each vector adds a dimension to the space that can be reached. In this context, h seems to be a parameter associated with vector a₃.
If h is zero (option b), vector a₃ could become a zero vector or fail to provide an additional dimension, and thus the set would not span R³. In all other cases (option a, c, and d), assuming a₁ and a₂ are linearly independent and non-zero, the vectors should span R³ as a₃ would not be a zero vector and would add the necessary third dimension to the spanned space.