What can be inferred about any set of vectors that includes the zero vector?

A set of vectors that includes the zero vector is always linearly dependent. The reason for this is tied to the definition of linear dependence, which states that a set of vectors is linearly dependent if at least one of the vectors can be expressed as a linear combination of the others.

In any set that contains the zero vector, we can always express the zero vector as (0 \cdot v_1 + 0 \cdot v_2 + ... + 0 \cdot v_n) for any vectors (v_1, v_2, ..., v_n) in that set. Since we can form a linear combination that results in the zero vector using coefficients that are not all zero (specifically, all coefficients being zero is always possible), this indicates that the set does not meet the criteria for linear independence.

In contrast, a set is defined as linearly independent only if no vector in the set can be expressed as a combination of the others, which is violated in the presence of the zero vector. Thus, the correct inference is that the presence of the zero vector guarantees linear dependence in the set of vectors.