Final answer:
If no two vectors are collinear, the set is linearly independent and is not in the span.
Step-by-step explanation:
The statement is False.
If no two vectors are collinear (none are zero), then the set is linearly independent. This means that none of the vectors in the set can be written as a linear combination of the others. If the set is linearly dependent, it means that at least one vector in the set can be written as a linear combination of the others.
If the set of vectors is in the span, it means that every vector in the set can be written as a linear combination of the given vectors. If the set is not in the span, it means that there are some vectors that cannot be expressed as a linear combination of the given vectors.
Therefore, if no two vectors are collinear, the set is linearly independent and is not in the span.
The answer is False.