Final answer:
The set S does not span R3 as it consists of only two vectors, which are not sufficient to span the three-dimensional space. The correct answer is B: s does not span R3. It spans a plane in R3.
Step-by-step explanation:
To determine whether the set S spans R3, we need to consider if we can express any vector in R3 as a linear combination of the vectors in set S. The set S = {(-3, 5, 0), (6, 6, 3)} consists of two vectors. To span R3, we need these vectors to be linearly independent and we need at least three linearly independent vectors since R3 is three-dimensional space.
However, this set only has two vectors, and no matter how they are scaled or combined, they will at most span a plane in R3, not the entire space. The correct answer is B: s does not span R3. S spans a plane in R3.
Geometrically, any linear combination of the two given vectors will still lie in the plane formed by them. If you imagine both vectors starting from the origin, they define a flat surface extending indefinitely, which is their span.