Question

Prove that the space containing the null vector has a dimension

Answer 1

Answer:

What's the largest linearly independent set in {0}? The only subsets in it are the empty set and the whole set. But any set containing the zero vector is linearly dependent; conversely, the empty set is certainly linearly independent (because you can't find a zero linear combination with non zero coefficients out of its elements). So the only linearly independent set in {0} is the empty set that has zero elements.