Final answer:
The theorem stating that every basis of a finite-dimensional vector space V has the same number of vectors is true and reflects a fundamental property called the invariant basis number property or dimension theorem. Option A is correct.
Step-by-step explanation:
The question "According to Theorem 10: Every basis of V has the SAME number of vectors" relates to a fundamental concept in linear algebra known as the dimension theorem or the invariant basis number property. This theorem states that all bases of a vector space have the same number of elements, which is known as the dimension of the vector space.
In the context of finite-dimensional vector spaces, the statement is true, as every basis for a given vector space V must contain the same number of vectors. If V is an infinite-dimensional vector space, the concept of a basis and dimension can be more complex, but typically, the theorem is discussed in relation to finite-dimensional vector spaces.