Question

Let A and B denote two bases of an n-dimensional vector space V. Then Select one: A. There is no vector in both A and B. B. A and B contain different vectors C. If there exists a vector in both A and B then A = B. D. A and B contain the same number of vectors. E. Some vector in A is also in B.

Answer 1

Answer:

correct answer is D: A and B contain the same number of vectors.

Step-by-step explanation:

this is a standard property of basis.

All bases contain the same number of elements (i.e equal to dimension of the vector space)

Answer 2

(D): A and B contain the same number of vectors.

Explanation:

All bases of an n-dimensional vector contain the same number of elements i.e., equal to dimension of the vector space.

therefore, (D) is the correct option.

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