Question: Please refer to the question below. Note: This is all that the question comes with! Question 2. Suppose that V is a vector space of

Please refer to the question below. Note: This is all that the question comes with!

Question 2. Suppose that V is a vector space of dimension 2 and {u, v} is a basis of V. Let a, b, c, de R. a, 2pt) Prove that the vectors {au + bu, cu + du} form a linearly independent subset of V if and only if ad-be # 0. b, 1pt) Prove that the vectors {au + bu, cu + du} form a basis of V if and only if ad - be # 0. (Use part 2a if needed.)

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