Question

3. Which of the following sets spans P2(R)?

(a) {1 + x, 2 + 2x 2}

(b) {2, 1 + x + x 2 , 3 + 2x + 2x 2}

(c) {1 + x, 1 + x 2 , x + x 2 , 1 + x + x 2}

4. Consider the vector space W = {(a, b) ∈ R 2 | b > 0} with defined by (a, b) ⊕ (c, d) = (ad + bc, bd) and scalar multiplication defined by k (a, b) = (kabk−1 , bk ) The set {(0, 2),(1, 1)} is linearly independent in W.

(a) True. (b) False.

6. There exists a vector space with exactly two vectors in it.

(a) True. (b) False.

Answer 1

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