In each case below either prove that the statement is True or disprove it by giving...

In each case below either prove that the statement is True or disprove it by giving an example showing that it is False.

(i) If B is a fixed 2 × 2 matrix, then the set U = {A|A ∈ M22, AB = 0} is a subspace of M22. T or F

(ii) If u, v, w are vectors in a vector space V , then span {u, v, w} = span {u + v, u + w, v + w} T or F

(iii) The set {x,sin2 x, cos2 x} is independent in F[0, 2π] T or F

(iv) {1 + x, x + x 2 , x2 + x 3 , x3} is a basis of P3. T or F

Expert Solution

Colby Messinger answered 2 years ago

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