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For each of the following statements, say whether the statement is true or false. (a) If...

For each of the following statements, say whether the statement is true or false.

(a) If S⊆T are sets of vectors, then span(S)⊆span(T).

(b) If S⊆T are sets of vectors, and S is linearly independent, then so is T.

(c) Every set of vectors is a subset of a basis.

(d) If S is a linearly independent set of vectors, and u is a vector not in the span of S, then S∪{u} is linearly independent.

(e) In a finite-dimensional vector space, all linearly independent sets of vectors have the same size.

(f) Every finite set of vectors contains a linearly independent subset with the same span.

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