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In: Advanced Math

1.Determine whether S spans V . Justify your answers. V = C ^0 [−1, 1] (the...

1.Determine whether S spans V . Justify your answers.

V = C ^0 [−1, 1] (the vector space of continuous functions on [−1, 1]) and S = {1, t, t2 , t3 , . . . }.

2.Let S be a set in a vector space V and v any vector. Prove that span(S) = span(S ∪ {v}) if and only if v ∈ span(S).

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