The span of an infinite collection v1, v2, v3,... V of vector space elements is defined as

The span of an infinite collection v1, v2, v3,... ˆˆ V of vector space elements is defined as the set of all finite linear cominations

is finite but arbitrary.
(a) Prove that the span defines a subspace of the vector space V.
(b) What is the span of the monomials 1, x, x2, x3. . . ?

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c, v,, where n <