Could you please just give me a simple explanation on part (b) with its subparts (a) & (b). Thank you (1) Let V be a vector space over any field F:(a)Prove that V is infinite dimensional iff there is a sequence of vectors (V₁, V2, V3, ... )in V such that V₁, V2, ..., Um is Linearly independent for each positive integer m.(b) Use the above to conclude the following two vector spaces are infinite dimensionalC-vector spaces:(a)(b)V = Fct(Z, C)V = C[t] (the vector space of all polynomials)

Given as, sequence of vectors(v1 v2 v3,.....) in v

Answered: mite dimensional iff there is a…

Advanced Engineering Mathematics

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Chapter2: Second-order Linear Odes

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mite dimensional iff there is a sequence of vectors (v₁, V2, is Linearly independent for each positive integer m.