Answer to Question #343821 in Linear Algebra for AbdulWahid Ibrahim

Question

If p(x) denotes the set of all polynomials one indeterminates x over field F, then show that p(x) is a vector space over F with addition defined as addition of polynomials and scalar multiplication defined as the product of polynomials by an element of F. i.e if p(x)={p(x)/p(x)=a₀+a₁x+...+aₙxₙ...}={∑∞,ₙ₌∞ aₙxⁿ for as ∈ f}.

Define addition and scalar multiplication to prove.

Answer 1

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