2. (a) Show that the list {p o(x), p 1(x), p 2(x),...,p n(x),...,} where Po(x) = 1, p₁(x) = 1 + x, P₁(x) = 1 + x +· ·+x³, is a basis of the vector space F[x] of all polynomials with coeficients in F. (b) What are the coordinates of the vector xn relative to the basis (po(x), p1(x),..., pj(x), ...)?

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A: Solution

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Q: (a) Show that the list {p o(x), p 1(x), p 2(x), ...,p n(x),...,} where po(x) = 1, p1(x) = 1+x, P;(x)…

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