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Prerna Chaudhary posted an Question
July 27, 2021 • 21:42 pm 30 points
  • IIT JAM
  • Mathematics (MA)

(infinite basis) : let f[x] be the vector space of all polynomials over the field f. then the set s = {1, x, x, ., x", ...} is a basis of f[x]

(Infinite basis) : Let F[x] be the vector space of all polynomials over the field F. Then the set S = {1, x, x, ., x^n, ...} is a basis of F[X]

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  • Ankur Rao

    as all these are linearly independent and we can write any polynomial by these so this is spanning polynomial of infinite degree. spanning and linearly independency imply basis or infinite basis.

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