1. Let a = √3+√3 (a) Find ma(z) F raational numbers). the minimal polynomial of a over Q (the field of (b) Explain why ma(z) is irreducible over Q (e) Determine [Q(a): Q] (the degree of the field extension) and give a basis in terms of a (d) express a-¹ in terms of the basis

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A: 1) Here i will first answer why they have taken 2rs=0Let,  be a vector space over any field , now…

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A: The quadratic approximation of a function f at x0 is: f(x0)+f'(x0)(x-x0)+f''(x0)(x-x0)22 = Q(x)

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Q: 6. a) State the Fundamental Theorem of Galois theory. b) Outline the proof of (a).

A: To Do:(a) State the Fundamental Theorem of Galois theory.(b) Outline the proof in (a).Note- Since…

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Q: II Coordinates 5. Fix some a € R, and define polynomials Po(X), P1(X), P2(X) = P(R) by Po(X) = 1,…

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Q: Let S = {1,2,3,4} and U = {ƒ € Fun(S) | ƒ(2) − 3ƒ(4) = 0, ƒ(3) = 0} Find a basis of U. Basis(U) = {}…

A: Given  S = 1, 2, 3, 4  and  U =  f ∈ Fun(S) / f2 - 3f4 = 0 , f3 = 0                      Let  f ∈ U…

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