Problem (1): Show that there is only one automorphism, the identity function, of Q.Problem (2): Show that there are exactly two automorphisms of Q[V2].Problem (3): Let a and B be algebraic elements over a field F. Prove that(F(a])[3] = (F[3])[a],and that this set is a field, often simply denoted by F[a, B].Problem (4): Let a =V3 + V2. Please do the following:(a) Show that a is a primitive element of Q[V3, V2).(b) Find the minimal polynomial for a over Q.

Since you have posted a multiple question according to guildlines I will solve first question…

Answered: Problem (1): Show that there is only…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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