10. Let o: Q(V2) → Q(/2) be the map given by ø(a+bv2) = a-bv2. Show that is a Q-linear field automorphism. By Eisenstein criterion, x2 – 2 is irreducible and hence {1, v2} is | a basis of Q(/2) over Q.

Elementary Linear Algebra (MindTap Course List)
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Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
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→ a E Z.
10. Let ø: Q(/2) → Q(2) be the map given by ø(a+bv2) = a-b2.
Show that o is a Q-linear field automorphism.
By Eisenstein criterion, x² –
2 is irreducible and hence {1, v2} is
a basis of Q(/2) over Q.
e to search
Transcribed Image Text:→ a E Z. 10. Let ø: Q(/2) → Q(2) be the map given by ø(a+bv2) = a-b2. Show that o is a Q-linear field automorphism. By Eisenstein criterion, x² – 2 is irreducible and hence {1, v2} is a basis of Q(/2) over Q. e to search
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