If K is a field and if ₁, 2, are distinct automorphisms of K, thenit is impossible to find elements b₁, b...b, not all zero, in K such that b₁ ₁(a) + b₂ $₂(a) +...+bron (a)=0, for all a € K.

This is a problem of Abstract Alhebra.

Answered: If K is a field and if 1, 2 are…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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If K is a field and if 1, 2 are distinct automorphisms of K, ther it is impossible to find elements b₁, b...b, not all zero, in K such that b₁ ₁(a) + b₂ $₂(a) +...+ b(a)=0, for all a € K.