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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 22E: Let ab in a field F. Show that x+a and x+b are relatively prime in F[x].

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Given an n x n-matriz A over a field K, the columns A¹,...,A" of
A are linearly dependent iff det(A) = det(A¹,...,A") = 0. Equivalently, A has rank n iff
det(A) = 0.

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