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Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 17EQ
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5. Prove that, if a rational number m/n, for m and n relatively prime integers, is a root of the polynomial equation aox' + a1x'-1 + ..+ a, = 0 %3D where the a, e Z, then n | ao and m a,.† Use this result to list the possible rational roots of the equations ensiolt altamarizam 1adi 6x2 + 9 = 0, ato3 - 8x² + 12 = 0. 6. Prove that if m is a positive integer which is not a square in Z then Vm is irrational (use Exercise 5).
Transcribed Image Text:5. Prove that, if a rational number m/n, for m and n relatively prime integers, is a root of the polynomial equation aox' + a1x'-1 + ..+ a, = 0 %3D where the a, e Z, then n | ao and m a,.† Use this result to list the possible rational roots of the equations ensiolt altamarizam 1adi 6x2 + 9 = 0, ato3 - 8x² + 12 = 0. 6. Prove that if m is a positive integer which is not a square in Z then Vm is irrational (use Exercise 5).
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