Let A be a n × n matrix with real entries and letλ1 = a + bi (where a and b are real and b = 0) bean eigenvalue of A. Let z1 = x+i y (where x and yboth have real entries) be an eigenvector belongingto λ1 and let z2 = x − i y.(a) Explain why z1 and z2 must be linearly independent.(b) Show that y ≠= 0 and that x and y are linearlyindependent.

Let A be a n × n matrix with real entries and letλ1 = a + bi (where a and b are real and b = 0) bean eigenvalue of A. Let z1 = x+i y (where x and yboth have real entries) be an eigenvector belongingto λ1 and let z2 = x − i y.(a) Explain why z1 and z2 must be linearly independent.(b) Show that y ≠= 0 and that x and y are linearlyindependent.

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 42EQ

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