Let A be a diagonalisable 3 x 3 matrix with real entries. Working over C on V = C³: (a) Is it possible that A has three distinct strictly complex eigenvalues? (b) Is it possible that A has two distinct strictly complex eigenvalues and one real one? (c) Is it possible that A has one strictly complex eigenvalue and two distinct real ones? (d) Is it possible that A has three distinct real eigenvalues? Select one: (a), (b) No and (a), (d) Yes (b), (d) No and (a), (c) Yes (a), (c) No and (b),(d) Yes (a), (d) No and (b), (c) Yes None of the others apply

Let A be a diagonalisable 3 x 3 matrix with real entries. Working over C on V = C³: (a) Is it possible that A has three distinct strictly complex eigenvalues? (b) Is it possible that A has two distinct strictly complex eigenvalues and one real one? (c) Is it possible that A has one strictly complex eigenvalue and two distinct real ones? (d) Is it possible that A has three distinct real eigenvalues? Select one: (a), (b) No and (a), (d) Yes (b), (d) No and (a), (c) Yes (a), (c) No and (b),(d) Yes (a), (d) No and (b), (c) Yes None of the others apply

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...

See similar textbooks