2: A linear transformation F: R5 → R5 is given in the standard base of a matrix A. Suppose you calculate the secular polynomial and get det (A − 2) = (λ − 3)(a − 2)³(2-1). Which of the following applies? (Note, only 1 answer) A) The number 2 is an eigenvalue of the transformation and its geometric multiplicity is 3. B) The number 2 is an eigenvalue of the transformation, with algebraic multiplicity 3. For the transformation to be diagonalizable, its geometric multiplicity must be 3. C) The number 2 is an eigenvalue of the transformation, but since the transformation does not have 6 different eigenvalues, it cannot be diagonalizable. D) We cannot know whether the number 2 is an eigenvalue or not.

2: A linear transformation F: R5 → R5 is given in the standard base of a matrix A. Suppose you calculate the secular polynomial and get det (A − 2) = (λ − 3)(a − 2)³(2-1). Which of the following applies? (Note, only 1 answer) A) The number 2 is an eigenvalue of the transformation and its geometric multiplicity is 3. B) The number 2 is an eigenvalue of the transformation, with algebraic multiplicity 3. For the transformation to be diagonalizable, its geometric multiplicity must be 3. C) The number 2 is an eigenvalue of the transformation, but since the transformation does not have 6 different eigenvalues, it cannot be diagonalizable. D) We cannot know whether the number 2 is an eigenvalue or not.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 9EQ

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