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.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 5P
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