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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please choose the true option
Transcribed Image Text: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) = (2-3)(a − 2)³(λ — 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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
