Let T: R³ → R³ be given by T(y) = a) Show that T is a linear map by finding the matrix A = [T] that represents it. b) Find the eigenvalues (c) Check that the trace of A is the sum of these eigenvalues. d) Find the eigenvectors of T. (e) Show that T is diagonalisable and write down the diagonal matrix D and the associated mati P with P¯'AP = D. (f) Check that AP = PD. a) Is T invertible?
Let T: R³ → R³ be given by T(y) = a) Show that T is a linear map by finding the matrix A = [T] that represents it. b) Find the eigenvalues (c) Check that the trace of A is the sum of these eigenvalues. d) Find the eigenvectors of T. (e) Show that T is diagonalisable and write down the diagonal matrix D and the associated mati P with P¯'AP = D. (f) Check that AP = PD. a) Is T invertible?
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 41EQ
Related questions
Question
100%
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 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning