5. Let A be an n x n matrix. (a) (b) Show that if A is an orthogonal matrix, then det(A) = ±1. Show that if A 0 and A³ = 0, then A is not diagonalizable. (Hint: Assume A is diagonalizable and then get a contraction.)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 26CM: Find an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[1331].
icon
Related questions
Question
5. Let A be an n x n matrix.
(a)
(b)
Show that if A is an orthogonal matrix, then det(A) = ±1.
Show that if A 0 and A³ = 0, then A is not diagonalizable. (Hint: Assume A is
diagonalizable and then get a contraction.)
Transcribed Image Text:5. Let A be an n x n matrix. (a) (b) Show that if A is an orthogonal matrix, then det(A) = ±1. Show that if A 0 and A³ = 0, then A is not diagonalizable. (Hint: Assume A is diagonalizable and then get a contraction.)
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning