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.)
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].
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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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F124b901b-30e0-465c-8843-0ac183671335%2F3e6c9d4c-20c6-47ae-9f48-37fedd605786%2F0orh2ts_processed.jpeg&w=3840&q=75)
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.)
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